Anisotropic x16 LOD (ratio of anisotropy)

Percentage Accurate: 98.0% → 97.7%

Time: 1.5min

Alternatives: 12

Speedup: N/A×

Specification

\[\left(\left(\left(\left(\left(\left(1 \leq w \land w \leq 16384\right) \land \left(1 \leq h \land h \leq 16384\right)\right) \land \left(10^{-20} \leq \left|dX.u\right| \land \left|dX.u\right| \leq 10^{+20}\right)\right) \land \left(10^{-20} \leq \left|dX.v\right| \land \left|dX.v\right| \leq 10^{+20}\right)\right) \land \left(10^{-20} \leq \left|dY.u\right| \land \left|dY.u\right| \leq 10^{+20}\right)\right) \land \left(10^{-20} \leq \left|dY.v\right| \land \left|dY.v\right| \leq 10^{+20}\right)\right) \land maxAniso = 16\]

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloor h\right\rfloor \cdot dX.v\\ t_1 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_2 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_3 := \left\lfloor w\right\rfloor \cdot dX.u\\ t_4 := \mathsf{max}\left(t\_3 \cdot t\_3 + t\_0 \cdot t\_0, t\_2 \cdot t\_2 + t\_1 \cdot t\_1\right)\\ t_5 := \sqrt{t\_4}\\ t_6 := \left|t\_3 \cdot t\_1 - t\_0 \cdot t\_2\right|\\ t_7 := \frac{t\_4}{t\_6}\\ t_8 := t\_7 > \left\lfloor maxAniso\right\rfloor \\ t_9 := \begin{array}{l} \mathbf{if}\;t\_8:\\ \;\;\;\;\frac{t\_5}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_6}{t\_5}\\ \end{array}\\ t_10 := \begin{array}{l} \mathbf{if}\;t\_8:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_7\\ \end{array}\\ \mathbf{if}\;t\_9 < 1:\\ \;\;\;\;\mathsf{max}\left(1, t\_10 \cdot t\_9\right)\\ \mathbf{else}:\\ \;\;\;\;t\_10\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor h) dX.v))
        (t_1 (* (floor h) dY.v))
        (t_2 (* (floor w) dY.u))
        (t_3 (* (floor w) dX.u))
        (t_4 (fmax (+ (* t_3 t_3) (* t_0 t_0)) (+ (* t_2 t_2) (* t_1 t_1))))
        (t_5 (sqrt t_4))
        (t_6 (fabs (- (* t_3 t_1) (* t_0 t_2))))
        (t_7 (/ t_4 t_6))
        (t_8 (> t_7 (floor maxAniso)))
        (t_9 (if t_8 (/ t_5 (floor maxAniso)) (/ t_6 t_5)))
        (t_10 (if t_8 (floor maxAniso) t_7)))
   (if (< t_9 1.0) (fmax 1.0 (* t_10 t_9)) t_10)))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(h) * dX_46_v;
	float t_1 = floorf(h) * dY_46_v;
	float t_2 = floorf(w) * dY_46_u;
	float t_3 = floorf(w) * dX_46_u;
	float t_4 = fmaxf(((t_3 * t_3) + (t_0 * t_0)), ((t_2 * t_2) + (t_1 * t_1)));
	float t_5 = sqrtf(t_4);
	float t_6 = fabsf(((t_3 * t_1) - (t_0 * t_2)));
	float t_7 = t_4 / t_6;
	int t_8 = t_7 > floorf(maxAniso);
	float tmp;
	if (t_8) {
		tmp = t_5 / floorf(maxAniso);
	} else {
		tmp = t_6 / t_5;
	}
	float t_9 = tmp;
	float tmp_1;
	if (t_8) {
		tmp_1 = floorf(maxAniso);
	} else {
		tmp_1 = t_7;
	}
	float t_10 = tmp_1;
	float tmp_2;
	if (t_9 < 1.0f) {
		tmp_2 = fmaxf(1.0f, (t_10 * t_9));
	} else {
		tmp_2 = t_10;
	}
	return tmp_2;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(h) * dX_46_v)
	t_1 = Float32(floor(h) * dY_46_v)
	t_2 = Float32(floor(w) * dY_46_u)
	t_3 = Float32(floor(w) * dX_46_u)
	t_4 = (Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)) != Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0))) ? Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1)) : ((Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1)) != Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1))) ? Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)) : max(Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)), Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1))))
	t_5 = sqrt(t_4)
	t_6 = abs(Float32(Float32(t_3 * t_1) - Float32(t_0 * t_2)))
	t_7 = Float32(t_4 / t_6)
	t_8 = t_7 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_8)
		tmp = Float32(t_5 / floor(maxAniso));
	else
		tmp = Float32(t_6 / t_5);
	end
	t_9 = tmp
	tmp_1 = Float32(0.0)
	if (t_8)
		tmp_1 = floor(maxAniso);
	else
		tmp_1 = t_7;
	end
	t_10 = tmp_1
	tmp_2 = Float32(0.0)
	if (t_9 < Float32(1.0))
		tmp_2 = (Float32(1.0) != Float32(1.0)) ? Float32(t_10 * t_9) : ((Float32(t_10 * t_9) != Float32(t_10 * t_9)) ? Float32(1.0) : max(Float32(1.0), Float32(t_10 * t_9)));
	else
		tmp_2 = t_10;
	end
	return tmp_2
end

MATLAB

function tmp_4 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = floor(h) * dX_46_v;
	t_1 = floor(h) * dY_46_v;
	t_2 = floor(w) * dY_46_u;
	t_3 = floor(w) * dX_46_u;
	t_4 = max(((t_3 * t_3) + (t_0 * t_0)), ((t_2 * t_2) + (t_1 * t_1)));
	t_5 = sqrt(t_4);
	t_6 = abs(((t_3 * t_1) - (t_0 * t_2)));
	t_7 = t_4 / t_6;
	t_8 = t_7 > floor(maxAniso);
	tmp = single(0.0);
	if (t_8)
		tmp = t_5 / floor(maxAniso);
	else
		tmp = t_6 / t_5;
	end
	t_9 = tmp;
	tmp_2 = single(0.0);
	if (t_8)
		tmp_2 = floor(maxAniso);
	else
		tmp_2 = t_7;
	end
	t_10 = tmp_2;
	tmp_3 = single(0.0);
	if (t_9 < single(1.0))
		tmp_3 = max(single(1.0), (t_10 * t_9));
	else
		tmp_3 = t_10;
	end
	tmp_4 = tmp_3;
end

Initial Program: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloor h\right\rfloor \cdot dX.v\\ t_1 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_2 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_3 := \left\lfloor w\right\rfloor \cdot dX.u\\ t_4 := \mathsf{max}\left(t\_3 \cdot t\_3 + t\_0 \cdot t\_0, t\_2 \cdot t\_2 + t\_1 \cdot t\_1\right)\\ t_5 := \sqrt{t\_4}\\ t_6 := \left|t\_3 \cdot t\_1 - t\_0 \cdot t\_2\right|\\ t_7 := \frac{t\_4}{t\_6}\\ t_8 := t\_7 > \left\lfloor maxAniso\right\rfloor \\ t_9 := \begin{array}{l} \mathbf{if}\;t\_8:\\ \;\;\;\;\frac{t\_5}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_6}{t\_5}\\ \end{array}\\ t_10 := \begin{array}{l} \mathbf{if}\;t\_8:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_7\\ \end{array}\\ \mathbf{if}\;t\_9 < 1:\\ \;\;\;\;\mathsf{max}\left(1, t\_10 \cdot t\_9\right)\\ \mathbf{else}:\\ \;\;\;\;t\_10\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor h) dX.v))
        (t_1 (* (floor h) dY.v))
        (t_2 (* (floor w) dY.u))
        (t_3 (* (floor w) dX.u))
        (t_4 (fmax (+ (* t_3 t_3) (* t_0 t_0)) (+ (* t_2 t_2) (* t_1 t_1))))
        (t_5 (sqrt t_4))
        (t_6 (fabs (- (* t_3 t_1) (* t_0 t_2))))
        (t_7 (/ t_4 t_6))
        (t_8 (> t_7 (floor maxAniso)))
        (t_9 (if t_8 (/ t_5 (floor maxAniso)) (/ t_6 t_5)))
        (t_10 (if t_8 (floor maxAniso) t_7)))
   (if (< t_9 1.0) (fmax 1.0 (* t_10 t_9)) t_10)))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(h) * dX_46_v;
	float t_1 = floorf(h) * dY_46_v;
	float t_2 = floorf(w) * dY_46_u;
	float t_3 = floorf(w) * dX_46_u;
	float t_4 = fmaxf(((t_3 * t_3) + (t_0 * t_0)), ((t_2 * t_2) + (t_1 * t_1)));
	float t_5 = sqrtf(t_4);
	float t_6 = fabsf(((t_3 * t_1) - (t_0 * t_2)));
	float t_7 = t_4 / t_6;
	int t_8 = t_7 > floorf(maxAniso);
	float tmp;
	if (t_8) {
		tmp = t_5 / floorf(maxAniso);
	} else {
		tmp = t_6 / t_5;
	}
	float t_9 = tmp;
	float tmp_1;
	if (t_8) {
		tmp_1 = floorf(maxAniso);
	} else {
		tmp_1 = t_7;
	}
	float t_10 = tmp_1;
	float tmp_2;
	if (t_9 < 1.0f) {
		tmp_2 = fmaxf(1.0f, (t_10 * t_9));
	} else {
		tmp_2 = t_10;
	}
	return tmp_2;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(h) * dX_46_v)
	t_1 = Float32(floor(h) * dY_46_v)
	t_2 = Float32(floor(w) * dY_46_u)
	t_3 = Float32(floor(w) * dX_46_u)
	t_4 = (Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)) != Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0))) ? Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1)) : ((Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1)) != Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1))) ? Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)) : max(Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)), Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1))))
	t_5 = sqrt(t_4)
	t_6 = abs(Float32(Float32(t_3 * t_1) - Float32(t_0 * t_2)))
	t_7 = Float32(t_4 / t_6)
	t_8 = t_7 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_8)
		tmp = Float32(t_5 / floor(maxAniso));
	else
		tmp = Float32(t_6 / t_5);
	end
	t_9 = tmp
	tmp_1 = Float32(0.0)
	if (t_8)
		tmp_1 = floor(maxAniso);
	else
		tmp_1 = t_7;
	end
	t_10 = tmp_1
	tmp_2 = Float32(0.0)
	if (t_9 < Float32(1.0))
		tmp_2 = (Float32(1.0) != Float32(1.0)) ? Float32(t_10 * t_9) : ((Float32(t_10 * t_9) != Float32(t_10 * t_9)) ? Float32(1.0) : max(Float32(1.0), Float32(t_10 * t_9)));
	else
		tmp_2 = t_10;
	end
	return tmp_2
end

MATLAB

function tmp_4 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = floor(h) * dX_46_v;
	t_1 = floor(h) * dY_46_v;
	t_2 = floor(w) * dY_46_u;
	t_3 = floor(w) * dX_46_u;
	t_4 = max(((t_3 * t_3) + (t_0 * t_0)), ((t_2 * t_2) + (t_1 * t_1)));
	t_5 = sqrt(t_4);
	t_6 = abs(((t_3 * t_1) - (t_0 * t_2)));
	t_7 = t_4 / t_6;
	t_8 = t_7 > floor(maxAniso);
	tmp = single(0.0);
	if (t_8)
		tmp = t_5 / floor(maxAniso);
	else
		tmp = t_6 / t_5;
	end
	t_9 = tmp;
	tmp_2 = single(0.0);
	if (t_8)
		tmp_2 = floor(maxAniso);
	else
		tmp_2 = t_7;
	end
	t_10 = tmp_2;
	tmp_3 = single(0.0);
	if (t_9 < single(1.0))
		tmp_3 = max(single(1.0), (t_10 * t_9));
	else
		tmp_3 = t_10;
	end
	tmp_4 = tmp_3;
end

