Anisotropic x16 LOD (ratio of anisotropy)

Percentage Accurate: 97.6% → 97.5%

Time: 1.6min

Alternatives: 10

Speedup: N/A×

• Could not converge on a ground truth

  1. w = 8.38399887084961
  2. h = 7.389083385467529
  3. dX.u = -4.100216164694128e-19
  4. dX.v = 8.048945082488046e-13
  5. dY.u = -1.1228939757715908e-16
  6. dY.v = 2.2462110296772586e-11
  7. maxAniso = 16.0

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: 97.6% 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: 97.5% accurate, 1.2× speedup

Math

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

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

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_u * dY_46_v) - (dX_46_v * dY_46_u);
	float t_2 = fmaxf(powf(hypotf((dX_46_v * floorf(h)), (dX_46_u * floorf(w))), 2.0f), powf(hypotf((floorf(w) * dY_46_u), (floorf(h) * dY_46_v)), 2.0f));
	float t_3 = sqrtf(t_2);
	float t_4 = fabsf((t_0 * t_1));
	float t_5 = t_2 / t_4;
	int t_6 = t_5 > floorf(maxAniso);
	float tmp;
	if (t_6) {
		tmp = t_3 / floorf(maxAniso);
	} else {
		tmp = t_4 * (1.0f / t_3);
	}
	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 = t_5;
		}
		tmp_2 = fmaxf(1.0f, (t_7 * tmp_3));
	} else if ((t_2 / fabsf((dY_46_v * (dX_46_u * t_0)))) > floorf(maxAniso)) {
		tmp_2 = floorf(maxAniso);
	} else {
		tmp_2 = powf(sqrtf((t_2 / fabsf((floorf(h) * (floorf(w) * t_1))))), 2.0f);
	}
	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(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))
	t_2 = ((hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0)) != (hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0))) ? (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0)) : (((hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0)) != (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0))) ? (hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0)) : max((hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0)), (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0))))
	t_3 = sqrt(t_2)
	t_4 = abs(Float32(t_0 * t_1))
	t_5 = Float32(t_2 / t_4)
	t_6 = t_5 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_6)
		tmp = Float32(t_3 / floor(maxAniso));
	else
		tmp = Float32(t_4 * Float32(Float32(1.0) / t_3));
	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 = t_5;
		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_2 / abs(Float32(dY_46_v * Float32(dX_46_u * t_0)))) > floor(maxAniso))
		tmp_2 = floor(maxAniso);
	else
		tmp_2 = sqrt(Float32(t_2 / abs(Float32(floor(h) * Float32(floor(w) * t_1))))) ^ Float32(2.0);
	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_u * dY_46_v) - (dX_46_v * dY_46_u);
	t_2 = max((hypot((dX_46_v * floor(h)), (dX_46_u * floor(w))) ^ single(2.0)), (hypot((floor(w) * dY_46_u), (floor(h) * dY_46_v)) ^ single(2.0)));
	t_3 = sqrt(t_2);
	t_4 = abs((t_0 * t_1));
	t_5 = t_2 / t_4;
	t_6 = t_5 > floor(maxAniso);
	tmp = single(0.0);
	if (t_6)
		tmp = t_3 / floor(maxAniso);
	else
		tmp = t_4 * (single(1.0) / t_3);
	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 = t_5;
		end
		tmp_3 = max(single(1.0), (t_7 * tmp_4));
	elseif ((t_2 / abs((dY_46_v * (dX_46_u * t_0)))) > floor(maxAniso))
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = sqrt((t_2 / abs((floor(h) * (floor(w) * t_1))))) ^ single(2.0);
	end
	tmp_5 = tmp_3;
end

Derivation

1. Initial program 96.5%

   \[\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 inf 97.4%

   \[\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.u \cdot \left(dY.v \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} \]
4. Step-by-step derivation

   1. associate-*r* 97.4%

      \[\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.u \cdot dY.v\right) \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(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.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 97.4%

   \[\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.u \cdot dY.v\right) \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(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.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 97.4%

   \[\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|dX.u \cdot \left(dY.v \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}} \]

8. Simplified 97.4%

   \[\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}:\\ \;\;\;\;\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)}} \cdot \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} < 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}:\\ \;\;\;\;\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)}} \cdot \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} \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|dY.v \cdot \left(dX.u \cdot \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(\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. Step-by-step derivation

   1. add-sqr-sqrt 97.5%

      \[\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(\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}:\\ \;\;\;\;\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)}} \cdot \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} < 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}:\\ \;\;\;\;\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)}} \cdot \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} \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|dY.v \cdot \left(dX.u \cdot \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}:\\ \;\;\;\;\sqrt{\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|}} \cdot \sqrt{\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} \]

   2. pow2 97.5%

      \[\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(\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}:\\ \;\;\;\;\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)}} \cdot \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} < 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}:\\ \;\;\;\;\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)}} \cdot \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} \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|dY.v \cdot \left(dX.u \cdot \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}:\\ \;\;\;\;{\left(\sqrt{\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|}}\right)}^{2}\\ \end{array} \]

10. Applied egg-rr 97.5%

    \[\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(\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}:\\ \;\;\;\;\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)}} \cdot \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} < 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}:\\ \;\;\;\;\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)}} \cdot \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} \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|dY.v \cdot \left(dX.u \cdot \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}:\\ \;\;\;\;{\left(\sqrt{\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 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|}}\right)}^{2}\\ \end{array} \]

11. Final simplification 97.5%

    \[\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(\left\lfloor h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\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|dY.v \cdot \left(dX.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}:\\ \;\;\;\;{\left(\sqrt{\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 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|}}\right)}^{2}\\ \end{array} \]
12. Add Preprocessing