Alternative 1: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\\ t_1 := \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ t_2 := dX.v \cdot \left\lfloor h\right\rfloor \\ t_3 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t\_2, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, t\_0\right)\\ t_4 := \sqrt{t\_3}\\ t_5 := \frac{t\_3}{t\_1}\\ t_6 := t\_5 > \left\lfloor maxAniso\right\rfloor \\ t_7 := \begin{array}{l} \mathbf{if}\;t\_6:\\ \;\;\;\;\frac{t\_4}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{t\_4}\\ \end{array}\\ \mathbf{if}\;t\_7 < 1:\\ \;\;\;\;\mathsf{max}\left(1, t\_7 \cdot \begin{array}{l} \mathbf{if}\;t\_6:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({t\_2}^{2}, t\_0\right)}{t\_1}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{t\_3}{\left|dX.v \cdot \left(\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (pow (hypot (* (floor w) dY.u) (* (floor h) dY.v)) 2.0))
        (t_1
         (fabs (* (floor w) (* (floor h) (- (* dX.u dY.v) (* dX.v dY.u))))))
        (t_2 (* dX.v (floor h)))
        (t_3 (fmax (pow (hypot t_2 (* dX.u (floor w))) 2.0) t_0))
        (t_4 (sqrt t_3))
        (t_5 (/ t_3 t_1))
        (t_6 (> t_5 (floor maxAniso)))
        (t_7 (if t_6 (/ t_4 (floor maxAniso)) (/ t_1 t_4))))
   (if (< t_7 1.0)
     (fmax
      1.0
      (* t_7 (if t_6 (floor maxAniso) (/ (fmax (pow t_2 2.0) t_0) t_1))))
     (if (>
          (/ t_3 (fabs (* dX.v (* (floor w) (* (floor h) dY.u)))))
          (floor maxAniso))
       (floor maxAniso)
       t_5))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = powf(hypotf((floorf(w) * dY_46_u), (floorf(h) * dY_46_v)), 2.0f);
	float t_1 = fabsf((floorf(w) * (floorf(h) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)))));
	float t_2 = dX_46_v * floorf(h);
	float t_3 = fmaxf(powf(hypotf(t_2, (dX_46_u * floorf(w))), 2.0f), t_0);
	float t_4 = sqrtf(t_3);
	float t_5 = t_3 / t_1;
	int t_6 = t_5 > floorf(maxAniso);
	float tmp;
	if (t_6) {
		tmp = t_4 / floorf(maxAniso);
	} else {
		tmp = t_1 / t_4;
	}
	float t_7 = tmp;
	float tmp_2;
	if (t_7 < 1.0f) {
		float tmp_3;
		if (t_6) {
			tmp_3 = floorf(maxAniso);
		} else {
			tmp_3 = fmaxf(powf(t_2, 2.0f), t_0) / t_1;
		}
		tmp_2 = fmaxf(1.0f, (t_7 * tmp_3));
	} else if ((t_3 / fabsf((dX_46_v * (floorf(w) * (floorf(h) * dY_46_u))))) > floorf(maxAniso)) {
		tmp_2 = floorf(maxAniso);
	} else {
		tmp_2 = t_5;
	}
	return tmp_2;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0)
	t_1 = abs(Float32(floor(w) * Float32(floor(h) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)))))
	t_2 = Float32(dX_46_v * floor(h))
	t_3 = ((hypot(t_2, Float32(dX_46_u * floor(w))) ^ Float32(2.0)) != (hypot(t_2, Float32(dX_46_u * floor(w))) ^ Float32(2.0))) ? t_0 : ((t_0 != t_0) ? (hypot(t_2, Float32(dX_46_u * floor(w))) ^ Float32(2.0)) : max((hypot(t_2, Float32(dX_46_u * floor(w))) ^ Float32(2.0)), t_0))
	t_4 = sqrt(t_3)
	t_5 = Float32(t_3 / t_1)
	t_6 = t_5 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_6)
		tmp = Float32(t_4 / floor(maxAniso));
	else
		tmp = Float32(t_1 / t_4);
	end
	t_7 = tmp
	tmp_2 = Float32(0.0)
	if (t_7 < Float32(1.0))
		tmp_3 = Float32(0.0)
		if (t_6)
			tmp_3 = floor(maxAniso);
		else
			tmp_3 = Float32((((t_2 ^ Float32(2.0)) != (t_2 ^ Float32(2.0))) ? t_0 : ((t_0 != t_0) ? (t_2 ^ Float32(2.0)) : max((t_2 ^ Float32(2.0)), t_0))) / t_1);
		end
		tmp_2 = (Float32(1.0) != Float32(1.0)) ? Float32(t_7 * tmp_3) : ((Float32(t_7 * tmp_3) != Float32(t_7 * tmp_3)) ? Float32(1.0) : max(Float32(1.0), Float32(t_7 * tmp_3)));
	elseif (Float32(t_3 / abs(Float32(dX_46_v * Float32(floor(w) * Float32(floor(h) * dY_46_u))))) > floor(maxAniso))
		tmp_2 = floor(maxAniso);
	else
		tmp_2 = t_5;
	end
	return tmp_2
end

MATLAB

function tmp_5 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = hypot((floor(w) * dY_46_u), (floor(h) * dY_46_v)) ^ single(2.0);
	t_1 = abs((floor(w) * (floor(h) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)))));
	t_2 = dX_46_v * floor(h);
	t_3 = max((hypot(t_2, (dX_46_u * floor(w))) ^ single(2.0)), t_0);
	t_4 = sqrt(t_3);
	t_5 = t_3 / t_1;
	t_6 = t_5 > floor(maxAniso);
	tmp = single(0.0);
	if (t_6)
		tmp = t_4 / floor(maxAniso);
	else
		tmp = t_1 / t_4;
	end
	t_7 = tmp;
	tmp_3 = single(0.0);
	if (t_7 < single(1.0))
		tmp_4 = single(0.0);
		if (t_6)
			tmp_4 = floor(maxAniso);
		else
			tmp_4 = max((t_2 ^ single(2.0)), t_0) / t_1;
		end
		tmp_3 = max(single(1.0), (t_7 * tmp_4));
	elseif ((t_3 / abs((dX_46_v * (floor(w) * (floor(h) * dY_46_u))))) > floor(maxAniso))
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_5;
	end
	tmp_5 = tmp_3;
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]
2. Add Preprocessing

3. Taylor expanded in dX.u around 0 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\color{blue}{-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)\right)}\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]
4. Step-by-step derivation

   1. mul-1-neg 97.8%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\color{blue}{-dX.v \cdot \left(dY.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)}\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

   2. distribute-lft-neg-in 97.8%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\color{blue}{\left(-dX.v\right) \cdot \left(dY.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)}\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

   3. *-commutative 97.8%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(-dX.v\right) \cdot \left(dY.u \cdot \color{blue}{\left(\left\lfloor w\right\rfloor \cdot \left\lfloor h\right\rfloor \right)}\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

   4. associate-*r* 97.8%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(-dX.v\right) \cdot \color{blue}{\left(\left(dY.u \cdot \left\lfloor w\right\rfloor \right) \cdot \left\lfloor h\right\rfloor \right)}\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

   5. *-commutative 97.8%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(-dX.v\right) \cdot \left(\color{blue}{\left(\left\lfloor w\right\rfloor \cdot dY.u\right)} \cdot \left\lfloor h\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

   6. associate-*l* 97.8%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\color{blue}{\left(\left(-dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right) \cdot \left\lfloor h\right\rfloor }\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

   7. distribute-lft-neg-in 97.8%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\color{blue}{\left(-dX.v \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right)} \cdot \left\lfloor h\right\rfloor \right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

   8. *-commutative 97.8%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(-dX.v \cdot \color{blue}{\left(dY.u \cdot \left\lfloor w\right\rfloor \right)}\right) \cdot \left\lfloor h\right\rfloor \right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

   9. associate-*r* 97.8%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(-\color{blue}{\left(dX.v \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor }\right) \cdot \left\lfloor h\right\rfloor \right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

   10. *-commutative 97.8%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(-\color{blue}{\left\lfloor w\right\rfloor \cdot \left(dX.v \cdot dY.u\right)}\right) \cdot \left\lfloor h\right\rfloor \right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

   11. *-commutative 97.8%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\color{blue}{\left\lfloor h\right\rfloor \cdot \left(-\left\lfloor w\right\rfloor \cdot \left(dX.v \cdot dY.u\right)\right)}\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

   12. distribute-rgt-neg-in 97.8%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \color{blue}{\left(\left\lfloor w\right\rfloor \cdot \left(-dX.v \cdot dY.u\right)\right)}\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

   13. distribute-rgt-neg-in 97.8%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \color{blue}{\left(dX.v \cdot \left(-dY.u\right)\right)}\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

5. Simplified 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\color{blue}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.v \cdot \left(-dY.u\right)\right)\right)}\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

6. Taylor expanded in w around 0 97.8%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|dX.u \cdot \left(dY.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|dX.u \cdot \left(dY.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|dX.u \cdot \left(dY.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|dX.u \cdot \left(dY.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|dX.u \cdot \left(dY.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|dX.u \cdot \left(dY.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|dX.u \cdot \left(dY.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ } \end{array}} \]

8. Simplified 97.8%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left|\left(\left\lfloor w\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right| \cdot \frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left|\left(\left\lfloor w\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right| \cdot \frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|dX.v \cdot \left(\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right|}\\ } \end{array}} \]

9. Taylor expanded in dX.v around 0 97.8%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|dX.v \cdot \left(dY.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ } \end{array}} \]

11. Simplified 97.8%

    \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|dX.v \cdot \left(\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ } \end{array}} \]

12. Taylor expanded in dX.v around inf 97.8%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|dX.v \cdot \left(\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ \end{array} \]
13. Step-by-step derivation

    1. unpow2 97.8%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.v \cdot dX.v\right) \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|dX.v \cdot \left(\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ \end{array} \]

    2. unpow2 97.8%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.v \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right), {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|dX.v \cdot \left(\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ \end{array} \]

    3. swap-sqr 97.8%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.v \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dX.v \cdot \left\lfloor h\right\rfloor \right), {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|dX.v \cdot \left(\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ \end{array} \]

    4. unpow2 97.8%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.v \cdot \left\lfloor h\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|dX.v \cdot \left(\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ \end{array} \]

14. Simplified 97.8%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.v \cdot \left\lfloor h\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|dX.v \cdot \left(\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ \end{array} \]
15. Add Preprocessing

Alternative 2: 98.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := dX.u \cdot \left\lfloor w\right\rfloor \\ t_1 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_2 := \frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dX.u\right), \left\lfloor h\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.v \cdot dX.v\right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left\lfloor w\right\rfloor \cdot \left(dY.u \cdot dY.u\right), \left\lfloor h\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dY.v \cdot dY.v\right)\right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left\lfloor w\right\rfloor \cdot \left(dX.v \cdot dY.u\right)\right)\right|}\\ t_3 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_4 := dX.v \cdot \left\lfloor h\right\rfloor \\ t_5 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t\_0, t\_4\right)\right)}^{2}, {\left(\mathsf{hypot}\left(t\_3, t\_1\right)\right)}^{2}\right)\\ t_6 := \sqrt{t\_5}\\ t_7 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t\_4, t\_0\right)\right)}^{2}, {\left(\mathsf{hypot}\left(t\_1, t\_3\right)\right)}^{2}\right)\\ t_8 := \sqrt{t\_7}\\ t_9 := \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\\ t_10 := \left|t\_9\right|\\ t_11 := \frac{t\_5}{t\_9}\\ t_12 := t\_11 > \left\lfloor maxAniso\right\rfloor \\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{t\_7}{t\_10} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{t\_8}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;t\_10 \cdot \frac{1}{t\_8}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t\_12:\\ \;\;\;\;\frac{t\_6}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_9}{t\_6}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t\_12:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_11\\ \end{array}\right)\\ \mathbf{elif}\;t\_2 > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* dX.u (floor w)))
        (t_1 (* (floor w) dY.u))
        (t_2
         (/
          (fmax
           (fma
            (floor w)
            (* (floor w) (* dX.u dX.u))
            (* (floor h) (* (floor h) (* dX.v dX.v))))
           (fma
            (floor w)
            (* (floor w) (* dY.u dY.u))
            (* (floor h) (* (floor h) (* dY.v dY.v)))))
          (fabs
           (*
            (floor h)
            (- (* dX.u (* (floor w) dY.v)) (* (floor w) (* dX.v dY.u)))))))
        (t_3 (* (floor h) dY.v))
        (t_4 (* dX.v (floor h)))
        (t_5 (fmax (pow (hypot t_0 t_4) 2.0) (pow (hypot t_3 t_1) 2.0)))
        (t_6 (sqrt t_5))
        (t_7 (fmax (pow (hypot t_4 t_0) 2.0) (pow (hypot t_1 t_3) 2.0)))
        (t_8 (sqrt t_7))
        (t_9 (* (- (* dX.u dY.v) (* dX.v dY.u)) (* (floor h) (floor w))))
        (t_10 (fabs t_9))
        (t_11 (/ t_5 t_9))
        (t_12 (> t_11 (floor maxAniso))))
   (if (<
        (if (> (/ t_7 t_10) (floor maxAniso))
          (/ t_8 (floor maxAniso))
          (* t_10 (/ 1.0 t_8)))
        1.0)
     (fmax
      1.0
      (*
       (if t_12 (/ t_6 (floor maxAniso)) (/ t_9 t_6))
       (if t_12 (floor maxAniso) t_11)))
     (if (> t_2 (floor maxAniso)) (floor maxAniso) t_2))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = dX_46_u * floorf(w);
	float t_1 = floorf(w) * dY_46_u;
	float t_2 = fmaxf(fmaf(floorf(w), (floorf(w) * (dX_46_u * dX_46_u)), (floorf(h) * (floorf(h) * (dX_46_v * dX_46_v)))), fmaf(floorf(w), (floorf(w) * (dY_46_u * dY_46_u)), (floorf(h) * (floorf(h) * (dY_46_v * dY_46_v))))) / fabsf((floorf(h) * ((dX_46_u * (floorf(w) * dY_46_v)) - (floorf(w) * (dX_46_v * dY_46_u)))));
	float t_3 = floorf(h) * dY_46_v;
	float t_4 = dX_46_v * floorf(h);
	float t_5 = fmaxf(powf(hypotf(t_0, t_4), 2.0f), powf(hypotf(t_3, t_1), 2.0f));
	float t_6 = sqrtf(t_5);
	float t_7 = fmaxf(powf(hypotf(t_4, t_0), 2.0f), powf(hypotf(t_1, t_3), 2.0f));
	float t_8 = sqrtf(t_7);
	float t_9 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floorf(h) * floorf(w));
	float t_10 = fabsf(t_9);
	float t_11 = t_5 / t_9;
	int t_12 = t_11 > floorf(maxAniso);
	float tmp;
	if ((t_7 / t_10) > floorf(maxAniso)) {
		tmp = t_8 / floorf(maxAniso);
	} else {
		tmp = t_10 * (1.0f / t_8);
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_12) {
			tmp_4 = t_6 / floorf(maxAniso);
		} else {
			tmp_4 = t_9 / t_6;
		}
		float tmp_5;
		if (t_12) {
			tmp_5 = floorf(maxAniso);
		} else {
			tmp_5 = t_11;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_2 > floorf(maxAniso)) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_2;
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(dX_46_u * floor(w))
	t_1 = Float32(floor(w) * dY_46_u)
	t_2 = Float32(((fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) != fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v))))) ? fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dY_46_v * dY_46_v)))) : ((fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dY_46_v * dY_46_v)))) != fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dY_46_v * dY_46_v))))) ? fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) : max(fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))), fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dY_46_v * dY_46_v))))))) / abs(Float32(floor(h) * Float32(Float32(dX_46_u * Float32(floor(w) * dY_46_v)) - Float32(floor(w) * Float32(dX_46_v * dY_46_u))))))
	t_3 = Float32(floor(h) * dY_46_v)
	t_4 = Float32(dX_46_v * floor(h))
	t_5 = ((hypot(t_0, t_4) ^ Float32(2.0)) != (hypot(t_0, t_4) ^ Float32(2.0))) ? (hypot(t_3, t_1) ^ Float32(2.0)) : (((hypot(t_3, t_1) ^ Float32(2.0)) != (hypot(t_3, t_1) ^ Float32(2.0))) ? (hypot(t_0, t_4) ^ Float32(2.0)) : max((hypot(t_0, t_4) ^ Float32(2.0)), (hypot(t_3, t_1) ^ Float32(2.0))))
	t_6 = sqrt(t_5)
	t_7 = ((hypot(t_4, t_0) ^ Float32(2.0)) != (hypot(t_4, t_0) ^ Float32(2.0))) ? (hypot(t_1, t_3) ^ Float32(2.0)) : (((hypot(t_1, t_3) ^ Float32(2.0)) != (hypot(t_1, t_3) ^ Float32(2.0))) ? (hypot(t_4, t_0) ^ Float32(2.0)) : max((hypot(t_4, t_0) ^ Float32(2.0)), (hypot(t_1, t_3) ^ Float32(2.0))))
	t_8 = sqrt(t_7)
	t_9 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * Float32(floor(h) * floor(w)))
	t_10 = abs(t_9)
	t_11 = Float32(t_5 / t_9)
	t_12 = t_11 > floor(maxAniso)
	tmp = Float32(0.0)
	if (Float32(t_7 / t_10) > floor(maxAniso))
		tmp = Float32(t_8 / floor(maxAniso));
	else
		tmp = Float32(t_10 * Float32(Float32(1.0) / t_8));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_12)
			tmp_4 = Float32(t_6 / floor(maxAniso));
		else
			tmp_4 = Float32(t_9 / t_6);
		end
		tmp_5 = Float32(0.0)
		if (t_12)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = t_11;
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_2 > floor(maxAniso))
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_2;
	end
	return tmp_3
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ } \end{array}} \]
4. Add Preprocessing

6. Applied egg-rr 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\color{blue}{1 \cdot \mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left\lfloor w\right\rfloor \cdot \left(dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left\lfloor w\right\rfloor \cdot \left(dX.v \cdot dY.u\right)\right)\right|}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left\lfloor w\right\rfloor \cdot \left(dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left\lfloor w\right\rfloor \cdot \left(dX.v \cdot dY.u\right)\right)\right|}\\ \end{array}\right)}\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ \end{array} \]

8. Simplified 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\color{blue}{\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)}\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ \end{array} \]

9. Taylor expanded in w around 0 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ } \end{array}} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ \end{array} \]

11. Simplified 97.3%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left|\left(\left\lfloor w\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right| \cdot \frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ } \end{array}} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ \end{array} \]

12. Final simplification 97.3%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left|\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right| \cdot \frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dX.u\right), \left\lfloor h\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.v \cdot dX.v\right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left\lfloor w\right\rfloor \cdot \left(dY.u \cdot dY.u\right), \left\lfloor h\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dY.v \cdot dY.v\right)\right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left\lfloor w\right\rfloor \cdot \left(dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dX.u\right), \left\lfloor h\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.v \cdot dX.v\right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left\lfloor w\right\rfloor \cdot \left(dY.u \cdot dY.u\right), \left\lfloor h\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dY.v \cdot dY.v\right)\right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left\lfloor w\right\rfloor \cdot \left(dX.v \cdot dY.u\right)\right)\right|}\\ \end{array} \]
13. Add Preprocessing

Alternative 3: 61.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\\ t_1 := dX.u \cdot \left\lfloor w\right\rfloor \\ t_2 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_3 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_4 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t\_1, dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(t\_2, t\_3\right)\right)}^{2}\right)\\ t_5 := \frac{t\_4}{t\_0}\\ t_6 := t\_5 > \left\lfloor maxAniso\right\rfloor \\ t_7 := \begin{array}{l} \mathbf{if}\;t\_6:\\ \;\;\;\;\frac{\sqrt{t\_4}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \sqrt{\frac{1}{t\_4}}\\ \end{array}\\ \mathbf{if}\;t\_7 < 1:\\ \;\;\;\;\mathsf{max}\left(1, t\_7 \cdot \begin{array}{l} \mathbf{if}\;t\_6:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\mathsf{max}\left({t\_1}^{2}, {\left(\mathsf{hypot}\left(t\_3, t\_2\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\right)\right)\\ \end{array}\right)\\ \mathbf{elif}\;t\_6:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (- (* dX.u dY.v) (* dX.v dY.u)) (* (floor h) (floor w))))
        (t_1 (* dX.u (floor w)))
        (t_2 (* (floor h) dY.v))
        (t_3 (* (floor w) dY.u))
        (t_4
         (fmax
          (pow (hypot t_1 (* dX.v (floor h))) 2.0)
          (pow (hypot t_2 t_3) 2.0)))
        (t_5 (/ t_4 t_0))
        (t_6 (> t_5 (floor maxAniso)))
        (t_7
         (if t_6 (/ (sqrt t_4) (floor maxAniso)) (* t_0 (sqrt (/ 1.0 t_4))))))
   (if (< t_7 1.0)
     (fmax
      1.0
      (*
       t_7
       (if t_6
         (floor maxAniso)
         (expm1
          (log1p
           (/
            (fmax (pow t_1 2.0) (pow (hypot t_3 t_2) 2.0))
            (* (floor w) (* (floor h) (* dX.u dY.v)))))))))
     (if t_6 (floor maxAniso) t_5))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floorf(h) * floorf(w));
	float t_1 = dX_46_u * floorf(w);
	float t_2 = floorf(h) * dY_46_v;
	float t_3 = floorf(w) * dY_46_u;
	float t_4 = fmaxf(powf(hypotf(t_1, (dX_46_v * floorf(h))), 2.0f), powf(hypotf(t_2, t_3), 2.0f));
	float t_5 = t_4 / t_0;
	int t_6 = t_5 > floorf(maxAniso);
	float tmp;
	if (t_6) {
		tmp = sqrtf(t_4) / floorf(maxAniso);
	} else {
		tmp = t_0 * sqrtf((1.0f / t_4));
	}
	float t_7 = tmp;
	float tmp_2;
	if (t_7 < 1.0f) {
		float tmp_3;
		if (t_6) {
			tmp_3 = floorf(maxAniso);
		} else {
			tmp_3 = expm1f(log1pf((fmaxf(powf(t_1, 2.0f), powf(hypotf(t_3, t_2), 2.0f)) / (floorf(w) * (floorf(h) * (dX_46_u * dY_46_v))))));
		}
		tmp_2 = fmaxf(1.0f, (t_7 * tmp_3));
	} else if (t_6) {
		tmp_2 = floorf(maxAniso);
	} else {
		tmp_2 = t_5;
	}
	return tmp_2;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * Float32(floor(h) * floor(w)))
	t_1 = Float32(dX_46_u * floor(w))
	t_2 = Float32(floor(h) * dY_46_v)
	t_3 = Float32(floor(w) * dY_46_u)
	t_4 = ((hypot(t_1, Float32(dX_46_v * floor(h))) ^ Float32(2.0)) != (hypot(t_1, Float32(dX_46_v * floor(h))) ^ Float32(2.0))) ? (hypot(t_2, t_3) ^ Float32(2.0)) : (((hypot(t_2, t_3) ^ Float32(2.0)) != (hypot(t_2, t_3) ^ Float32(2.0))) ? (hypot(t_1, Float32(dX_46_v * floor(h))) ^ Float32(2.0)) : max((hypot(t_1, Float32(dX_46_v * floor(h))) ^ Float32(2.0)), (hypot(t_2, t_3) ^ Float32(2.0))))
	t_5 = Float32(t_4 / t_0)
	t_6 = t_5 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_6)
		tmp = Float32(sqrt(t_4) / floor(maxAniso));
	else
		tmp = Float32(t_0 * sqrt(Float32(Float32(1.0) / t_4)));
	end
	t_7 = tmp
	tmp_2 = Float32(0.0)
	if (t_7 < Float32(1.0))
		tmp_3 = Float32(0.0)
		if (t_6)
			tmp_3 = floor(maxAniso);
		else
			tmp_3 = expm1(log1p(Float32((((t_1 ^ Float32(2.0)) != (t_1 ^ Float32(2.0))) ? (hypot(t_3, t_2) ^ Float32(2.0)) : (((hypot(t_3, t_2) ^ Float32(2.0)) != (hypot(t_3, t_2) ^ Float32(2.0))) ? (t_1 ^ Float32(2.0)) : max((t_1 ^ Float32(2.0)), (hypot(t_3, t_2) ^ Float32(2.0))))) / Float32(floor(w) * Float32(floor(h) * Float32(dX_46_u * dY_46_v))))));
		end
		tmp_2 = (Float32(1.0) != Float32(1.0)) ? Float32(t_7 * tmp_3) : ((Float32(t_7 * tmp_3) != Float32(t_7 * tmp_3)) ? Float32(1.0) : max(Float32(1.0), Float32(t_7 * tmp_3)));
	elseif (t_6)
		tmp_2 = floor(maxAniso);
	else
		tmp_2 = t_5;
	end
	return tmp_2
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ } \end{array}} \]
4. Add Preprocessing

5. Taylor expanded in w around 0 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.5%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ } \end{array}} \]

8. Taylor expanded in dX.u around inf 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
9. Step-by-step derivation

   1. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \right)}^{2} \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   2. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   3. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   4. swap-sqr 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   5. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \cdot dX.u\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   6. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

10. Simplified 57.9%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

11. Taylor expanded in dX.u around inf 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{dX.u \cdot \left(dY.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
12. Step-by-step derivation

13. Simplified 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
14. Step-by-step derivation

    1. expm1-log1p-u 60.9%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\right)\right)\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

    2. expm1-undefine 60.9%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;e^{\mathsf{log1p}\left(\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\right)} - 1\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

15. Applied egg-rr 60.9%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;e^{\mathsf{log1p}\left(\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\right)} - 1\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
16. Step-by-step derivation

    1. expm1-define 60.9%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\right)\right)\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

17. Simplified 60.9%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\right)\right)\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

18. Final simplification 60.9%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\right)\right)\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)}\\ \end{array} \]
19. Add Preprocessing

Alternative 4: 60.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\\ t_1 := dX.u \cdot \left\lfloor w\right\rfloor \\ t_2 := {\left(\mathsf{hypot}\left(t\_1, dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}\\ t_3 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_4 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_5 := {\left(\mathsf{hypot}\left(t\_4, t\_3\right)\right)}^{2}\\ t_6 := \mathsf{max}\left(t\_2, {\left(\mathsf{hypot}\left(t\_3, t\_4\right)\right)}^{2}\right)\\ t_7 := \frac{\sqrt{t\_6}}{\left\lfloor maxAniso\right\rfloor }\\ t_8 := \frac{t\_6}{t\_0}\\ t_9 := t\_8 > \left\lfloor maxAniso\right\rfloor \\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \sqrt{\frac{1}{t\_6}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \log \left(e^{{\left(\mathsf{max}\left(t\_2, t\_5\right)\right)}^{-0.5}}\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({t\_1}^{2}, t\_5\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;t\_9:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_8\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (- (* dX.u dY.v) (* dX.v dY.u)) (* (floor h) (floor w))))
        (t_1 (* dX.u (floor w)))
        (t_2 (pow (hypot t_1 (* dX.v (floor h))) 2.0))
        (t_3 (* (floor h) dY.v))
        (t_4 (* (floor w) dY.u))
        (t_5 (pow (hypot t_4 t_3) 2.0))
        (t_6 (fmax t_2 (pow (hypot t_3 t_4) 2.0)))
        (t_7 (/ (sqrt t_6) (floor maxAniso)))
        (t_8 (/ t_6 t_0))
        (t_9 (> t_8 (floor maxAniso))))
   (if (< (if t_9 t_7 (* t_0 (sqrt (/ 1.0 t_6)))) 1.0)
     (fmax
      1.0
      (*
       (if t_9 t_7 (* t_0 (log (exp (pow (fmax t_2 t_5) -0.5)))))
       (if t_9
         (floor maxAniso)
         (/
          (fmax (pow t_1 2.0) t_5)
          (* (floor w) (* (floor h) (* dX.u dY.v)))))))
     (if t_9 (floor maxAniso) t_8))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floorf(h) * floorf(w));
	float t_1 = dX_46_u * floorf(w);
	float t_2 = powf(hypotf(t_1, (dX_46_v * floorf(h))), 2.0f);
	float t_3 = floorf(h) * dY_46_v;
	float t_4 = floorf(w) * dY_46_u;
	float t_5 = powf(hypotf(t_4, t_3), 2.0f);
	float t_6 = fmaxf(t_2, powf(hypotf(t_3, t_4), 2.0f));
	float t_7 = sqrtf(t_6) / floorf(maxAniso);
	float t_8 = t_6 / t_0;
	int t_9 = t_8 > floorf(maxAniso);
	float tmp;
	if (t_9) {
		tmp = t_7;
	} else {
		tmp = t_0 * sqrtf((1.0f / t_6));
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_9) {
			tmp_4 = t_7;
		} else {
			tmp_4 = t_0 * logf(expf(powf(fmaxf(t_2, t_5), -0.5f)));
		}
		float tmp_5;
		if (t_9) {
			tmp_5 = floorf(maxAniso);
		} else {
			tmp_5 = fmaxf(powf(t_1, 2.0f), t_5) / (floorf(w) * (floorf(h) * (dX_46_u * dY_46_v)));
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_9) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_8;
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * Float32(floor(h) * floor(w)))
	t_1 = Float32(dX_46_u * floor(w))
	t_2 = hypot(t_1, Float32(dX_46_v * floor(h))) ^ Float32(2.0)
	t_3 = Float32(floor(h) * dY_46_v)
	t_4 = Float32(floor(w) * dY_46_u)
	t_5 = hypot(t_4, t_3) ^ Float32(2.0)
	t_6 = (t_2 != t_2) ? (hypot(t_3, t_4) ^ Float32(2.0)) : (((hypot(t_3, t_4) ^ Float32(2.0)) != (hypot(t_3, t_4) ^ Float32(2.0))) ? t_2 : max(t_2, (hypot(t_3, t_4) ^ Float32(2.0))))
	t_7 = Float32(sqrt(t_6) / floor(maxAniso))
	t_8 = Float32(t_6 / t_0)
	t_9 = t_8 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_9)
		tmp = t_7;
	else
		tmp = Float32(t_0 * sqrt(Float32(Float32(1.0) / t_6)));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_9)
			tmp_4 = t_7;
		else
			tmp_4 = Float32(t_0 * log(exp((((t_2 != t_2) ? t_5 : ((t_5 != t_5) ? t_2 : max(t_2, t_5))) ^ Float32(-0.5)))));
		end
		tmp_5 = Float32(0.0)
		if (t_9)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = Float32((((t_1 ^ Float32(2.0)) != (t_1 ^ Float32(2.0))) ? t_5 : ((t_5 != t_5) ? (t_1 ^ Float32(2.0)) : max((t_1 ^ Float32(2.0)), t_5))) / Float32(floor(w) * Float32(floor(h) * Float32(dX_46_u * dY_46_v))));
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_9)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_8;
	end
	return tmp_3
end