Alternative 2: 97.5% accurate, 1.2× speedup

Math

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

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor h) (floor w)))
        (t_1
         (fmax
          (pow (hypot (* dX.v (floor h)) (* dX.u (floor w))) 2.0)
          (pow (hypot (* (floor w) dY.u) (* (floor h) dY.v)) 2.0)))
        (t_2 (sqrt t_1))
        (t_3 (/ t_2 (floor maxAniso)))
        (t_4 (fabs (* t_0 (- (* dX.u dY.v) (* dX.v dY.u)))))
        (t_5 (/ t_1 t_4))
        (t_6 (> t_5 (floor maxAniso))))
   (if (< (if t_6 t_3 (/ t_4 t_2)) 1.0)
     (fmax
      1.0
      (* (if t_6 t_3 (* t_4 (/ 1.0 t_2))) (if t_6 (floor maxAniso) t_5)))
     (if (> (/ t_1 (fabs (* dY.v (* dX.u t_0)))) (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 = floorf(h) * floorf(w);
	float t_1 = fmaxf(powf(hypotf((dX_46_v * floorf(h)), (dX_46_u * floorf(w))), 2.0f), powf(hypotf((floorf(w) * dY_46_u), (floorf(h) * dY_46_v)), 2.0f));
	float t_2 = sqrtf(t_1);
	float t_3 = t_2 / floorf(maxAniso);
	float t_4 = fabsf((t_0 * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u))));
	float t_5 = t_1 / t_4;
	int t_6 = t_5 > floorf(maxAniso);
	float tmp;
	if (t_6) {
		tmp = t_3;
	} else {
		tmp = t_4 / t_2;
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_6) {
			tmp_4 = t_3;
		} else {
			tmp_4 = t_4 * (1.0f / t_2);
		}
		float tmp_5;
		if (t_6) {
			tmp_5 = floorf(maxAniso);
		} else {
			tmp_5 = t_5;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if ((t_1 / fabsf((dY_46_v * (dX_46_u * t_0)))) > floorf(maxAniso)) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_5;
	}
	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) * floor(w))
	t_1 = ((hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0)) != (hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0))) ? (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0)) : (((hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0)) != (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0))) ? (hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0)) : max((hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0)), (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0))))
	t_2 = sqrt(t_1)
	t_3 = Float32(t_2 / floor(maxAniso))
	t_4 = abs(Float32(t_0 * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))))
	t_5 = Float32(t_1 / t_4)
	t_6 = t_5 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_6)
		tmp = t_3;
	else
		tmp = Float32(t_4 / t_2);
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_6)
			tmp_4 = t_3;
		else
			tmp_4 = Float32(t_4 * Float32(Float32(1.0) / t_2));
		end
		tmp_5 = Float32(0.0)
		if (t_6)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = t_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 (Float32(t_1 / abs(Float32(dY_46_v * Float32(dX_46_u * t_0)))) > floor(maxAniso))
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_5;
	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) * floor(w);
	t_1 = max((hypot((dX_46_v * floor(h)), (dX_46_u * floor(w))) ^ single(2.0)), (hypot((floor(w) * dY_46_u), (floor(h) * dY_46_v)) ^ single(2.0)));
	t_2 = sqrt(t_1);
	t_3 = t_2 / floor(maxAniso);
	t_4 = abs((t_0 * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u))));
	t_5 = t_1 / t_4;
	t_6 = t_5 > floor(maxAniso);
	tmp = single(0.0);
	if (t_6)
		tmp = t_3;
	else
		tmp = t_4 / t_2;
	end
	tmp_4 = single(0.0);
	if (tmp < single(1.0))
		tmp_5 = single(0.0);
		if (t_6)
			tmp_5 = t_3;
		else
			tmp_5 = t_4 * (single(1.0) / t_2);
		end
		tmp_6 = single(0.0);
		if (t_6)
			tmp_6 = floor(maxAniso);
		else
			tmp_6 = t_5;
		end
		tmp_4 = max(single(1.0), (tmp_5 * tmp_6));
	elseif ((t_1 / abs((dY_46_v * (dX_46_u * t_0)))) > floor(maxAniso))
		tmp_4 = floor(maxAniso);
	else
		tmp_4 = t_5;
	end
	tmp_7 = tmp_4;
end

Derivation

1. Initial program 96.5%

   \[\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 inf 97.4%

   \[\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.u \cdot \left(dY.v \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} \]
4. Step-by-step derivation

   1. associate-*r* 97.4%

      \[\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.u \cdot dY.v\right) \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(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.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 97.4%

   \[\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.u \cdot dY.v\right) \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(\left\lfloor w\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dX.u\right) + \left(\left\lfloor h\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot dX.v\right), \left(\left\lfloor w\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot dY.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 97.4%

   \[\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|dX.u \cdot \left(dY.v \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}} \]

8. Simplified 97.4%

   \[\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}:\\ \;\;\;\;\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)}} \cdot \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} < 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}:\\ \;\;\;\;\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)}} \cdot \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} \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|dY.v \cdot \left(dX.u \cdot \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(\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. Step-by-step derivation

   1. associate-*l/ 97.4%

      \[\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(\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}:\\ \;\;\;\;\frac{1 \cdot \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|}{\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}:\\ \;\;\;\;\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)}} \cdot \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} \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|dY.v \cdot \left(dX.u \cdot \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(\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} \]

   2. *-un-lft-identity 97.4%

      \[\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(\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}:\\ \;\;\;\;\frac{\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|}{\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}:\\ \;\;\;\;\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)}} \cdot \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} \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|dY.v \cdot \left(dX.u \cdot \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(\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} \]

   3. *-commutative 97.4%

      \[\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(\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}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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(\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}:\\ \;\;\;\;\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)}} \cdot \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} \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|dY.v \cdot \left(dX.u \cdot \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(\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} \]

   4. associate-*r* 97.4%

      \[\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(\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}:\\ \;\;\;\;\frac{\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|}{\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}:\\ \;\;\;\;\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)}} \cdot \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} \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|dY.v \cdot \left(dX.u \cdot \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(\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} \]

10. Applied egg-rr 97.4%

    \[\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(\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}:\\ \;\;\;\;\frac{\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|}{\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}:\\ \;\;\;\;\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)}} \cdot \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} \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|dY.v \cdot \left(dX.u \cdot \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(\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} \]
11. Step-by-step derivation

    1. associate-*r* 97.4%

       \[\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(\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}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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(\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}:\\ \;\;\;\;\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)}} \cdot \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} \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|dY.v \cdot \left(dX.u \cdot \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(\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} \]

    2. *-commutative 97.4%

       \[\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(\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}:\\ \;\;\;\;\frac{\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|}{\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}:\\ \;\;\;\;\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)}} \cdot \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} \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|dY.v \cdot \left(dX.u \cdot \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(\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} \]

12. Simplified 97.4%

    \[\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(\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}:\\ \;\;\;\;\frac{\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|}{\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}:\\ \;\;\;\;\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)}} \cdot \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} \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|dY.v \cdot \left(dX.u \cdot \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(\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} \]

13. Final simplification 97.4%

    \[\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(\left\lfloor h\right\rfloor \cdot \left\lfloor w\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}:\\ \;\;\;\;\frac{\left|\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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(\left\lfloor h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\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|dY.v \cdot \left(dX.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(\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 h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right|}\\ \end{array} \]
14. Add Preprocessing