MATLAB

function tmp_7 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floor(h) * floor(w));
	t_1 = dX_46_u * floor(w);
	t_2 = hypot(t_1, (dX_46_v * floor(h))) ^ single(2.0);
	t_3 = floor(h) * dY_46_v;
	t_4 = floor(w) * dY_46_u;
	t_5 = hypot(t_4, t_3) ^ single(2.0);
	t_6 = max(t_2, (hypot(t_3, t_4) ^ single(2.0)));
	t_7 = sqrt(t_6) / floor(maxAniso);
	t_8 = t_6 / t_0;
	t_9 = t_8 > floor(maxAniso);
	tmp = single(0.0);
	if (t_9)
		tmp = t_7;
	else
		tmp = t_0 * sqrt((single(1.0) / t_6));
	end
	tmp_4 = single(0.0);
	if (tmp < single(1.0))
		tmp_5 = single(0.0);
		if (t_9)
			tmp_5 = t_7;
		else
			tmp_5 = t_0 * log(exp((max(t_2, t_5) ^ single(-0.5))));
		end
		tmp_6 = single(0.0);
		if (t_9)
			tmp_6 = floor(maxAniso);
		else
			tmp_6 = max((t_1 ^ single(2.0)), t_5) / (floor(w) * (floor(h) * (dX_46_u * dY_46_v)));
		end
		tmp_4 = max(single(1.0), (tmp_5 * tmp_6));
	elseif (t_9)
		tmp_4 = floor(maxAniso);
	else
		tmp_4 = t_8;
	end
	tmp_7 = tmp_4;
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ } \end{array}} \]
4. Add Preprocessing

5. Taylor expanded in w around 0 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.5%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ } \end{array}} \]

8. Taylor expanded in dX.u around inf 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
9. Step-by-step derivation

   1. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \right)}^{2} \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   2. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   3. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   4. swap-sqr 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   5. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \cdot dX.u\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   6. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

10. Simplified 57.9%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

11. Taylor expanded in dX.u around inf 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{dX.u \cdot \left(dY.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
12. Step-by-step derivation

13. Simplified 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

15. Applied egg-rr 59.8%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\log \left(e^{{\left(\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)\right)}^{-0.5}}\right) \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

16. Final simplification 59.8%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \log \left(e^{{\left(\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)\right)}^{-0.5}}\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)}\\ \end{array} \]
17. Add Preprocessing

Alternative 5: 60.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_1 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_2 := {\left(\mathsf{hypot}\left(t\_1, t\_0\right)\right)}^{2}\\ t_3 := dX.u \cdot \left\lfloor w\right\rfloor \\ t_4 := {\left(\mathsf{hypot}\left(t\_3, dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}\\ t_5 := \mathsf{max}\left(t\_4, {\left(\mathsf{hypot}\left(t\_0, t\_1\right)\right)}^{2}\right)\\ t_6 := \frac{\sqrt{t\_5}}{\left\lfloor maxAniso\right\rfloor }\\ t_7 := dX.u \cdot dY.v - dX.v \cdot dY.u\\ t_8 := t\_7 \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\\ t_9 := \frac{t\_5}{t\_8}\\ t_10 := t\_9 > \left\lfloor maxAniso\right\rfloor \\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t\_10:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;t\_8 \cdot \sqrt{\frac{1}{t\_5}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t\_10:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;t\_8 \cdot {\left({\left(\frac{1}{\mathsf{max}\left(t\_4, t\_2\right)}\right)}^{1.5}\right)}^{0.3333333333333333}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t\_10:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({t\_3}^{2}, t\_2\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot t\_7\right)}\\ \end{array}\right)\\ \mathbf{elif}\;t\_10:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_9\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor h) dY.v))
        (t_1 (* (floor w) dY.u))
        (t_2 (pow (hypot t_1 t_0) 2.0))
        (t_3 (* dX.u (floor w)))
        (t_4 (pow (hypot t_3 (* dX.v (floor h))) 2.0))
        (t_5 (fmax t_4 (pow (hypot t_0 t_1) 2.0)))
        (t_6 (/ (sqrt t_5) (floor maxAniso)))
        (t_7 (- (* dX.u dY.v) (* dX.v dY.u)))
        (t_8 (* t_7 (* (floor h) (floor w))))
        (t_9 (/ t_5 t_8))
        (t_10 (> t_9 (floor maxAniso))))
   (if (< (if t_10 t_6 (* t_8 (sqrt (/ 1.0 t_5)))) 1.0)
     (fmax
      1.0
      (*
       (if t_10
         t_6
         (* t_8 (pow (pow (/ 1.0 (fmax t_4 t_2)) 1.5) 0.3333333333333333)))
       (if t_10
         (floor maxAniso)
         (/ (fmax (pow t_3 2.0) t_2) (* (floor w) (* (floor h) t_7))))))
     (if t_10 (floor maxAniso) t_9))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(h) * dY_46_v;
	float t_1 = floorf(w) * dY_46_u;
	float t_2 = powf(hypotf(t_1, t_0), 2.0f);
	float t_3 = dX_46_u * floorf(w);
	float t_4 = powf(hypotf(t_3, (dX_46_v * floorf(h))), 2.0f);
	float t_5 = fmaxf(t_4, powf(hypotf(t_0, t_1), 2.0f));
	float t_6 = sqrtf(t_5) / floorf(maxAniso);
	float t_7 = (dX_46_u * dY_46_v) - (dX_46_v * dY_46_u);
	float t_8 = t_7 * (floorf(h) * floorf(w));
	float t_9 = t_5 / t_8;
	int t_10 = t_9 > floorf(maxAniso);
	float tmp;
	if (t_10) {
		tmp = t_6;
	} else {
		tmp = t_8 * sqrtf((1.0f / t_5));
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_10) {
			tmp_4 = t_6;
		} else {
			tmp_4 = t_8 * powf(powf((1.0f / fmaxf(t_4, t_2)), 1.5f), 0.3333333333333333f);
		}
		float tmp_5;
		if (t_10) {
			tmp_5 = floorf(maxAniso);
		} else {
			tmp_5 = fmaxf(powf(t_3, 2.0f), t_2) / (floorf(w) * (floorf(h) * t_7));
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_10) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_9;
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(h) * dY_46_v)
	t_1 = Float32(floor(w) * dY_46_u)
	t_2 = hypot(t_1, t_0) ^ Float32(2.0)
	t_3 = Float32(dX_46_u * floor(w))
	t_4 = hypot(t_3, Float32(dX_46_v * floor(h))) ^ Float32(2.0)
	t_5 = (t_4 != t_4) ? (hypot(t_0, t_1) ^ Float32(2.0)) : (((hypot(t_0, t_1) ^ Float32(2.0)) != (hypot(t_0, t_1) ^ Float32(2.0))) ? t_4 : max(t_4, (hypot(t_0, t_1) ^ Float32(2.0))))
	t_6 = Float32(sqrt(t_5) / floor(maxAniso))
	t_7 = Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))
	t_8 = Float32(t_7 * Float32(floor(h) * floor(w)))
	t_9 = Float32(t_5 / t_8)
	t_10 = t_9 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_10)
		tmp = t_6;
	else
		tmp = Float32(t_8 * sqrt(Float32(Float32(1.0) / t_5)));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_10)
			tmp_4 = t_6;
		else
			tmp_4 = Float32(t_8 * ((Float32(Float32(1.0) / ((t_4 != t_4) ? t_2 : ((t_2 != t_2) ? t_4 : max(t_4, t_2)))) ^ Float32(1.5)) ^ Float32(0.3333333333333333)));
		end
		tmp_5 = Float32(0.0)
		if (t_10)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = Float32((((t_3 ^ Float32(2.0)) != (t_3 ^ Float32(2.0))) ? t_2 : ((t_2 != t_2) ? (t_3 ^ Float32(2.0)) : max((t_3 ^ Float32(2.0)), t_2))) / Float32(floor(w) * Float32(floor(h) * t_7)));
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_10)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_9;
	end
	return tmp_3
end

MATLAB

function tmp_7 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = floor(h) * dY_46_v;
	t_1 = floor(w) * dY_46_u;
	t_2 = hypot(t_1, t_0) ^ single(2.0);
	t_3 = dX_46_u * floor(w);
	t_4 = hypot(t_3, (dX_46_v * floor(h))) ^ single(2.0);
	t_5 = max(t_4, (hypot(t_0, t_1) ^ single(2.0)));
	t_6 = sqrt(t_5) / floor(maxAniso);
	t_7 = (dX_46_u * dY_46_v) - (dX_46_v * dY_46_u);
	t_8 = t_7 * (floor(h) * floor(w));
	t_9 = t_5 / t_8;
	t_10 = t_9 > floor(maxAniso);
	tmp = single(0.0);
	if (t_10)
		tmp = t_6;
	else
		tmp = t_8 * sqrt((single(1.0) / t_5));
	end
	tmp_4 = single(0.0);
	if (tmp < single(1.0))
		tmp_5 = single(0.0);
		if (t_10)
			tmp_5 = t_6;
		else
			tmp_5 = t_8 * (((single(1.0) / max(t_4, t_2)) ^ single(1.5)) ^ single(0.3333333333333333));
		end
		tmp_6 = single(0.0);
		if (t_10)
			tmp_6 = floor(maxAniso);
		else
			tmp_6 = max((t_3 ^ single(2.0)), t_2) / (floor(w) * (floor(h) * t_7));
		end
		tmp_4 = max(single(1.0), (tmp_5 * tmp_6));
	elseif (t_10)
		tmp_4 = floor(maxAniso);
	else
		tmp_4 = t_9;
	end
	tmp_7 = tmp_4;
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ } \end{array}} \]
4. Add Preprocessing

5. Taylor expanded in w around 0 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.5%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ } \end{array}} \]

8. Taylor expanded in dX.u around inf 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
9. Step-by-step derivation

   1. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \right)}^{2} \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   2. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   3. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   4. swap-sqr 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   5. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \cdot dX.u\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   6. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

10. Simplified 57.9%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
11. Step-by-step derivation

    1. add-cbrt-cube 59.6%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

    2. pow1/3 59.6%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;{\left(\left(\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\right)}^{0.3333333333333333} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

12. Applied egg-rr 59.6%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}\right)}^{1.5}\right)}^{0.3333333333333333} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

13. Taylor expanded in w around 0 59.6%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}\right)}^{1.5}\right)}^{0.3333333333333333} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
14. Step-by-step derivation

    1. associate-*r* 59.6%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}\right)}^{1.5}\right)}^{0.3333333333333333} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\color{blue}{\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

15. Simplified 59.6%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}\right)}^{1.5}\right)}^{0.3333333333333333} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

16. Final simplification 59.6%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot {\left({\left(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}\right)}^{1.5}\right)}^{0.3333333333333333}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)}\\ \end{array} \]
17. Add Preprocessing

Alternative 6: 60.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\\ t_1 := dX.u \cdot \left\lfloor w\right\rfloor \\ t_2 := {\left(\mathsf{hypot}\left(t\_1, dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}\\ t_3 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_4 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_5 := {\left(\mathsf{hypot}\left(t\_3, t\_4\right)\right)}^{2}\\ t_6 := \mathsf{max}\left(t\_2, t\_5\right)\\ t_7 := \frac{\sqrt{t\_6}}{\left\lfloor maxAniso\right\rfloor }\\ t_8 := \frac{t\_6}{t\_0}\\ t_9 := t\_8 > \left\lfloor maxAniso\right\rfloor \\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \sqrt{\frac{1}{t\_6}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot {\left({\left(\frac{1}{\mathsf{max}\left(t\_2, {\left(\mathsf{hypot}\left(t\_4, t\_3\right)\right)}^{2}\right)}\right)}^{1.5}\right)}^{0.3333333333333333}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({t\_1}^{2}, t\_5\right)}{t\_0}\\ \end{array}\right)\\ \mathbf{elif}\;t\_9:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_8\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (- (* dX.u dY.v) (* dX.v dY.u)) (* (floor h) (floor w))))
        (t_1 (* dX.u (floor w)))
        (t_2 (pow (hypot t_1 (* dX.v (floor h))) 2.0))
        (t_3 (* (floor h) dY.v))
        (t_4 (* (floor w) dY.u))
        (t_5 (pow (hypot t_3 t_4) 2.0))
        (t_6 (fmax t_2 t_5))
        (t_7 (/ (sqrt t_6) (floor maxAniso)))
        (t_8 (/ t_6 t_0))
        (t_9 (> t_8 (floor maxAniso))))
   (if (< (if t_9 t_7 (* t_0 (sqrt (/ 1.0 t_6)))) 1.0)
     (fmax
      1.0
      (*
       (if t_9
         t_7
         (*
          t_0
          (pow
           (pow (/ 1.0 (fmax t_2 (pow (hypot t_4 t_3) 2.0))) 1.5)
           0.3333333333333333)))
       (if t_9 (floor maxAniso) (/ (fmax (pow t_1 2.0) t_5) t_0))))
     (if t_9 (floor maxAniso) t_8))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floorf(h) * floorf(w));
	float t_1 = dX_46_u * floorf(w);
	float t_2 = powf(hypotf(t_1, (dX_46_v * floorf(h))), 2.0f);
	float t_3 = floorf(h) * dY_46_v;
	float t_4 = floorf(w) * dY_46_u;
	float t_5 = powf(hypotf(t_3, t_4), 2.0f);
	float t_6 = fmaxf(t_2, t_5);
	float t_7 = sqrtf(t_6) / floorf(maxAniso);
	float t_8 = t_6 / t_0;
	int t_9 = t_8 > floorf(maxAniso);
	float tmp;
	if (t_9) {
		tmp = t_7;
	} else {
		tmp = t_0 * sqrtf((1.0f / t_6));
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_9) {
			tmp_4 = t_7;
		} else {
			tmp_4 = t_0 * powf(powf((1.0f / fmaxf(t_2, powf(hypotf(t_4, t_3), 2.0f))), 1.5f), 0.3333333333333333f);
		}
		float tmp_5;
		if (t_9) {
			tmp_5 = floorf(maxAniso);
		} else {
			tmp_5 = fmaxf(powf(t_1, 2.0f), t_5) / t_0;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_9) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_8;
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * Float32(floor(h) * floor(w)))
	t_1 = Float32(dX_46_u * floor(w))
	t_2 = hypot(t_1, Float32(dX_46_v * floor(h))) ^ Float32(2.0)
	t_3 = Float32(floor(h) * dY_46_v)
	t_4 = Float32(floor(w) * dY_46_u)
	t_5 = hypot(t_3, t_4) ^ Float32(2.0)
	t_6 = (t_2 != t_2) ? t_5 : ((t_5 != t_5) ? t_2 : max(t_2, t_5))
	t_7 = Float32(sqrt(t_6) / floor(maxAniso))
	t_8 = Float32(t_6 / t_0)
	t_9 = t_8 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_9)
		tmp = t_7;
	else
		tmp = Float32(t_0 * sqrt(Float32(Float32(1.0) / t_6)));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_9)
			tmp_4 = t_7;
		else
			tmp_4 = Float32(t_0 * ((Float32(Float32(1.0) / ((t_2 != t_2) ? (hypot(t_4, t_3) ^ Float32(2.0)) : (((hypot(t_4, t_3) ^ Float32(2.0)) != (hypot(t_4, t_3) ^ Float32(2.0))) ? t_2 : max(t_2, (hypot(t_4, t_3) ^ Float32(2.0)))))) ^ Float32(1.5)) ^ Float32(0.3333333333333333)));
		end
		tmp_5 = Float32(0.0)
		if (t_9)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = Float32((((t_1 ^ Float32(2.0)) != (t_1 ^ Float32(2.0))) ? t_5 : ((t_5 != t_5) ? (t_1 ^ Float32(2.0)) : max((t_1 ^ Float32(2.0)), t_5))) / t_0);
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_9)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_8;
	end
	return tmp_3
end

MATLAB

function tmp_7 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floor(h) * floor(w));
	t_1 = dX_46_u * floor(w);
	t_2 = hypot(t_1, (dX_46_v * floor(h))) ^ single(2.0);
	t_3 = floor(h) * dY_46_v;
	t_4 = floor(w) * dY_46_u;
	t_5 = hypot(t_3, t_4) ^ single(2.0);
	t_6 = max(t_2, t_5);
	t_7 = sqrt(t_6) / floor(maxAniso);
	t_8 = t_6 / t_0;
	t_9 = t_8 > floor(maxAniso);
	tmp = single(0.0);
	if (t_9)
		tmp = t_7;
	else
		tmp = t_0 * sqrt((single(1.0) / t_6));
	end
	tmp_4 = single(0.0);
	if (tmp < single(1.0))
		tmp_5 = single(0.0);
		if (t_9)
			tmp_5 = t_7;
		else
			tmp_5 = t_0 * (((single(1.0) / max(t_2, (hypot(t_4, t_3) ^ single(2.0)))) ^ single(1.5)) ^ single(0.3333333333333333));
		end
		tmp_6 = single(0.0);
		if (t_9)
			tmp_6 = floor(maxAniso);
		else
			tmp_6 = max((t_1 ^ single(2.0)), t_5) / t_0;
		end
		tmp_4 = max(single(1.0), (tmp_5 * tmp_6));
	elseif (t_9)
		tmp_4 = floor(maxAniso);
	else
		tmp_4 = t_8;
	end
	tmp_7 = tmp_4;
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ } \end{array}} \]
4. Add Preprocessing

5. Taylor expanded in w around 0 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.5%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ } \end{array}} \]

8. Taylor expanded in dX.u around inf 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
9. Step-by-step derivation

   1. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \right)}^{2} \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   2. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   3. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   4. swap-sqr 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   5. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \cdot dX.u\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   6. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

10. Simplified 57.9%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
11. Step-by-step derivation

    1. add-cbrt-cube 59.6%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

    2. pow1/3 59.6%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;{\left(\left(\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\right)}^{0.3333333333333333} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

12. Applied egg-rr 59.6%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}\right)}^{1.5}\right)}^{0.3333333333333333} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

13. Final simplification 59.6%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot {\left({\left(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}\right)}^{1.5}\right)}^{0.3333333333333333}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)}\\ \end{array} \]
14. Add Preprocessing

Alternative 7: 60.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\\ t_1 := dX.u \cdot \left\lfloor w\right\rfloor \\ t_2 := {\left(\mathsf{hypot}\left(t\_1, dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}\\ t_3 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_4 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_5 := {\left(\mathsf{hypot}\left(t\_3, t\_4\right)\right)}^{2}\\ t_6 := \mathsf{max}\left(t\_2, t\_5\right)\\ t_7 := \frac{\sqrt{t\_6}}{\left\lfloor maxAniso\right\rfloor }\\ t_8 := \frac{t\_6}{t\_0}\\ t_9 := t\_8 > \left\lfloor maxAniso\right\rfloor \\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \sqrt{\frac{1}{t\_6}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({t\_1}^{2}, t\_5\right)}{t\_0}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \sqrt[3]{{\left(\frac{1}{\mathsf{max}\left(t\_2, {\left(\mathsf{hypot}\left(t\_4, t\_3\right)\right)}^{2}\right)}\right)}^{1.5}}\\ \end{array}\right)\\ \mathbf{elif}\;t\_9:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_8\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (- (* dX.u dY.v) (* dX.v dY.u)) (* (floor h) (floor w))))
        (t_1 (* dX.u (floor w)))
        (t_2 (pow (hypot t_1 (* dX.v (floor h))) 2.0))
        (t_3 (* (floor h) dY.v))
        (t_4 (* (floor w) dY.u))
        (t_5 (pow (hypot t_3 t_4) 2.0))
        (t_6 (fmax t_2 t_5))
        (t_7 (/ (sqrt t_6) (floor maxAniso)))
        (t_8 (/ t_6 t_0))
        (t_9 (> t_8 (floor maxAniso))))
   (if (< (if t_9 t_7 (* t_0 (sqrt (/ 1.0 t_6)))) 1.0)
     (fmax
      1.0
      (*
       (if t_9 (floor maxAniso) (/ (fmax (pow t_1 2.0) t_5) t_0))
       (if t_9
         t_7
         (*
          t_0
          (cbrt (pow (/ 1.0 (fmax t_2 (pow (hypot t_4 t_3) 2.0))) 1.5))))))
     (if t_9 (floor maxAniso) t_8))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floorf(h) * floorf(w));
	float t_1 = dX_46_u * floorf(w);
	float t_2 = powf(hypotf(t_1, (dX_46_v * floorf(h))), 2.0f);
	float t_3 = floorf(h) * dY_46_v;
	float t_4 = floorf(w) * dY_46_u;
	float t_5 = powf(hypotf(t_3, t_4), 2.0f);
	float t_6 = fmaxf(t_2, t_5);
	float t_7 = sqrtf(t_6) / floorf(maxAniso);
	float t_8 = t_6 / t_0;
	int t_9 = t_8 > floorf(maxAniso);
	float tmp;
	if (t_9) {
		tmp = t_7;
	} else {
		tmp = t_0 * sqrtf((1.0f / t_6));
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_9) {
			tmp_4 = floorf(maxAniso);
		} else {
			tmp_4 = fmaxf(powf(t_1, 2.0f), t_5) / t_0;
		}
		float tmp_5;
		if (t_9) {
			tmp_5 = t_7;
		} else {
			tmp_5 = t_0 * cbrtf(powf((1.0f / fmaxf(t_2, powf(hypotf(t_4, t_3), 2.0f))), 1.5f));
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_9) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_8;
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * Float32(floor(h) * floor(w)))
	t_1 = Float32(dX_46_u * floor(w))
	t_2 = hypot(t_1, Float32(dX_46_v * floor(h))) ^ Float32(2.0)
	t_3 = Float32(floor(h) * dY_46_v)
	t_4 = Float32(floor(w) * dY_46_u)
	t_5 = hypot(t_3, t_4) ^ Float32(2.0)
	t_6 = (t_2 != t_2) ? t_5 : ((t_5 != t_5) ? t_2 : max(t_2, t_5))
	t_7 = Float32(sqrt(t_6) / floor(maxAniso))
	t_8 = Float32(t_6 / t_0)
	t_9 = t_8 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_9)
		tmp = t_7;
	else
		tmp = Float32(t_0 * sqrt(Float32(Float32(1.0) / t_6)));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_9)
			tmp_4 = floor(maxAniso);
		else
			tmp_4 = Float32((((t_1 ^ Float32(2.0)) != (t_1 ^ Float32(2.0))) ? t_5 : ((t_5 != t_5) ? (t_1 ^ Float32(2.0)) : max((t_1 ^ Float32(2.0)), t_5))) / t_0);
		end
		tmp_5 = Float32(0.0)
		if (t_9)
			tmp_5 = t_7;
		else
			tmp_5 = Float32(t_0 * cbrt((Float32(Float32(1.0) / ((t_2 != t_2) ? (hypot(t_4, t_3) ^ Float32(2.0)) : (((hypot(t_4, t_3) ^ Float32(2.0)) != (hypot(t_4, t_3) ^ Float32(2.0))) ? t_2 : max(t_2, (hypot(t_4, t_3) ^ Float32(2.0)))))) ^ Float32(1.5))));
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_9)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_8;
	end
	return tmp_3
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ } \end{array}} \]
4. Add Preprocessing

5. Taylor expanded in w around 0 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.5%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ } \end{array}} \]

8. Taylor expanded in dX.u around inf 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
9. Step-by-step derivation

   1. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \right)}^{2} \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   2. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   3. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   4. swap-sqr 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   5. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \cdot dX.u\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   6. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

10. Simplified 57.9%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
11. Step-by-step derivation

    1. add-cbrt-cube 59.6%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

    2. add-sqr-sqrt 59.6%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)} \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

    3. pow1 59.6%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}\right)}^{1} \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

12. Applied egg-rr 59.6%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}\right)}^{1.5}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

13. Final simplification 59.6%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt[3]{{\left(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}\right)}^{1.5}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)}\\ \end{array} \]
14. Add Preprocessing