Alternative 3: 96.7% accurate, 1.2× speedup

Math

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

FPCore

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

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 = fmaxf(powf(hypotf((dX_46_v * floorf(h)), (dX_46_u * floorf(w))), 2.0f), powf(hypotf((floorf(w) * dY_46_u), (floorf(h) * dY_46_v)), 2.0f));
	float t_1 = sqrtf(t_0);
	float t_2 = t_1 / floorf(maxAniso);
	float t_3 = 1.0f / t_1;
	float t_4 = fabsf(((floorf(h) * floorf(w)) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u))));
	float t_5 = t_0 / t_4;
	int t_6 = t_5 > floorf(maxAniso);
	float tmp;
	if (t_6) {
		tmp = floorf(maxAniso);
	} else {
		tmp = t_5;
	}
	float t_7 = tmp;
	float tmp_1;
	if (t_6) {
		tmp_1 = t_2;
	} else {
		tmp_1 = t_3 * fabsf((dX_46_v * (floorf(w) * (floorf(h) * dY_46_u))));
	}
	float tmp_3;
	if (tmp_1 < 1.0f) {
		float tmp_4;
		if (t_6) {
			tmp_4 = t_2;
		} else {
			tmp_4 = t_4 * t_3;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * t_7));
	} else {
		tmp_3 = t_7;
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = ((hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0)) != (hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0))) ? (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0)) : (((hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0)) != (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0))) ? (hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0)) : max((hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0)), (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0))))
	t_1 = sqrt(t_0)
	t_2 = Float32(t_1 / floor(maxAniso))
	t_3 = Float32(Float32(1.0) / t_1)
	t_4 = abs(Float32(Float32(floor(h) * floor(w)) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))))
	t_5 = Float32(t_0 / t_4)
	t_6 = t_5 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_6)
		tmp = floor(maxAniso);
	else
		tmp = t_5;
	end
	t_7 = tmp
	tmp_1 = Float32(0.0)
	if (t_6)
		tmp_1 = t_2;
	else
		tmp_1 = Float32(t_3 * abs(Float32(dX_46_v * Float32(floor(w) * Float32(floor(h) * dY_46_u)))));
	end
	tmp_3 = Float32(0.0)
	if (tmp_1 < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_6)
			tmp_4 = t_2;
		else
			tmp_4 = Float32(t_4 * t_3);
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * t_7) : ((Float32(tmp_4 * t_7) != Float32(tmp_4 * t_7)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * t_7)));
	else
		tmp_3 = t_7;
	end
	return tmp_3
end

MATLAB

function tmp_6 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = max((hypot((dX_46_v * floor(h)), (dX_46_u * floor(w))) ^ single(2.0)), (hypot((floor(w) * dY_46_u), (floor(h) * dY_46_v)) ^ single(2.0)));
	t_1 = sqrt(t_0);
	t_2 = t_1 / floor(maxAniso);
	t_3 = single(1.0) / t_1;
	t_4 = abs(((floor(h) * floor(w)) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u))));
	t_5 = t_0 / t_4;
	t_6 = t_5 > floor(maxAniso);
	tmp = single(0.0);
	if (t_6)
		tmp = floor(maxAniso);
	else
		tmp = t_5;
	end
	t_7 = tmp;
	tmp_2 = single(0.0);
	if (t_6)
		tmp_2 = t_2;
	else
		tmp_2 = t_3 * abs((dX_46_v * (floor(w) * (floor(h) * dY_46_u))));
	end
	tmp_4 = single(0.0);
	if (tmp_2 < single(1.0))
		tmp_5 = single(0.0);
		if (t_6)
			tmp_5 = t_2;
		else
			tmp_5 = t_4 * t_3;
		end
		tmp_4 = max(single(1.0), (tmp_5 * t_7));
	else
		tmp_4 = t_7;
	end
	tmp_6 = tmp_4;
end

Derivation

1. Initial program 96.5%

   \[\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 95.9%

   \[\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|-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|}{\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} \]
4. Step-by-step derivation

   1. mul-1-neg 95.9%

      \[\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|-dX.v \cdot \left(dY.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\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. associate-*r* 95.9%

      \[\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(dX.v \cdot dY.u\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \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. distribute-rgt-neg-in 95.9%

      \[\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(dX.v \cdot dY.u\right) \cdot \left(-\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \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} \]

   4. *-commutative 95.9%

      \[\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(dX.v \cdot dY.u\right) \cdot \left(-\left\lfloor w\right\rfloor \cdot \left\lfloor h\right\rfloor \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} \]

   5. distribute-rgt-neg-in 95.9%

      \[\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(dX.v \cdot dY.u\right) \cdot \left(\left\lfloor w\right\rfloor \cdot \left(-\left\lfloor h\right\rfloor \right)\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} \]

   6. associate-*l* 95.9%

      \[\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(dX.v \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor \right) \cdot \left(-\left\lfloor h\right\rfloor \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} \]

   7. *-commutative 95.9%

      \[\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 \left(dX.v \cdot dY.u\right)\right) \cdot \left(-\left\lfloor h\right\rfloor \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} \]

   8. distribute-rgt-neg-in 95.9%

      \[\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 \left(dX.v \cdot dY.u\right)\right) \cdot \left\lfloor h\right\rfloor \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} \]

   9. distribute-lft-neg-in 95.9%

      \[\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 \left(dX.v \cdot dY.u\right)\right) \cdot \left\lfloor h\right\rfloor \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} \]

   10. *-commutative 95.9%

       \[\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\lfloor h\right\rfloor \cdot \left(-\left\lfloor w\right\rfloor \cdot \left(dX.v \cdot dY.u\right)\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} \]

   11. distribute-rgt-neg-in 95.9%

       \[\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\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(-dX.v \cdot dY.u\right)\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} \]

   12. distribute-rgt-neg-in 95.9%

       \[\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\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.v \cdot \left(-dY.u\right)\right)\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} \]

5. Simplified 95.9%

   \[\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\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.v \cdot \left(-dY.u\right)\right)\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} \]

6. Taylor expanded in w around 0 95.9%

   \[\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|-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| \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|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}} \]

8. Simplified 95.9%

   \[\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}:\\ \;\;\;\;\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)}} \cdot \left|dX.v \cdot \left(\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot dY.u\right)\right)\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}:\\ \;\;\;\;\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)}} \cdot \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} \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|\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}} \]

9. Final simplification 95.9%

   \[\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(\left\lfloor h\right\rfloor \cdot \left\lfloor w\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}:\\ \;\;\;\;\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)}} \cdot \left|dX.v \cdot \left(\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot dY.u\right)\right)\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 h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\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|\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right|}\\ \end{array} \]
10. Add Preprocessing