Alternative 8: 60.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\\ t_1 := dX.u \cdot \left\lfloor w\right\rfloor \\ t_2 := {\left(\mathsf{hypot}\left(t\_1, dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}\\ t_3 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_4 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_5 := {\left(\mathsf{hypot}\left(t\_4, t\_3\right)\right)}^{2}\\ t_6 := \mathsf{max}\left(t\_2, {\left(\mathsf{hypot}\left(t\_3, t\_4\right)\right)}^{2}\right)\\ t_7 := \frac{\sqrt{t\_6}}{\left\lfloor maxAniso\right\rfloor }\\ t_8 := \frac{t\_6}{t\_0}\\ t_9 := t\_8 > \left\lfloor maxAniso\right\rfloor \\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \sqrt{\frac{1}{t\_6}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({t\_1}^{2}, t\_5\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot {\left({\left(\frac{1}{\mathsf{max}\left(t\_2, t\_5\right)}\right)}^{1.5}\right)}^{0.3333333333333333}\\ \end{array}\right)\\ \mathbf{elif}\;t\_9:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_8\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (- (* dX.u dY.v) (* dX.v dY.u)) (* (floor h) (floor w))))
        (t_1 (* dX.u (floor w)))
        (t_2 (pow (hypot t_1 (* dX.v (floor h))) 2.0))
        (t_3 (* (floor h) dY.v))
        (t_4 (* (floor w) dY.u))
        (t_5 (pow (hypot t_4 t_3) 2.0))
        (t_6 (fmax t_2 (pow (hypot t_3 t_4) 2.0)))
        (t_7 (/ (sqrt t_6) (floor maxAniso)))
        (t_8 (/ t_6 t_0))
        (t_9 (> t_8 (floor maxAniso))))
   (if (< (if t_9 t_7 (* t_0 (sqrt (/ 1.0 t_6)))) 1.0)
     (fmax
      1.0
      (*
       (if t_9
         (floor maxAniso)
         (/
          (fmax (pow t_1 2.0) t_5)
          (* (floor w) (* (floor h) (* dX.u dY.v)))))
       (if t_9
         t_7
         (* t_0 (pow (pow (/ 1.0 (fmax t_2 t_5)) 1.5) 0.3333333333333333)))))
     (if t_9 (floor maxAniso) t_8))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floorf(h) * floorf(w));
	float t_1 = dX_46_u * floorf(w);
	float t_2 = powf(hypotf(t_1, (dX_46_v * floorf(h))), 2.0f);
	float t_3 = floorf(h) * dY_46_v;
	float t_4 = floorf(w) * dY_46_u;
	float t_5 = powf(hypotf(t_4, t_3), 2.0f);
	float t_6 = fmaxf(t_2, powf(hypotf(t_3, t_4), 2.0f));
	float t_7 = sqrtf(t_6) / floorf(maxAniso);
	float t_8 = t_6 / t_0;
	int t_9 = t_8 > floorf(maxAniso);
	float tmp;
	if (t_9) {
		tmp = t_7;
	} else {
		tmp = t_0 * sqrtf((1.0f / t_6));
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_9) {
			tmp_4 = floorf(maxAniso);
		} else {
			tmp_4 = fmaxf(powf(t_1, 2.0f), t_5) / (floorf(w) * (floorf(h) * (dX_46_u * dY_46_v)));
		}
		float tmp_5;
		if (t_9) {
			tmp_5 = t_7;
		} else {
			tmp_5 = t_0 * powf(powf((1.0f / fmaxf(t_2, t_5)), 1.5f), 0.3333333333333333f);
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_9) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_8;
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * Float32(floor(h) * floor(w)))
	t_1 = Float32(dX_46_u * floor(w))
	t_2 = hypot(t_1, Float32(dX_46_v * floor(h))) ^ Float32(2.0)
	t_3 = Float32(floor(h) * dY_46_v)
	t_4 = Float32(floor(w) * dY_46_u)
	t_5 = hypot(t_4, t_3) ^ Float32(2.0)
	t_6 = (t_2 != t_2) ? (hypot(t_3, t_4) ^ Float32(2.0)) : (((hypot(t_3, t_4) ^ Float32(2.0)) != (hypot(t_3, t_4) ^ Float32(2.0))) ? t_2 : max(t_2, (hypot(t_3, t_4) ^ Float32(2.0))))
	t_7 = Float32(sqrt(t_6) / floor(maxAniso))
	t_8 = Float32(t_6 / t_0)
	t_9 = t_8 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_9)
		tmp = t_7;
	else
		tmp = Float32(t_0 * sqrt(Float32(Float32(1.0) / t_6)));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_9)
			tmp_4 = floor(maxAniso);
		else
			tmp_4 = Float32((((t_1 ^ Float32(2.0)) != (t_1 ^ Float32(2.0))) ? t_5 : ((t_5 != t_5) ? (t_1 ^ Float32(2.0)) : max((t_1 ^ Float32(2.0)), t_5))) / Float32(floor(w) * Float32(floor(h) * Float32(dX_46_u * dY_46_v))));
		end
		tmp_5 = Float32(0.0)
		if (t_9)
			tmp_5 = t_7;
		else
			tmp_5 = Float32(t_0 * ((Float32(Float32(1.0) / ((t_2 != t_2) ? t_5 : ((t_5 != t_5) ? t_2 : max(t_2, t_5)))) ^ Float32(1.5)) ^ Float32(0.3333333333333333)));
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_9)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_8;
	end
	return tmp_3
end

MATLAB

function tmp_7 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floor(h) * floor(w));
	t_1 = dX_46_u * floor(w);
	t_2 = hypot(t_1, (dX_46_v * floor(h))) ^ single(2.0);
	t_3 = floor(h) * dY_46_v;
	t_4 = floor(w) * dY_46_u;
	t_5 = hypot(t_4, t_3) ^ single(2.0);
	t_6 = max(t_2, (hypot(t_3, t_4) ^ single(2.0)));
	t_7 = sqrt(t_6) / floor(maxAniso);
	t_8 = t_6 / t_0;
	t_9 = t_8 > floor(maxAniso);
	tmp = single(0.0);
	if (t_9)
		tmp = t_7;
	else
		tmp = t_0 * sqrt((single(1.0) / t_6));
	end
	tmp_4 = single(0.0);
	if (tmp < single(1.0))
		tmp_5 = single(0.0);
		if (t_9)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = max((t_1 ^ single(2.0)), t_5) / (floor(w) * (floor(h) * (dX_46_u * dY_46_v)));
		end
		tmp_6 = single(0.0);
		if (t_9)
			tmp_6 = t_7;
		else
			tmp_6 = t_0 * (((single(1.0) / max(t_2, t_5)) ^ single(1.5)) ^ single(0.3333333333333333));
		end
		tmp_4 = max(single(1.0), (tmp_5 * tmp_6));
	elseif (t_9)
		tmp_4 = floor(maxAniso);
	else
		tmp_4 = t_8;
	end
	tmp_7 = tmp_4;
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ } \end{array}} \]
4. Add Preprocessing

5. Taylor expanded in w around 0 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.5%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ } \end{array}} \]

8. Taylor expanded in dX.u around inf 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
9. Step-by-step derivation

   1. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \right)}^{2} \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   2. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   3. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   4. swap-sqr 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   5. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \cdot dX.u\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   6. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

10. Simplified 57.9%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

11. Taylor expanded in dX.u around inf 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{dX.u \cdot \left(dY.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
12. Step-by-step derivation

13. Simplified 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
14. Step-by-step derivation

    1. add-cbrt-cube 59.6%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

    2. pow1/3 59.6%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;{\left(\left(\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\right)}^{0.3333333333333333} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

15. Applied egg-rr 59.5%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}\right)}^{1.5}\right)}^{0.3333333333333333} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

16. Final simplification 59.5%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot {\left({\left(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}\right)}^{1.5}\right)}^{0.3333333333333333}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)}\\ \end{array} \]
17. Add Preprocessing

Alternative 9: 60.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\\ t_1 := dX.u \cdot \left\lfloor w\right\rfloor \\ t_2 := {\left(\mathsf{hypot}\left(t\_1, dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}\\ t_3 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_4 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_5 := {\left(\mathsf{hypot}\left(t\_4, t\_3\right)\right)}^{2}\\ t_6 := \mathsf{max}\left(t\_2, {\left(\mathsf{hypot}\left(t\_3, t\_4\right)\right)}^{2}\right)\\ t_7 := \frac{\sqrt{t\_6}}{\left\lfloor maxAniso\right\rfloor }\\ t_8 := \frac{t\_6}{t\_0}\\ t_9 := t\_8 > \left\lfloor maxAniso\right\rfloor \\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \sqrt{\frac{1}{t\_6}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({t\_1}^{2}, t\_5\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \sqrt[3]{{\left(\frac{1}{\mathsf{max}\left(t\_2, t\_5\right)}\right)}^{1.5}}\\ \end{array}\right)\\ \mathbf{elif}\;t\_9:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_8\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (- (* dX.u dY.v) (* dX.v dY.u)) (* (floor h) (floor w))))
        (t_1 (* dX.u (floor w)))
        (t_2 (pow (hypot t_1 (* dX.v (floor h))) 2.0))
        (t_3 (* (floor h) dY.v))
        (t_4 (* (floor w) dY.u))
        (t_5 (pow (hypot t_4 t_3) 2.0))
        (t_6 (fmax t_2 (pow (hypot t_3 t_4) 2.0)))
        (t_7 (/ (sqrt t_6) (floor maxAniso)))
        (t_8 (/ t_6 t_0))
        (t_9 (> t_8 (floor maxAniso))))
   (if (< (if t_9 t_7 (* t_0 (sqrt (/ 1.0 t_6)))) 1.0)
     (fmax
      1.0
      (*
       (if t_9
         (floor maxAniso)
         (/
          (fmax (pow t_1 2.0) t_5)
          (* (floor w) (* (floor h) (* dX.u dY.v)))))
       (if t_9 t_7 (* t_0 (cbrt (pow (/ 1.0 (fmax t_2 t_5)) 1.5))))))
     (if t_9 (floor maxAniso) t_8))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floorf(h) * floorf(w));
	float t_1 = dX_46_u * floorf(w);
	float t_2 = powf(hypotf(t_1, (dX_46_v * floorf(h))), 2.0f);
	float t_3 = floorf(h) * dY_46_v;
	float t_4 = floorf(w) * dY_46_u;
	float t_5 = powf(hypotf(t_4, t_3), 2.0f);
	float t_6 = fmaxf(t_2, powf(hypotf(t_3, t_4), 2.0f));
	float t_7 = sqrtf(t_6) / floorf(maxAniso);
	float t_8 = t_6 / t_0;
	int t_9 = t_8 > floorf(maxAniso);
	float tmp;
	if (t_9) {
		tmp = t_7;
	} else {
		tmp = t_0 * sqrtf((1.0f / t_6));
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_9) {
			tmp_4 = floorf(maxAniso);
		} else {
			tmp_4 = fmaxf(powf(t_1, 2.0f), t_5) / (floorf(w) * (floorf(h) * (dX_46_u * dY_46_v)));
		}
		float tmp_5;
		if (t_9) {
			tmp_5 = t_7;
		} else {
			tmp_5 = t_0 * cbrtf(powf((1.0f / fmaxf(t_2, t_5)), 1.5f));
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_9) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_8;
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * Float32(floor(h) * floor(w)))
	t_1 = Float32(dX_46_u * floor(w))
	t_2 = hypot(t_1, Float32(dX_46_v * floor(h))) ^ Float32(2.0)
	t_3 = Float32(floor(h) * dY_46_v)
	t_4 = Float32(floor(w) * dY_46_u)
	t_5 = hypot(t_4, t_3) ^ Float32(2.0)
	t_6 = (t_2 != t_2) ? (hypot(t_3, t_4) ^ Float32(2.0)) : (((hypot(t_3, t_4) ^ Float32(2.0)) != (hypot(t_3, t_4) ^ Float32(2.0))) ? t_2 : max(t_2, (hypot(t_3, t_4) ^ Float32(2.0))))
	t_7 = Float32(sqrt(t_6) / floor(maxAniso))
	t_8 = Float32(t_6 / t_0)
	t_9 = t_8 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_9)
		tmp = t_7;
	else
		tmp = Float32(t_0 * sqrt(Float32(Float32(1.0) / t_6)));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_9)
			tmp_4 = floor(maxAniso);
		else
			tmp_4 = Float32((((t_1 ^ Float32(2.0)) != (t_1 ^ Float32(2.0))) ? t_5 : ((t_5 != t_5) ? (t_1 ^ Float32(2.0)) : max((t_1 ^ Float32(2.0)), t_5))) / Float32(floor(w) * Float32(floor(h) * Float32(dX_46_u * dY_46_v))));
		end
		tmp_5 = Float32(0.0)
		if (t_9)
			tmp_5 = t_7;
		else
			tmp_5 = Float32(t_0 * cbrt((Float32(Float32(1.0) / ((t_2 != t_2) ? t_5 : ((t_5 != t_5) ? t_2 : max(t_2, t_5)))) ^ Float32(1.5))));
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_9)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_8;
	end
	return tmp_3
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ } \end{array}} \]
4. Add Preprocessing

5. Taylor expanded in w around 0 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.5%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ } \end{array}} \]

8. Taylor expanded in dX.u around inf 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
9. Step-by-step derivation

   1. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \right)}^{2} \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   2. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   3. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   4. swap-sqr 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   5. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \cdot dX.u\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   6. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

10. Simplified 57.9%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

11. Taylor expanded in dX.u around inf 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{dX.u \cdot \left(dY.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
12. Step-by-step derivation

13. Simplified 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
14. Step-by-step derivation

    1. add-cbrt-cube 59.6%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

    2. add-sqr-sqrt 59.6%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)} \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

    3. pow1 59.6%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}\right)}^{1} \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

15. Applied egg-rr 59.5%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}\right)}^{1.5}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

16. Final simplification 59.5%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt[3]{{\left(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}\right)}^{1.5}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)}\\ \end{array} \]
17. Add Preprocessing

Alternative 10: 59.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \\ t_1 := dX.v \cdot \left\lfloor h\right\rfloor \\ t_2 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_3 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_4 := {\left(\mathsf{hypot}\left(t\_3, t\_2\right)\right)}^{2}\\ t_5 := dX.u \cdot \left\lfloor w\right\rfloor \\ t_6 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t\_5, t\_1\right)\right)}^{2}, {\left(\mathsf{hypot}\left(t\_2, t\_3\right)\right)}^{2}\right)\\ t_7 := dX.u \cdot dY.v - dX.v \cdot dY.u\\ t_8 := t\_7 \cdot t\_0\\ t_9 := \frac{t\_6}{t\_8}\\ t_10 := t\_9 > \left\lfloor maxAniso\right\rfloor \\ t_11 := \begin{array}{l} \mathbf{if}\;t\_10:\\ \;\;\;\;\frac{\sqrt{t\_6}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;t\_8 \cdot \sqrt{\frac{1}{t\_6}}\\ \end{array}\\ \mathbf{if}\;t\_11 < 1:\\ \;\;\;\;\mathsf{max}\left(1, t\_11 \cdot \begin{array}{l} \mathbf{if}\;t\_10:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({t\_5}^{2}, t\_4\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{1}{t\_0 \cdot \frac{t\_7}{\mathsf{max}\left({\left(\mathsf{hypot}\left(t\_1, t\_5\right)\right)}^{2}, t\_4\right)}} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_9\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor h) (floor w)))
        (t_1 (* dX.v (floor h)))
        (t_2 (* (floor h) dY.v))
        (t_3 (* (floor w) dY.u))
        (t_4 (pow (hypot t_3 t_2) 2.0))
        (t_5 (* dX.u (floor w)))
        (t_6 (fmax (pow (hypot t_5 t_1) 2.0) (pow (hypot t_2 t_3) 2.0)))
        (t_7 (- (* dX.u dY.v) (* dX.v dY.u)))
        (t_8 (* t_7 t_0))
        (t_9 (/ t_6 t_8))
        (t_10 (> t_9 (floor maxAniso)))
        (t_11
         (if t_10 (/ (sqrt t_6) (floor maxAniso)) (* t_8 (sqrt (/ 1.0 t_6))))))
   (if (< t_11 1.0)
     (fmax
      1.0
      (*
       t_11
       (if t_10
         (floor maxAniso)
         (/
          (fmax (pow t_5 2.0) t_4)
          (* (floor w) (* (floor h) (* dX.u dY.v)))))))
     (if (>
          (/ 1.0 (* t_0 (/ t_7 (fmax (pow (hypot t_1 t_5) 2.0) t_4))))
          (floor maxAniso))
       (floor maxAniso)
       t_9))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(h) * floorf(w);
	float t_1 = dX_46_v * floorf(h);
	float t_2 = floorf(h) * dY_46_v;
	float t_3 = floorf(w) * dY_46_u;
	float t_4 = powf(hypotf(t_3, t_2), 2.0f);
	float t_5 = dX_46_u * floorf(w);
	float t_6 = fmaxf(powf(hypotf(t_5, t_1), 2.0f), powf(hypotf(t_2, t_3), 2.0f));
	float t_7 = (dX_46_u * dY_46_v) - (dX_46_v * dY_46_u);
	float t_8 = t_7 * t_0;
	float t_9 = t_6 / t_8;
	int t_10 = t_9 > floorf(maxAniso);
	float tmp;
	if (t_10) {
		tmp = sqrtf(t_6) / floorf(maxAniso);
	} else {
		tmp = t_8 * sqrtf((1.0f / t_6));
	}
	float t_11 = tmp;
	float tmp_2;
	if (t_11 < 1.0f) {
		float tmp_3;
		if (t_10) {
			tmp_3 = floorf(maxAniso);
		} else {
			tmp_3 = fmaxf(powf(t_5, 2.0f), t_4) / (floorf(w) * (floorf(h) * (dX_46_u * dY_46_v)));
		}
		tmp_2 = fmaxf(1.0f, (t_11 * tmp_3));
	} else if ((1.0f / (t_0 * (t_7 / fmaxf(powf(hypotf(t_1, t_5), 2.0f), t_4)))) > floorf(maxAniso)) {
		tmp_2 = floorf(maxAniso);
	} else {
		tmp_2 = t_9;
	}
	return tmp_2;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(h) * floor(w))
	t_1 = Float32(dX_46_v * floor(h))
	t_2 = Float32(floor(h) * dY_46_v)
	t_3 = Float32(floor(w) * dY_46_u)
	t_4 = hypot(t_3, t_2) ^ Float32(2.0)
	t_5 = Float32(dX_46_u * floor(w))
	t_6 = ((hypot(t_5, t_1) ^ Float32(2.0)) != (hypot(t_5, t_1) ^ Float32(2.0))) ? (hypot(t_2, t_3) ^ Float32(2.0)) : (((hypot(t_2, t_3) ^ Float32(2.0)) != (hypot(t_2, t_3) ^ Float32(2.0))) ? (hypot(t_5, t_1) ^ Float32(2.0)) : max((hypot(t_5, t_1) ^ Float32(2.0)), (hypot(t_2, t_3) ^ Float32(2.0))))
	t_7 = Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))
	t_8 = Float32(t_7 * t_0)
	t_9 = Float32(t_6 / t_8)
	t_10 = t_9 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_10)
		tmp = Float32(sqrt(t_6) / floor(maxAniso));
	else
		tmp = Float32(t_8 * sqrt(Float32(Float32(1.0) / t_6)));
	end
	t_11 = tmp
	tmp_2 = Float32(0.0)
	if (t_11 < Float32(1.0))
		tmp_3 = Float32(0.0)
		if (t_10)
			tmp_3 = floor(maxAniso);
		else
			tmp_3 = Float32((((t_5 ^ Float32(2.0)) != (t_5 ^ Float32(2.0))) ? t_4 : ((t_4 != t_4) ? (t_5 ^ Float32(2.0)) : max((t_5 ^ Float32(2.0)), t_4))) / Float32(floor(w) * Float32(floor(h) * Float32(dX_46_u * dY_46_v))));
		end
		tmp_2 = (Float32(1.0) != Float32(1.0)) ? Float32(t_11 * tmp_3) : ((Float32(t_11 * tmp_3) != Float32(t_11 * tmp_3)) ? Float32(1.0) : max(Float32(1.0), Float32(t_11 * tmp_3)));
	elseif (Float32(Float32(1.0) / Float32(t_0 * Float32(t_7 / (((hypot(t_1, t_5) ^ Float32(2.0)) != (hypot(t_1, t_5) ^ Float32(2.0))) ? t_4 : ((t_4 != t_4) ? (hypot(t_1, t_5) ^ Float32(2.0)) : max((hypot(t_1, t_5) ^ Float32(2.0)), t_4)))))) > floor(maxAniso))
		tmp_2 = floor(maxAniso);
	else
		tmp_2 = t_9;
	end
	return tmp_2
end

MATLAB

function tmp_5 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = floor(h) * floor(w);
	t_1 = dX_46_v * floor(h);
	t_2 = floor(h) * dY_46_v;
	t_3 = floor(w) * dY_46_u;
	t_4 = hypot(t_3, t_2) ^ single(2.0);
	t_5 = dX_46_u * floor(w);
	t_6 = max((hypot(t_5, t_1) ^ single(2.0)), (hypot(t_2, t_3) ^ single(2.0)));
	t_7 = (dX_46_u * dY_46_v) - (dX_46_v * dY_46_u);
	t_8 = t_7 * t_0;
	t_9 = t_6 / t_8;
	t_10 = t_9 > floor(maxAniso);
	tmp = single(0.0);
	if (t_10)
		tmp = sqrt(t_6) / floor(maxAniso);
	else
		tmp = t_8 * sqrt((single(1.0) / t_6));
	end
	t_11 = tmp;
	tmp_3 = single(0.0);
	if (t_11 < single(1.0))
		tmp_4 = single(0.0);
		if (t_10)
			tmp_4 = floor(maxAniso);
		else
			tmp_4 = max((t_5 ^ single(2.0)), t_4) / (floor(w) * (floor(h) * (dX_46_u * dY_46_v)));
		end
		tmp_3 = max(single(1.0), (t_11 * tmp_4));
	elseif ((single(1.0) / (t_0 * (t_7 / max((hypot(t_1, t_5) ^ single(2.0)), t_4)))) > floor(maxAniso))
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_9;
	end
	tmp_5 = tmp_3;
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ } \end{array}} \]
4. Add Preprocessing

5. Taylor expanded in w around 0 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.5%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ } \end{array}} \]

8. Taylor expanded in dX.u around inf 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
9. Step-by-step derivation

   1. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \right)}^{2} \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   2. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   3. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   4. swap-sqr 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   5. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \cdot dX.u\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   6. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

10. Simplified 57.9%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

11. Taylor expanded in dX.u around inf 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{dX.u \cdot \left(dY.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
12. Step-by-step derivation

13. Simplified 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
14. Step-by-step derivation

    1. clear-num 58.0%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\color{blue}{\frac{1}{\frac{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

    2. inv-pow 58.0%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\color{blue}{{\left(\frac{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}\right)}^{-1}} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

15. Applied egg-rr 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\color{blue}{{\left(\frac{\left(\left\lfloor w\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}\right)}^{-1}} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
16. Step-by-step derivation

    1. unpow-1 58.0%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\color{blue}{\frac{1}{\frac{\left(\left\lfloor w\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

    2. associate-/l* 59.0%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{1}{\color{blue}{\left(\left\lfloor w\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \frac{dX.u \cdot dY.v - dX.v \cdot dY.u}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

17. Simplified 59.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\color{blue}{\frac{1}{\left(\left\lfloor w\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \frac{dX.u \cdot dY.v - dX.v \cdot dY.u}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

18. Final simplification 59.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{1}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \frac{dX.u \cdot dY.v - dX.v \cdot dY.u}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)}\\ \end{array} \]
19. Add Preprocessing

Alternative 11: 59.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := dX.v \cdot \left\lfloor h\right\rfloor \\ t_1 := \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\\ t_2 := dX.u \cdot \left\lfloor w\right\rfloor \\ t_3 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_4 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_5 := {\left(\mathsf{hypot}\left(t\_4, t\_3\right)\right)}^{2}\\ t_6 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t\_2, t\_0\right)\right)}^{2}, {\left(\mathsf{hypot}\left(t\_3, t\_4\right)\right)}^{2}\right)\\ t_7 := \frac{\sqrt{t\_6}}{\left\lfloor maxAniso\right\rfloor }\\ t_8 := t\_1 \cdot \sqrt{\frac{1}{t\_6}}\\ t_9 := \frac{t\_6}{t\_1}\\ t_10 := t\_9 > \left\lfloor maxAniso\right\rfloor \\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t\_10:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_8\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t\_10:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({t\_2}^{2}, t\_5\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(t\_0, t\_2\right)\right)}^{2}, t\_5\right)}{\left\lfloor h\right\rfloor \cdot \left(-dX.v \cdot t\_4\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_8\\ \end{array}\right)\\ \mathbf{elif}\;t\_10:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_9\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* dX.v (floor h)))
        (t_1 (* (- (* dX.u dY.v) (* dX.v dY.u)) (* (floor h) (floor w))))
        (t_2 (* dX.u (floor w)))
        (t_3 (* (floor h) dY.v))
        (t_4 (* (floor w) dY.u))
        (t_5 (pow (hypot t_4 t_3) 2.0))
        (t_6 (fmax (pow (hypot t_2 t_0) 2.0) (pow (hypot t_3 t_4) 2.0)))
        (t_7 (/ (sqrt t_6) (floor maxAniso)))
        (t_8 (* t_1 (sqrt (/ 1.0 t_6))))
        (t_9 (/ t_6 t_1))
        (t_10 (> t_9 (floor maxAniso))))
   (if (< (if t_10 t_7 t_8) 1.0)
     (fmax
      1.0
      (*
       (if t_10
         (floor maxAniso)
         (/
          (fmax (pow t_2 2.0) t_5)
          (* (floor w) (* (floor h) (* dX.u dY.v)))))
       (if (>
            (/
             (fmax (pow (hypot t_0 t_2) 2.0) t_5)
             (* (floor h) (- (* dX.v t_4))))
            (floor maxAniso))
         t_7
         t_8)))
     (if t_10 (floor maxAniso) t_9))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = dX_46_v * floorf(h);
	float t_1 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floorf(h) * floorf(w));
	float t_2 = dX_46_u * floorf(w);
	float t_3 = floorf(h) * dY_46_v;
	float t_4 = floorf(w) * dY_46_u;
	float t_5 = powf(hypotf(t_4, t_3), 2.0f);
	float t_6 = fmaxf(powf(hypotf(t_2, t_0), 2.0f), powf(hypotf(t_3, t_4), 2.0f));
	float t_7 = sqrtf(t_6) / floorf(maxAniso);
	float t_8 = t_1 * sqrtf((1.0f / t_6));
	float t_9 = t_6 / t_1;
	int t_10 = t_9 > floorf(maxAniso);
	float tmp;
	if (t_10) {
		tmp = t_7;
	} else {
		tmp = t_8;
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_10) {
			tmp_4 = floorf(maxAniso);
		} else {
			tmp_4 = fmaxf(powf(t_2, 2.0f), t_5) / (floorf(w) * (floorf(h) * (dX_46_u * dY_46_v)));
		}
		float tmp_5;
		if ((fmaxf(powf(hypotf(t_0, t_2), 2.0f), t_5) / (floorf(h) * -(dX_46_v * t_4))) > floorf(maxAniso)) {
			tmp_5 = t_7;
		} else {
			tmp_5 = t_8;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_10) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_9;
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(dX_46_v * floor(h))
	t_1 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * Float32(floor(h) * floor(w)))
	t_2 = Float32(dX_46_u * floor(w))
	t_3 = Float32(floor(h) * dY_46_v)
	t_4 = Float32(floor(w) * dY_46_u)
	t_5 = hypot(t_4, t_3) ^ Float32(2.0)
	t_6 = ((hypot(t_2, t_0) ^ Float32(2.0)) != (hypot(t_2, t_0) ^ Float32(2.0))) ? (hypot(t_3, t_4) ^ Float32(2.0)) : (((hypot(t_3, t_4) ^ Float32(2.0)) != (hypot(t_3, t_4) ^ Float32(2.0))) ? (hypot(t_2, t_0) ^ Float32(2.0)) : max((hypot(t_2, t_0) ^ Float32(2.0)), (hypot(t_3, t_4) ^ Float32(2.0))))
	t_7 = Float32(sqrt(t_6) / floor(maxAniso))
	t_8 = Float32(t_1 * sqrt(Float32(Float32(1.0) / t_6)))
	t_9 = Float32(t_6 / t_1)
	t_10 = t_9 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_10)
		tmp = t_7;
	else
		tmp = t_8;
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_10)
			tmp_4 = floor(maxAniso);
		else
			tmp_4 = Float32((((t_2 ^ Float32(2.0)) != (t_2 ^ Float32(2.0))) ? t_5 : ((t_5 != t_5) ? (t_2 ^ Float32(2.0)) : max((t_2 ^ Float32(2.0)), t_5))) / Float32(floor(w) * Float32(floor(h) * Float32(dX_46_u * dY_46_v))));
		end
		tmp_5 = Float32(0.0)
		if (Float32((((hypot(t_0, t_2) ^ Float32(2.0)) != (hypot(t_0, t_2) ^ Float32(2.0))) ? t_5 : ((t_5 != t_5) ? (hypot(t_0, t_2) ^ Float32(2.0)) : max((hypot(t_0, t_2) ^ Float32(2.0)), t_5))) / Float32(floor(h) * Float32(-Float32(dX_46_v * t_4)))) > floor(maxAniso))
			tmp_5 = t_7;
		else
			tmp_5 = t_8;
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_10)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_9;
	end
	return tmp_3
end