Alternative 4: 70.0% accurate, 1.2× speedup

Math

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

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0
         (fmax
          (pow (hypot (* dX.v (floor h)) (* dX.u (floor w))) 2.0)
          (pow (hypot (* (floor w) dY.u) (* (floor h) dY.v)) 2.0)))
        (t_1 (sqrt t_0))
        (t_2 (/ t_1 (floor maxAniso)))
        (t_3 (* (* (floor h) (floor w)) (- (* dX.u dY.v) (* dX.v dY.u))))
        (t_4 (fabs t_3))
        (t_5 (* t_4 (/ 1.0 t_1)))
        (t_6 (/ t_0 t_4))
        (t_7 (> t_6 (floor maxAniso)))
        (t_8 (if t_7 (floor maxAniso) t_6)))
   (if (< (if (> (/ t_0 t_3) (floor maxAniso)) t_2 t_5) 1.0)
     (fmax 1.0 (* (if t_7 t_2 t_5) t_8))
     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 = fmaxf(powf(hypotf((dX_46_v * floorf(h)), (dX_46_u * floorf(w))), 2.0f), powf(hypotf((floorf(w) * dY_46_u), (floorf(h) * dY_46_v)), 2.0f));
	float t_1 = sqrtf(t_0);
	float t_2 = t_1 / floorf(maxAniso);
	float t_3 = (floorf(h) * floorf(w)) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u));
	float t_4 = fabsf(t_3);
	float t_5 = t_4 * (1.0f / t_1);
	float t_6 = t_0 / t_4;
	int t_7 = t_6 > floorf(maxAniso);
	float tmp;
	if (t_7) {
		tmp = floorf(maxAniso);
	} else {
		tmp = t_6;
	}
	float t_8 = tmp;
	float tmp_1;
	if ((t_0 / t_3) > floorf(maxAniso)) {
		tmp_1 = t_2;
	} else {
		tmp_1 = t_5;
	}
	float tmp_3;
	if (tmp_1 < 1.0f) {
		float tmp_4;
		if (t_7) {
			tmp_4 = t_2;
		} else {
			tmp_4 = t_5;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * t_8));
	} 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 = ((hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0)) != (hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0))) ? (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0)) : (((hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0)) != (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0))) ? (hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0)) : max((hypot(Float32(dX_46_v * floor(h)), Float32(dX_46_u * floor(w))) ^ Float32(2.0)), (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0))))
	t_1 = sqrt(t_0)
	t_2 = Float32(t_1 / floor(maxAniso))
	t_3 = Float32(Float32(floor(h) * floor(w)) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)))
	t_4 = abs(t_3)
	t_5 = Float32(t_4 * Float32(Float32(1.0) / t_1))
	t_6 = Float32(t_0 / t_4)
	t_7 = t_6 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_7)
		tmp = floor(maxAniso);
	else
		tmp = t_6;
	end
	t_8 = tmp
	tmp_1 = Float32(0.0)
	if (Float32(t_0 / t_3) > floor(maxAniso))
		tmp_1 = t_2;
	else
		tmp_1 = t_5;
	end
	tmp_3 = Float32(0.0)
	if (tmp_1 < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_7)
			tmp_4 = t_2;
		else
			tmp_4 = t_5;
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * t_8) : ((Float32(tmp_4 * t_8) != Float32(tmp_4 * t_8)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * t_8)));
	else
		tmp_3 = t_8;
	end
	return tmp_3
end

MATLAB

function tmp_6 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = max((hypot((dX_46_v * floor(h)), (dX_46_u * floor(w))) ^ single(2.0)), (hypot((floor(w) * dY_46_u), (floor(h) * dY_46_v)) ^ single(2.0)));
	t_1 = sqrt(t_0);
	t_2 = t_1 / floor(maxAniso);
	t_3 = (floor(h) * floor(w)) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u));
	t_4 = abs(t_3);
	t_5 = t_4 * (single(1.0) / t_1);
	t_6 = t_0 / t_4;
	t_7 = t_6 > floor(maxAniso);
	tmp = single(0.0);
	if (t_7)
		tmp = floor(maxAniso);
	else
		tmp = t_6;
	end
	t_8 = tmp;
	tmp_2 = single(0.0);
	if ((t_0 / t_3) > floor(maxAniso))
		tmp_2 = t_2;
	else
		tmp_2 = t_5;
	end
	tmp_4 = single(0.0);
	if (tmp_2 < single(1.0))
		tmp_5 = single(0.0);
		if (t_7)
			tmp_5 = t_2;
		else
			tmp_5 = t_5;
		end
		tmp_4 = max(single(1.0), (tmp_5 * t_8));
	else
		tmp_4 = t_8;
	end
	tmp_6 = tmp_4;
end

Derivation

1. Initial program 96.5%

   \[\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 w around 0 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\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)}{\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{\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} \]

5. Simplified 71.6%

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

6. Taylor expanded in dX.u around 0 71.6%

   \[\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\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)} > \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|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}} \]

8. Simplified 71.6%

   \[\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\lfloor h\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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{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)}} \cdot \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} < 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}:\\ \;\;\;\;\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)}} \cdot \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} \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|\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}} \]

9. Final simplification 71.6%

   \[\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 h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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 h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\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|\left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\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 h\right\rfloor \cdot \left\lfloor w\right\rfloor \right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right|}\\ \end{array} \]
10. Add Preprocessing

Alternative 5: 60.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ t_1 := dX.u \cdot \left\lfloor w\right\rfloor \\ t_2 := {\left(\mathsf{hypot}\left(t\_1, dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}\\ t_3 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_4 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_5 := {\left(\mathsf{hypot}\left(t\_3, t\_4\right)\right)}^{2}\\ t_6 := \mathsf{max}\left(t\_2, t\_5\right)\\ t_7 := \frac{\sqrt{t\_6}}{\left\lfloor maxAniso\right\rfloor }\\ t_8 := \frac{t\_6}{t\_0}\\ t_9 := t\_8 > \left\lfloor maxAniso\right\rfloor \\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \sqrt{\frac{1}{t\_6}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \left(e^{\mathsf{log1p}\left({\left(\mathsf{max}\left(t\_2, {\left(\mathsf{hypot}\left(t\_4, t\_3\right)\right)}^{2}\right)\right)}^{-0.5}\right)} + -1\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({t\_1}^{2}, t\_5\right)}{t\_0}\\ \end{array}\right)\\ \mathbf{elif}\;t\_9:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_8\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor h) (* (floor w) (- (* dX.u dY.v) (* dX.v dY.u)))))
        (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
          (+
           (exp (log1p (pow (fmax t_2 (pow (hypot t_4 t_3) 2.0)) -0.5)))
           -1.0)))
       (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 = floorf(h) * (floorf(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)));
	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 * (expf(log1pf(powf(fmaxf(t_2, powf(hypotf(t_4, t_3), 2.0f)), -0.5f))) + -1.0f);
		}
		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(floor(h) * Float32(floor(w) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))))
	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(exp(log1p((((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(-0.5)))) + Float32(-1.0)));
		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

Derivation

1. Initial program 96.5%

   \[\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 96.5%

   \[\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 96.5%

   \[\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 57.2%

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

8. Taylor expanded in dX.u around inf 57.6%

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

   1. *-commutative 57.6%

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

   2. unpow2 57.6%

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

   3. unpow2 57.6%

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

   4. swap-sqr 57.6%

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

   5. unpow2 57.6%

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

   6. *-commutative 57.6%

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

10. Simplified 57.6%

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

    1. expm1-log1p-u 57.6%

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

    2. expm1-undefine 60.4%

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

12. Applied egg-rr 60.4%

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

13. Final simplification 60.4%

    \[\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\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)} > \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\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({\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\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)} > \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\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 \left(e^{\mathsf{log1p}\left({\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)} + -1\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\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)} > \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\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 , 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 h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \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.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 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} \]
14. Add Preprocessing