MATLAB

function tmp_7 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = dX_46_v * floor(h);
	t_1 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floor(h) * floor(w));
	t_2 = dX_46_u * floor(w);
	t_3 = floor(h) * dY_46_v;
	t_4 = floor(w) * dY_46_u;
	t_5 = hypot(t_4, t_3) ^ single(2.0);
	t_6 = max((hypot(t_2, t_0) ^ single(2.0)), (hypot(t_3, t_4) ^ single(2.0)));
	t_7 = sqrt(t_6) / floor(maxAniso);
	t_8 = t_1 * sqrt((single(1.0) / t_6));
	t_9 = t_6 / t_1;
	t_10 = t_9 > floor(maxAniso);
	tmp = single(0.0);
	if (t_10)
		tmp = t_7;
	else
		tmp = t_8;
	end
	tmp_4 = single(0.0);
	if (tmp < single(1.0))
		tmp_5 = single(0.0);
		if (t_10)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = max((t_2 ^ single(2.0)), t_5) / (floor(w) * (floor(h) * (dX_46_u * dY_46_v)));
		end
		tmp_6 = single(0.0);
		if ((max((hypot(t_0, t_2) ^ single(2.0)), t_5) / (floor(h) * -(dX_46_v * t_4))) > floor(maxAniso))
			tmp_6 = t_7;
		else
			tmp_6 = t_8;
		end
		tmp_4 = max(single(1.0), (tmp_5 * tmp_6));
	elseif (t_10)
		tmp_4 = floor(maxAniso);
	else
		tmp_4 = t_9;
	end
	tmp_7 = tmp_4;
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ } \end{array}} \]
4. Add Preprocessing

5. Taylor expanded in w around 0 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.5%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ } \end{array}} \]

8. Taylor expanded in dX.u around inf 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
9. Step-by-step derivation

   1. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \right)}^{2} \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   2. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   3. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   4. swap-sqr 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   5. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \cdot dX.u\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   6. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

10. Simplified 57.9%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

11. Taylor expanded in dX.u around inf 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{dX.u \cdot \left(dY.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
12. Step-by-step derivation

13. Simplified 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

14. Taylor expanded in dX.u around 0 58.6%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\color{blue}{-1 \cdot \frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{dX.v \cdot \left(dY.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)}} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

16. Simplified 58.6%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\color{blue}{\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(dX.v \cdot \left(-\left\lfloor w\right\rfloor \cdot dY.u\right)\right)}} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

17. Final simplification 58.6%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(-dX.v \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)}\\ \end{array} \]
18. Add Preprocessing

Alternative 12: 59.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)\\ t_1 := \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\\ t_2 := dX.u \cdot \left\lfloor w\right\rfloor \\ t_3 := dX.v \cdot \left\lfloor h\right\rfloor \\ t_4 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_5 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_6 := {\left(\mathsf{hypot}\left(t\_5, t\_4\right)\right)}^{2}\\ t_7 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t\_2, t\_3\right)\right)}^{2}, {\left(\mathsf{hypot}\left(t\_4, t\_5\right)\right)}^{2}\right)\\ t_8 := \frac{t\_7}{t\_1}\\ t_9 := t\_8 > \left\lfloor maxAniso\right\rfloor \\ t_10 := \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;\frac{\sqrt{t\_7}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \sqrt{\frac{1}{t\_7}}\\ \end{array}\\ \mathbf{if}\;t\_10 < 1:\\ \;\;\;\;\mathsf{max}\left(1, t\_10 \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(t\_3, t\_2\right)\right)}^{2}, t\_6\right)}{t\_0} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({t\_2}^{2}, t\_6\right)}{t\_0}\\ \end{array}\right)\\ \mathbf{elif}\;t\_9:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_8\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor w) (* (floor h) (* dX.u dY.v))))
        (t_1 (* (- (* dX.u dY.v) (* dX.v dY.u)) (* (floor h) (floor w))))
        (t_2 (* dX.u (floor w)))
        (t_3 (* dX.v (floor h)))
        (t_4 (* (floor h) dY.v))
        (t_5 (* (floor w) dY.u))
        (t_6 (pow (hypot t_5 t_4) 2.0))
        (t_7 (fmax (pow (hypot t_2 t_3) 2.0) (pow (hypot t_4 t_5) 2.0)))
        (t_8 (/ t_7 t_1))
        (t_9 (> t_8 (floor maxAniso)))
        (t_10
         (if t_9 (/ (sqrt t_7) (floor maxAniso)) (* t_1 (sqrt (/ 1.0 t_7))))))
   (if (< t_10 1.0)
     (fmax
      1.0
      (*
       t_10
       (if (> (/ (fmax (pow (hypot t_3 t_2) 2.0) t_6) t_0) (floor maxAniso))
         (floor maxAniso)
         (/ (fmax (pow t_2 2.0) t_6) t_0))))
     (if t_9 (floor maxAniso) t_8))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(w) * (floorf(h) * (dX_46_u * dY_46_v));
	float t_1 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floorf(h) * floorf(w));
	float t_2 = dX_46_u * floorf(w);
	float t_3 = dX_46_v * floorf(h);
	float t_4 = floorf(h) * dY_46_v;
	float t_5 = floorf(w) * dY_46_u;
	float t_6 = powf(hypotf(t_5, t_4), 2.0f);
	float t_7 = fmaxf(powf(hypotf(t_2, t_3), 2.0f), powf(hypotf(t_4, t_5), 2.0f));
	float t_8 = t_7 / t_1;
	int t_9 = t_8 > floorf(maxAniso);
	float tmp;
	if (t_9) {
		tmp = sqrtf(t_7) / floorf(maxAniso);
	} else {
		tmp = t_1 * sqrtf((1.0f / t_7));
	}
	float t_10 = tmp;
	float tmp_2;
	if (t_10 < 1.0f) {
		float tmp_3;
		if ((fmaxf(powf(hypotf(t_3, t_2), 2.0f), t_6) / t_0) > floorf(maxAniso)) {
			tmp_3 = floorf(maxAniso);
		} else {
			tmp_3 = fmaxf(powf(t_2, 2.0f), t_6) / t_0;
		}
		tmp_2 = fmaxf(1.0f, (t_10 * tmp_3));
	} else if (t_9) {
		tmp_2 = floorf(maxAniso);
	} else {
		tmp_2 = t_8;
	}
	return tmp_2;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(w) * Float32(floor(h) * Float32(dX_46_u * dY_46_v)))
	t_1 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * Float32(floor(h) * floor(w)))
	t_2 = Float32(dX_46_u * floor(w))
	t_3 = Float32(dX_46_v * floor(h))
	t_4 = Float32(floor(h) * dY_46_v)
	t_5 = Float32(floor(w) * dY_46_u)
	t_6 = hypot(t_5, t_4) ^ Float32(2.0)
	t_7 = ((hypot(t_2, t_3) ^ Float32(2.0)) != (hypot(t_2, t_3) ^ Float32(2.0))) ? (hypot(t_4, t_5) ^ Float32(2.0)) : (((hypot(t_4, t_5) ^ Float32(2.0)) != (hypot(t_4, t_5) ^ Float32(2.0))) ? (hypot(t_2, t_3) ^ Float32(2.0)) : max((hypot(t_2, t_3) ^ Float32(2.0)), (hypot(t_4, t_5) ^ Float32(2.0))))
	t_8 = Float32(t_7 / t_1)
	t_9 = t_8 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_9)
		tmp = Float32(sqrt(t_7) / floor(maxAniso));
	else
		tmp = Float32(t_1 * sqrt(Float32(Float32(1.0) / t_7)));
	end
	t_10 = tmp
	tmp_2 = Float32(0.0)
	if (t_10 < Float32(1.0))
		tmp_3 = Float32(0.0)
		if (Float32((((hypot(t_3, t_2) ^ Float32(2.0)) != (hypot(t_3, t_2) ^ Float32(2.0))) ? t_6 : ((t_6 != t_6) ? (hypot(t_3, t_2) ^ Float32(2.0)) : max((hypot(t_3, t_2) ^ Float32(2.0)), t_6))) / t_0) > floor(maxAniso))
			tmp_3 = floor(maxAniso);
		else
			tmp_3 = Float32((((t_2 ^ Float32(2.0)) != (t_2 ^ Float32(2.0))) ? t_6 : ((t_6 != t_6) ? (t_2 ^ Float32(2.0)) : max((t_2 ^ Float32(2.0)), t_6))) / t_0);
		end
		tmp_2 = (Float32(1.0) != Float32(1.0)) ? Float32(t_10 * tmp_3) : ((Float32(t_10 * tmp_3) != Float32(t_10 * tmp_3)) ? Float32(1.0) : max(Float32(1.0), Float32(t_10 * tmp_3)));
	elseif (t_9)
		tmp_2 = floor(maxAniso);
	else
		tmp_2 = t_8;
	end
	return tmp_2
end

MATLAB

function tmp_5 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = floor(w) * (floor(h) * (dX_46_u * dY_46_v));
	t_1 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floor(h) * floor(w));
	t_2 = dX_46_u * floor(w);
	t_3 = dX_46_v * floor(h);
	t_4 = floor(h) * dY_46_v;
	t_5 = floor(w) * dY_46_u;
	t_6 = hypot(t_5, t_4) ^ single(2.0);
	t_7 = max((hypot(t_2, t_3) ^ single(2.0)), (hypot(t_4, t_5) ^ single(2.0)));
	t_8 = t_7 / t_1;
	t_9 = t_8 > floor(maxAniso);
	tmp = single(0.0);
	if (t_9)
		tmp = sqrt(t_7) / floor(maxAniso);
	else
		tmp = t_1 * sqrt((single(1.0) / t_7));
	end
	t_10 = tmp;
	tmp_3 = single(0.0);
	if (t_10 < single(1.0))
		tmp_4 = single(0.0);
		if ((max((hypot(t_3, t_2) ^ single(2.0)), t_6) / t_0) > floor(maxAniso))
			tmp_4 = floor(maxAniso);
		else
			tmp_4 = max((t_2 ^ single(2.0)), t_6) / t_0;
		end
		tmp_3 = max(single(1.0), (t_10 * tmp_4));
	elseif (t_9)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_8;
	end
	tmp_5 = tmp_3;
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right) + \left(\left\lfloor h\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dY.v\right) - \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dX.v \cdot dX.v\right) \cdot \left\lfloor h\right\rfloor \right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(dY.v \cdot dY.v\right) \cdot \left\lfloor h\right\rfloor \right)\right)\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(\left\lfloor w\right\rfloor \cdot dY.v\right) - \left(dY.u \cdot dX.v\right) \cdot \left\lfloor w\right\rfloor \right)\right|}\\ } \end{array}} \]
4. Add Preprocessing

5. Taylor expanded in w around 0 97.2%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{1}{\left\lfloor maxAniso\right\rfloor } \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{\left|\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot \left(dY.v \cdot \left\lfloor w\right\rfloor \right) - dX.v \cdot \left(dY.u \cdot \left\lfloor w\right\rfloor \right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.5%

   \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ } \end{array}} \]

8. Taylor expanded in dX.u around inf 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
9. Step-by-step derivation

   1. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \right)}^{2} \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   2. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot {dX.u}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   3. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   4. swap-sqr 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   5. unpow2 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloor w\right\rfloor \cdot dX.u\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

   6. *-commutative 57.9%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

10. Simplified 57.9%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

11. Taylor expanded in dX.u around inf 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{dX.u \cdot \left(dY.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]
12. Step-by-step derivation

13. Simplified 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

14. Taylor expanded in dX.u around inf 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\color{blue}{\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloor w\right\rfloor \right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}\right)}{dX.u \cdot \left(dY.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)}} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

16. Simplified 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\color{blue}{\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

17. Final simplification 58.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.u \cdot \left\lfloor w\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)}\\ \end{array} \]
18. Add Preprocessing

Reproduce

herbie shell --seed 2024165 
(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
  :name "Anisotropic x16 LOD (ratio of anisotropy)"
  :precision binary32
  :pre (and (and (and (and (and (and (and (<= 1.0 w) (<= w 16384.0)) (and (<= 1.0 h) (<= h 16384.0))) (and (<= 1e-20 (fabs dX.u)) (<= (fabs dX.u) 1e+20))) (and (<= 1e-20 (fabs dX.v)) (<= (fabs dX.v) 1e+20))) (and (<= 1e-20 (fabs dY.u)) (<= (fabs dY.u) 1e+20))) (and (<= 1e-20 (fabs dY.v)) (<= (fabs dY.v) 1e+20))) (== maxAniso 16.0))
  (if (< (if (> (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (/ (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))) (floor maxAniso)) (/ (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))) (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))))) 1.0) (fmax 1.0 (* (if (> (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (floor maxAniso) (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))))) (if (> (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (/ (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))) (floor maxAniso)) (/ (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u)))) (sqrt (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v))))))))) (if (> (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))) (floor maxAniso)) (floor maxAniso) (/ (fmax (+ (* (* (floor w) dX.u) (* (floor w) dX.u)) (* (* (floor h) dX.v) (* (floor h) dX.v))) (+ (* (* (floor w) dY.u) (* (floor w) dY.u)) (* (* (floor h) dY.v) (* (floor h) dY.v)))) (fabs (- (* (* (floor w) dX.u) (* (floor h) dY.v)) (* (* (floor h) dX.v) (* (floor w) dY.u))))))))