Alternative 6: 60.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := dX.v \cdot \left\lfloor h\right\rfloor \\ t_1 := \left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ t_2 := dX.u \cdot \left\lfloor w\right\rfloor \\ t_3 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_4 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_5 := {\left(\mathsf{hypot}\left(t\_3, t\_4\right)\right)}^{2}\\ t_6 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t\_2, t\_0\right)\right)}^{2}, t\_5\right)\\ t_7 := \frac{\sqrt{t\_6}}{\left\lfloor maxAniso\right\rfloor }\\ t_8 := \frac{t\_6}{t\_1}\\ t_9 := t\_8 > \left\lfloor maxAniso\right\rfloor \\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \sqrt{\frac{1}{t\_6}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({t\_2}^{2}, t\_5\right)}{t\_1}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;t\_7\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot {\left({\left(\mathsf{max}\left({\left(\mathsf{hypot}\left(t\_0, t\_2\right)\right)}^{2}, {\left(\mathsf{hypot}\left(t\_4, t\_3\right)\right)}^{2}\right)\right)}^{2}\right)}^{-0.25}\\ \end{array}\right)\\ \mathbf{elif}\;t\_9:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;t\_8\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* dX.v (floor h)))
        (t_1 (* (floor h) (* (floor w) (- (* dX.u dY.v) (* dX.v dY.u)))))
        (t_2 (* dX.u (floor w)))
        (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 (pow (hypot t_2 t_0) 2.0) t_5))
        (t_7 (/ (sqrt t_6) (floor maxAniso)))
        (t_8 (/ t_6 t_1))
        (t_9 (> t_8 (floor maxAniso))))
   (if (< (if t_9 t_7 (* t_1 (sqrt (/ 1.0 t_6)))) 1.0)
     (fmax
      1.0
      (*
       (if t_9 (floor maxAniso) (/ (fmax (pow t_2 2.0) t_5) t_1))
       (if t_9
         t_7
         (*
          t_1
          (pow
           (pow (fmax (pow (hypot t_0 t_2) 2.0) (pow (hypot t_4 t_3) 2.0)) 2.0)
           -0.25)))))
     (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_v * floorf(h);
	float t_1 = floorf(h) * (floorf(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)));
	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_3, t_4), 2.0f);
	float t_6 = fmaxf(powf(hypotf(t_2, t_0), 2.0f), t_5);
	float t_7 = sqrtf(t_6) / floorf(maxAniso);
	float t_8 = t_6 / t_1;
	int t_9 = t_8 > floorf(maxAniso);
	float tmp;
	if (t_9) {
		tmp = t_7;
	} else {
		tmp = t_1 * 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_2, 2.0f), t_5) / t_1;
		}
		float tmp_5;
		if (t_9) {
			tmp_5 = t_7;
		} else {
			tmp_5 = t_1 * powf(powf(fmaxf(powf(hypotf(t_0, t_2), 2.0f), powf(hypotf(t_4, t_3), 2.0f)), 2.0f), -0.25f);
		}
		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(dX_46_v * floor(h))
	t_1 = Float32(floor(h) * Float32(floor(w) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))))
	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_3, t_4) ^ Float32(2.0)
	t_6 = ((hypot(t_2, t_0) ^ Float32(2.0)) != (hypot(t_2, t_0) ^ Float32(2.0))) ? t_5 : ((t_5 != t_5) ? (hypot(t_2, t_0) ^ Float32(2.0)) : max((hypot(t_2, t_0) ^ Float32(2.0)), t_5))
	t_7 = Float32(sqrt(t_6) / floor(maxAniso))
	t_8 = Float32(t_6 / t_1)
	t_9 = t_8 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_9)
		tmp = t_7;
	else
		tmp = Float32(t_1 * 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_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))) / t_1);
		end
		tmp_5 = Float32(0.0)
		if (t_9)
			tmp_5 = t_7;
		else
			tmp_5 = Float32(t_1 * (((((hypot(t_0, t_2) ^ Float32(2.0)) != (hypot(t_0, t_2) ^ Float32(2.0))) ? (hypot(t_4, t_3) ^ Float32(2.0)) : (((hypot(t_4, t_3) ^ Float32(2.0)) != (hypot(t_4, t_3) ^ Float32(2.0))) ? (hypot(t_0, t_2) ^ Float32(2.0)) : max((hypot(t_0, t_2) ^ Float32(2.0)), (hypot(t_4, t_3) ^ Float32(2.0))))) ^ Float32(2.0)) ^ Float32(-0.25)));
		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_v * floor(h);
	t_1 = floor(h) * (floor(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)));
	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_3, t_4) ^ single(2.0);
	t_6 = max((hypot(t_2, t_0) ^ single(2.0)), t_5);
	t_7 = sqrt(t_6) / floor(maxAniso);
	t_8 = t_6 / t_1;
	t_9 = t_8 > floor(maxAniso);
	tmp = single(0.0);
	if (t_9)
		tmp = t_7;
	else
		tmp = t_1 * 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_2 ^ single(2.0)), t_5) / t_1;
		end
		tmp_6 = single(0.0);
		if (t_9)
			tmp_6 = t_7;
		else
			tmp_6 = t_1 * ((max((hypot(t_0, t_2) ^ single(2.0)), (hypot(t_4, t_3) ^ single(2.0))) ^ single(2.0)) ^ single(-0.25));
		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 96.5%

   \[\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 96.5%

   \[\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 96.5%

   \[\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 57.2%

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

8. Taylor expanded in dX.u around inf 57.6%

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

   1. *-commutative 57.6%

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

   2. unpow2 57.6%

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

   3. unpow2 57.6%

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

   4. swap-sqr 57.6%

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

   5. unpow2 57.6%

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

   6. *-commutative 57.6%

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

10. Simplified 57.6%

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

    1. add-log-exp 58.2%

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

    2. pow1/2 58.2%

       \[\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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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} < 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \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(\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\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)}^{0.5}}\right) \cdot \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({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\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)} > \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\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\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)} > \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\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} \]

    3. inv-pow 58.2%

       \[\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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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} < 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \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({\left(\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\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}\right)}^{0.5}}\right) \cdot \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({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\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)} > \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\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\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)} > \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\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} \]

    4. pow-pow 58.2%

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

12. Applied egg-rr 58.2%

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

    1. rem-log-exp 57.6%

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

    2. sqr-pow 57.6%

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

    3. pow-prod-down 60.2%

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

14. Applied egg-rr 60.2%

    \[\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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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} < 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \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(\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)}^{2}\right)}^{-0.25} \cdot \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({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\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)} > \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\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\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)} > \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\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} \]
15. Step-by-step derivation

16. Simplified 60.2%

    \[\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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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} < 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \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(\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)\right)}^{2}\right)}^{-0.25} \cdot \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({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\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)} > \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\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\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)} > \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\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} \]

17. Final simplification 60.2%

    \[\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\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)} > \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\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({\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\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)} > \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\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} \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\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)} > \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\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 {\left({\left(\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)\right)}^{2}\right)}^{-0.25}\\ \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\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)} > \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\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} \]
18. Add Preprocessing

Alternative 7: 58.8% accurate, 1.3× speedup

Math

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

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* dX.v (floor h)))
        (t_1 (* (floor h) dY.v))
        (t_2 (* (floor w) dY.u))
        (t_3 (pow (hypot t_1 t_2) 2.0))
        (t_4 (* dX.u (floor w)))
        (t_5 (fmax (pow (hypot t_4 t_0) 2.0) t_3))
        (t_6 (* (floor w) (- (* dX.u dY.v) (* dX.v dY.u))))
        (t_7 (* (floor h) t_6))
        (t_8 (/ t_5 t_7))
        (t_9 (> t_8 (floor maxAniso)))
        (t_10
         (if t_9 (/ (sqrt t_5) (floor maxAniso)) (* t_7 (sqrt (/ 1.0 t_5))))))
   (if (< t_10 1.0)
     (fmax
      1.0
      (* t_10 (if t_9 (floor maxAniso) (/ (fmax (pow t_4 2.0) t_3) t_7))))
     (if (>
          (/
           (/ 1.0 (floor h))
           (/ t_6 (fmax (pow (hypot t_0 t_4) 2.0) (pow (hypot t_2 t_1) 2.0))))
          (floor maxAniso))
       (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_v * floorf(h);
	float t_1 = floorf(h) * dY_46_v;
	float t_2 = floorf(w) * dY_46_u;
	float t_3 = powf(hypotf(t_1, t_2), 2.0f);
	float t_4 = dX_46_u * floorf(w);
	float t_5 = fmaxf(powf(hypotf(t_4, t_0), 2.0f), t_3);
	float t_6 = floorf(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u));
	float t_7 = floorf(h) * t_6;
	float t_8 = t_5 / t_7;
	int t_9 = t_8 > floorf(maxAniso);
	float tmp;
	if (t_9) {
		tmp = sqrtf(t_5) / floorf(maxAniso);
	} else {
		tmp = t_7 * sqrtf((1.0f / t_5));
	}
	float t_10 = tmp;
	float tmp_2;
	if (t_10 < 1.0f) {
		float tmp_3;
		if (t_9) {
			tmp_3 = floorf(maxAniso);
		} else {
			tmp_3 = fmaxf(powf(t_4, 2.0f), t_3) / t_7;
		}
		tmp_2 = fmaxf(1.0f, (t_10 * tmp_3));
	} else if (((1.0f / floorf(h)) / (t_6 / fmaxf(powf(hypotf(t_0, t_4), 2.0f), powf(hypotf(t_2, t_1), 2.0f)))) > floorf(maxAniso)) {
		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(dX_46_v * floor(h))
	t_1 = Float32(floor(h) * dY_46_v)
	t_2 = Float32(floor(w) * dY_46_u)
	t_3 = hypot(t_1, t_2) ^ Float32(2.0)
	t_4 = Float32(dX_46_u * floor(w))
	t_5 = ((hypot(t_4, t_0) ^ Float32(2.0)) != (hypot(t_4, t_0) ^ Float32(2.0))) ? t_3 : ((t_3 != t_3) ? (hypot(t_4, t_0) ^ Float32(2.0)) : max((hypot(t_4, t_0) ^ Float32(2.0)), t_3))
	t_6 = Float32(floor(w) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)))
	t_7 = Float32(floor(h) * t_6)
	t_8 = Float32(t_5 / t_7)
	t_9 = t_8 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_9)
		tmp = Float32(sqrt(t_5) / floor(maxAniso));
	else
		tmp = Float32(t_7 * sqrt(Float32(Float32(1.0) / t_5)));
	end
	t_10 = tmp
	tmp_2 = Float32(0.0)
	if (t_10 < Float32(1.0))
		tmp_3 = Float32(0.0)
		if (t_9)
			tmp_3 = floor(maxAniso);
		else
			tmp_3 = Float32((((t_4 ^ Float32(2.0)) != (t_4 ^ Float32(2.0))) ? t_3 : ((t_3 != t_3) ? (t_4 ^ Float32(2.0)) : max((t_4 ^ Float32(2.0)), t_3))) / t_7);
		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 (Float32(Float32(Float32(1.0) / floor(h)) / Float32(t_6 / (((hypot(t_0, t_4) ^ Float32(2.0)) != (hypot(t_0, t_4) ^ Float32(2.0))) ? (hypot(t_2, t_1) ^ Float32(2.0)) : (((hypot(t_2, t_1) ^ Float32(2.0)) != (hypot(t_2, t_1) ^ Float32(2.0))) ? (hypot(t_0, t_4) ^ Float32(2.0)) : max((hypot(t_0, t_4) ^ Float32(2.0)), (hypot(t_2, t_1) ^ Float32(2.0))))))) > floor(maxAniso))
		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 = dX_46_v * floor(h);
	t_1 = floor(h) * dY_46_v;
	t_2 = floor(w) * dY_46_u;
	t_3 = hypot(t_1, t_2) ^ single(2.0);
	t_4 = dX_46_u * floor(w);
	t_5 = max((hypot(t_4, t_0) ^ single(2.0)), t_3);
	t_6 = floor(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u));
	t_7 = floor(h) * t_6;
	t_8 = t_5 / t_7;
	t_9 = t_8 > floor(maxAniso);
	tmp = single(0.0);
	if (t_9)
		tmp = sqrt(t_5) / floor(maxAniso);
	else
		tmp = t_7 * sqrt((single(1.0) / t_5));
	end
	t_10 = tmp;
	tmp_3 = single(0.0);
	if (t_10 < single(1.0))
		tmp_4 = single(0.0);
		if (t_9)
			tmp_4 = floor(maxAniso);
		else
			tmp_4 = max((t_4 ^ single(2.0)), t_3) / t_7;
		end
		tmp_3 = max(single(1.0), (t_10 * tmp_4));
	elseif (((single(1.0) / floor(h)) / (t_6 / max((hypot(t_0, t_4) ^ single(2.0)), (hypot(t_2, t_1) ^ single(2.0))))) > floor(maxAniso))
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_8;
	end
	tmp_5 = tmp_3;
end

Derivation

1. Initial program 96.5%

   \[\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 96.5%

   \[\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 96.5%

   \[\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 57.2%

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

8. Taylor expanded in dX.u around inf 57.6%

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

   1. *-commutative 57.6%

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

   2. unpow2 57.6%

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

   3. unpow2 57.6%

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

   4. swap-sqr 57.6%

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

   5. unpow2 57.6%

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

   6. *-commutative 57.6%

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

10. Simplified 57.6%

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

    1. clear-num 57.6%

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

    2. inv-pow 57.6%

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

12. Applied egg-rr 57.6%

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

    1. unpow-1 57.6%

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

    2. associate-/l* 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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} < 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\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)} > \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\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{1}{\color{blue}{\left\lfloor h\right\rfloor \cdot \frac{\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot \left(-dY.u\right)\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\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} \]

    3. 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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} < 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\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)} > \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\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}\;\color{blue}{\frac{\frac{1}{\left\lfloor h\right\rfloor }}{\frac{\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot \left(-dY.u\right)\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\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} \]

    4. fma-undefine 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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} < 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\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)} > \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\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{\frac{1}{\left\lfloor h\right\rfloor }}{\frac{\left\lfloor w\right\rfloor \cdot \color{blue}{\left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\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\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} \]

    5. distribute-rgt-neg-out 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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} < 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\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)} > \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\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{\frac{1}{\left\lfloor h\right\rfloor }}{\frac{\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v + \color{blue}{\left(-dX.v \cdot dY.u\right)}\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\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} \]

    6. sub-neg 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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} < 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\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)} > \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\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{\frac{1}{\left\lfloor h\right\rfloor }}{\frac{\left\lfloor w\right\rfloor \cdot \color{blue}{\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\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} \]

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

15. 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\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)} > \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\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({\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\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)} > \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\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({\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\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)} > \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\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{\frac{1}{\left\lfloor h\right\rfloor }}{\frac{\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}{\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\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} \]
16. Add Preprocessing

Alternative 8: 58.5% accurate, 1.3× speedup

Math

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

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* dX.v (floor h)))
        (t_1 (* (floor h) dY.v))
        (t_2 (* (floor w) dY.u))
        (t_3 (pow (hypot t_2 t_1) 2.0))
        (t_4 (* dX.u (floor w)))
        (t_5 (fmax (pow (hypot t_4 t_0) 2.0) (pow (hypot t_1 t_2) 2.0)))
        (t_6 (* (floor w) (- (* dX.u dY.v) (* dX.v dY.u))))
        (t_7 (* (floor h) t_6))
        (t_8 (/ t_5 t_7))
        (t_9 (> t_8 (floor maxAniso)))
        (t_10
         (if t_9 (/ (sqrt t_5) (floor maxAniso)) (* t_7 (sqrt (/ 1.0 t_5))))))
   (if (< t_10 1.0)
     (fmax
      1.0
      (*
       t_10
       (if t_9
         (floor maxAniso)
         (/
          (fmax (pow t_4 2.0) t_3)
          (* dY.v (* dX.u (* (floor h) (floor w))))))))
     (if (>
          (/ (/ 1.0 (floor h)) (/ t_6 (fmax (pow (hypot t_0 t_4) 2.0) t_3)))
          (floor maxAniso))
       (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_v * floorf(h);
	float t_1 = floorf(h) * dY_46_v;
	float t_2 = floorf(w) * dY_46_u;
	float t_3 = powf(hypotf(t_2, t_1), 2.0f);
	float t_4 = dX_46_u * floorf(w);
	float t_5 = fmaxf(powf(hypotf(t_4, t_0), 2.0f), powf(hypotf(t_1, t_2), 2.0f));
	float t_6 = floorf(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u));
	float t_7 = floorf(h) * t_6;
	float t_8 = t_5 / t_7;
	int t_9 = t_8 > floorf(maxAniso);
	float tmp;
	if (t_9) {
		tmp = sqrtf(t_5) / floorf(maxAniso);
	} else {
		tmp = t_7 * sqrtf((1.0f / t_5));
	}
	float t_10 = tmp;
	float tmp_2;
	if (t_10 < 1.0f) {
		float tmp_3;
		if (t_9) {
			tmp_3 = floorf(maxAniso);
		} else {
			tmp_3 = fmaxf(powf(t_4, 2.0f), t_3) / (dY_46_v * (dX_46_u * (floorf(h) * floorf(w))));
		}
		tmp_2 = fmaxf(1.0f, (t_10 * tmp_3));
	} else if (((1.0f / floorf(h)) / (t_6 / fmaxf(powf(hypotf(t_0, t_4), 2.0f), t_3))) > floorf(maxAniso)) {
		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(dX_46_v * floor(h))
	t_1 = Float32(floor(h) * dY_46_v)
	t_2 = Float32(floor(w) * dY_46_u)
	t_3 = hypot(t_2, t_1) ^ Float32(2.0)
	t_4 = Float32(dX_46_u * floor(w))
	t_5 = ((hypot(t_4, t_0) ^ Float32(2.0)) != (hypot(t_4, t_0) ^ Float32(2.0))) ? (hypot(t_1, t_2) ^ Float32(2.0)) : (((hypot(t_1, t_2) ^ Float32(2.0)) != (hypot(t_1, t_2) ^ Float32(2.0))) ? (hypot(t_4, t_0) ^ Float32(2.0)) : max((hypot(t_4, t_0) ^ Float32(2.0)), (hypot(t_1, t_2) ^ Float32(2.0))))
	t_6 = Float32(floor(w) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)))
	t_7 = Float32(floor(h) * t_6)
	t_8 = Float32(t_5 / t_7)
	t_9 = t_8 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_9)
		tmp = Float32(sqrt(t_5) / floor(maxAniso));
	else
		tmp = Float32(t_7 * sqrt(Float32(Float32(1.0) / t_5)));
	end
	t_10 = tmp
	tmp_2 = Float32(0.0)
	if (t_10 < Float32(1.0))
		tmp_3 = Float32(0.0)
		if (t_9)
			tmp_3 = floor(maxAniso);
		else
			tmp_3 = Float32((((t_4 ^ Float32(2.0)) != (t_4 ^ Float32(2.0))) ? t_3 : ((t_3 != t_3) ? (t_4 ^ Float32(2.0)) : max((t_4 ^ Float32(2.0)), t_3))) / Float32(dY_46_v * Float32(dX_46_u * Float32(floor(h) * floor(w)))));
		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 (Float32(Float32(Float32(1.0) / floor(h)) / Float32(t_6 / (((hypot(t_0, t_4) ^ Float32(2.0)) != (hypot(t_0, t_4) ^ Float32(2.0))) ? t_3 : ((t_3 != t_3) ? (hypot(t_0, t_4) ^ Float32(2.0)) : max((hypot(t_0, t_4) ^ Float32(2.0)), t_3))))) > floor(maxAniso))
		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 = dX_46_v * floor(h);
	t_1 = floor(h) * dY_46_v;
	t_2 = floor(w) * dY_46_u;
	t_3 = hypot(t_2, t_1) ^ single(2.0);
	t_4 = dX_46_u * floor(w);
	t_5 = max((hypot(t_4, t_0) ^ single(2.0)), (hypot(t_1, t_2) ^ single(2.0)));
	t_6 = floor(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u));
	t_7 = floor(h) * t_6;
	t_8 = t_5 / t_7;
	t_9 = t_8 > floor(maxAniso);
	tmp = single(0.0);
	if (t_9)
		tmp = sqrt(t_5) / floor(maxAniso);
	else
		tmp = t_7 * sqrt((single(1.0) / t_5));
	end
	t_10 = tmp;
	tmp_3 = single(0.0);
	if (t_10 < single(1.0))
		tmp_4 = single(0.0);
		if (t_9)
			tmp_4 = floor(maxAniso);
		else
			tmp_4 = max((t_4 ^ single(2.0)), t_3) / (dY_46_v * (dX_46_u * (floor(h) * floor(w))));
		end
		tmp_3 = max(single(1.0), (t_10 * tmp_4));
	elseif (((single(1.0) / floor(h)) / (t_6 / max((hypot(t_0, t_4) ^ single(2.0)), t_3))) > floor(maxAniso))
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_8;
	end
	tmp_5 = tmp_3;
end

Derivation

1. Initial program 96.5%

   \[\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 96.5%

   \[\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 96.5%

   \[\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 57.2%

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

8. Taylor expanded in dX.u around inf 57.6%

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

   1. *-commutative 57.6%

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

   2. unpow2 57.6%

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

   3. unpow2 57.6%

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

   4. swap-sqr 57.6%

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

   5. unpow2 57.6%

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

   6. *-commutative 57.6%

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

10. Simplified 57.6%

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

11. Taylor expanded in dX.u around inf 56.8%

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

13. Simplified 56.8%

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

    1. clear-num 57.6%

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

    2. inv-pow 57.6%

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

15. Applied egg-rr 56.8%

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

    1. unpow-1 57.6%

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

    2. associate-/l* 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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} < 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\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)} > \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\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{1}{\color{blue}{\left\lfloor h\right\rfloor \cdot \frac{\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot \left(-dY.u\right)\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\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} \]

    3. 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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} < 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\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)} > \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\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}\;\color{blue}{\frac{\frac{1}{\left\lfloor h\right\rfloor }}{\frac{\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot \left(-dY.u\right)\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\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} \]

    4. fma-undefine 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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} < 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\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)} > \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\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{\frac{1}{\left\lfloor h\right\rfloor }}{\frac{\left\lfloor w\right\rfloor \cdot \color{blue}{\left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\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\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} \]

    5. distribute-rgt-neg-out 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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} < 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\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)} > \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\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{\frac{1}{\left\lfloor h\right\rfloor }}{\frac{\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v + \color{blue}{\left(-dX.v \cdot dY.u\right)}\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\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} \]

    6. sub-neg 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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} < 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\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)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \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({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\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)} > \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\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{\frac{1}{\left\lfloor h\right\rfloor }}{\frac{\left\lfloor w\right\rfloor \cdot \color{blue}{\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\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} \]

17. Simplified 58.8%

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

18. Final simplification 58.8%

    \[\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\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)} > \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\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({\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\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)} > \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\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({\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\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)} > \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)}{dY.v \cdot \left(dX.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\frac{1}{\left\lfloor h\right\rfloor }}{\frac{\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}{\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\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} \]
19. Add Preprocessing

Alternative 9: 58.4% accurate, 1.3× speedup

Math

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

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* dX.v (floor h)))
        (t_1 (* (floor h) (* (floor w) (- (* dX.u dY.v) (* dX.v dY.u)))))
        (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)
          (* dY.v (* dX.u (* (floor h) (floor w))))))
       (if (>
            (/
             (fmax (pow (hypot t_0 t_2) 2.0) t_5)
             (* (floor h) (* (floor w) (* dX.v (- dY.u)))))
            (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 = floorf(h) * (floorf(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)));
	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) / (dY_46_v * (dX_46_u * (floorf(h) * floorf(w))));
		}
		float tmp_5;
		if ((fmaxf(powf(hypotf(t_0, t_2), 2.0f), t_5) / (floorf(h) * (floorf(w) * (dX_46_v * -dY_46_u)))) > 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(floor(h) * Float32(floor(w) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))))
	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(dY_46_v * Float32(dX_46_u * Float32(floor(h) * floor(w)))));
		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(floor(w) * Float32(dX_46_v * Float32(-dY_46_u))))) > 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 = floor(h) * (floor(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)));
	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) / (dY_46_v * (dX_46_u * (floor(h) * floor(w))));
		end
		tmp_6 = single(0.0);
		if ((max((hypot(t_0, t_2) ^ single(2.0)), t_5) / (floor(h) * (floor(w) * (dX_46_v * -dY_46_u)))) > 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 96.5%

   \[\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 96.5%

   \[\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 96.5%

   \[\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 57.2%

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

8. Taylor expanded in dX.u around inf 57.6%

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

   1. *-commutative 57.6%

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

   2. unpow2 57.6%

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

   3. unpow2 57.6%

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

   4. swap-sqr 57.6%

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

   5. unpow2 57.6%

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

   6. *-commutative 57.6%

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

10. Simplified 57.6%

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

11. Taylor expanded in dX.u around inf 56.8%

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

13. Simplified 56.8%

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

14. Taylor expanded in dX.u around 0 57.5%

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

16. Simplified 57.5%

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

17. Final simplification 57.5%

    \[\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\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)} > \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\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({\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\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)} > \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)}{dY.v \cdot \left(dX.u \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor w\right\rfloor \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(\left\lfloor w\right\rfloor \cdot \left(dX.v \cdot \left(-dY.u\right)\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\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({\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\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)} > \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\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} \]
18. Add Preprocessing

Alternative 10: 57.8% accurate, 1.3× speedup

Math

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

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* dY.v (* dX.u (* (floor h) (floor w)))))
        (t_1 (* (floor h) (* (floor w) (- (* dX.u dY.v) (* dX.v dY.u)))))
        (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 = dY_46_v * (dX_46_u * (floorf(h) * floorf(w)));
	float t_1 = floorf(h) * (floorf(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)));
	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(dY_46_v * Float32(dX_46_u * Float32(floor(h) * floor(w))))
	t_1 = Float32(floor(h) * Float32(floor(w) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))))
	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 = dY_46_v * (dX_46_u * (floor(h) * floor(w)));
	t_1 = floor(h) * (floor(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)));
	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 96.5%

   \[\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 96.5%

   \[\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 96.5%

   \[\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 57.2%

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

8. Taylor expanded in dX.u around inf 57.6%

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

   1. *-commutative 57.6%

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

   2. unpow2 57.6%

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

   3. unpow2 57.6%

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

   4. swap-sqr 57.6%

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

   5. unpow2 57.6%

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

   6. *-commutative 57.6%

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

10. Simplified 57.6%

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

11. Taylor expanded in dX.u around inf 56.8%

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

13. Simplified 56.8%

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

14. Taylor expanded in dX.u around inf 56.8%

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

16. Simplified 56.8%

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

17. Final simplification 56.8%

    \[\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\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)} > \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\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({\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\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)} > \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\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({\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)}{dY.v \cdot \left(dX.u \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)}{dY.v \cdot \left(dX.u \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 , 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 h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \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.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 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} \]
18. Add Preprocessing

Reproduce

herbie shell --seed 2024182 
(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))))))))