Anisotropic x16 LOD (ratio of anisotropy)

Percentage Accurate: 97.8% → 97.7%

Time: 1.6min

Alternatives: 9

Speedup: N/A×

Specification

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

Math

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

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: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

MATLAB

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

Alternative 1: 97.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (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_1 t_3) (* 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))))
   (if (< t_9 1.0)
     (fmax 1.0 (* t_9 (if t_8 (floor maxAniso) t_7)))
     (if (>
          (/ t_4 (fabs (* (* dX.u dY.v) (* (floor w) (floor h)))))
          (floor maxAniso))
       (floor maxAniso)
       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 = 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_1 * t_3) - (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_2;
	if (t_9 < 1.0f) {
		float tmp_3;
		if (t_8) {
			tmp_3 = floorf(maxAniso);
		} else {
			tmp_3 = t_7;
		}
		tmp_2 = fmaxf(1.0f, (t_9 * tmp_3));
	} else if ((t_4 / fabsf(((dX_46_u * dY_46_v) * (floorf(w) * floorf(h))))) > floorf(maxAniso)) {
		tmp_2 = floorf(maxAniso);
	} else {
		tmp_2 = t_7;
	}
	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_1 * t_3) - 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_2 = Float32(0.0)
	if (t_9 < Float32(1.0))
		tmp_3 = Float32(0.0)
		if (t_8)
			tmp_3 = floor(maxAniso);
		else
			tmp_3 = t_7;
		end
		tmp_2 = (Float32(1.0) != Float32(1.0)) ? Float32(t_9 * tmp_3) : ((Float32(t_9 * tmp_3) != Float32(t_9 * tmp_3)) ? Float32(1.0) : max(Float32(1.0), Float32(t_9 * tmp_3)));
	elseif (Float32(t_4 / abs(Float32(Float32(dX_46_u * dY_46_v) * Float32(floor(w) * floor(h))))) > floor(maxAniso))
		tmp_2 = floor(maxAniso);
	else
		tmp_2 = t_7;
	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) * 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_1 * t_3) - (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_3 = single(0.0);
	if (t_9 < single(1.0))
		tmp_4 = single(0.0);
		if (t_8)
			tmp_4 = floor(maxAniso);
		else
			tmp_4 = t_7;
		end
		tmp_3 = max(single(1.0), (t_9 * tmp_4));
	elseif ((t_4 / abs(((dX_46_u * dY_46_v) * (floor(w) * floor(h))))) > floor(maxAniso))
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_7;
	end
	tmp_5 = tmp_3;
end

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in dX.u around inf 98.7%

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

   1. associate-*r* 98.7%

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

5. Simplified 98.7%

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

6. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\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\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(dX.u \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]
7. Add Preprocessing

Alternative 2: 96.9% accurate, 1.0× speedup

Math

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

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 (/ t_5 (floor maxAniso)))
        (t_7 (fabs (- (* t_1 t_3) (* t_0 t_2))))
        (t_8 (/ t_4 t_7))
        (t_9 (> t_8 (floor maxAniso)))
        (t_10 (if t_9 (floor maxAniso) t_8)))
   (if (<
        (if t_9 t_6 (/ (fabs (* (* dX.u dY.v) (* (floor w) (floor h)))) t_5))
        1.0)
     (fmax 1.0 (* (if t_9 t_6 (/ t_7 t_5)) t_10))
     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 = t_5 / floorf(maxAniso);
	float t_7 = fabsf(((t_1 * t_3) - (t_0 * t_2)));
	float t_8 = t_4 / t_7;
	int t_9 = t_8 > floorf(maxAniso);
	float tmp;
	if (t_9) {
		tmp = floorf(maxAniso);
	} else {
		tmp = t_8;
	}
	float t_10 = tmp;
	float tmp_1;
	if (t_9) {
		tmp_1 = t_6;
	} else {
		tmp_1 = fabsf(((dX_46_u * dY_46_v) * (floorf(w) * floorf(h)))) / t_5;
	}
	float tmp_3;
	if (tmp_1 < 1.0f) {
		float tmp_4;
		if (t_9) {
			tmp_4 = t_6;
		} else {
			tmp_4 = t_7 / t_5;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * t_10));
	} else {
		tmp_3 = t_10;
	}
	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) * 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 = Float32(t_5 / floor(maxAniso))
	t_7 = abs(Float32(Float32(t_1 * t_3) - Float32(t_0 * t_2)))
	t_8 = Float32(t_4 / t_7)
	t_9 = t_8 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_9)
		tmp = floor(maxAniso);
	else
		tmp = t_8;
	end
	t_10 = tmp
	tmp_1 = Float32(0.0)
	if (t_9)
		tmp_1 = t_6;
	else
		tmp_1 = Float32(abs(Float32(Float32(dX_46_u * dY_46_v) * Float32(floor(w) * floor(h)))) / t_5);
	end
	tmp_3 = Float32(0.0)
	if (tmp_1 < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_9)
			tmp_4 = t_6;
		else
			tmp_4 = Float32(t_7 / t_5);
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * t_10) : ((Float32(tmp_4 * t_10) != Float32(tmp_4 * t_10)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * t_10)));
	else
		tmp_3 = t_10;
	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 = 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 = t_5 / floor(maxAniso);
	t_7 = abs(((t_1 * t_3) - (t_0 * t_2)));
	t_8 = t_4 / t_7;
	t_9 = t_8 > floor(maxAniso);
	tmp = single(0.0);
	if (t_9)
		tmp = floor(maxAniso);
	else
		tmp = t_8;
	end
	t_10 = tmp;
	tmp_2 = single(0.0);
	if (t_9)
		tmp_2 = t_6;
	else
		tmp_2 = abs(((dX_46_u * dY_46_v) * (floor(w) * floor(h)))) / t_5;
	end
	tmp_4 = single(0.0);
	if (tmp_2 < single(1.0))
		tmp_5 = single(0.0);
		if (t_9)
			tmp_5 = t_6;
		else
			tmp_5 = t_7 / t_5;
		end
		tmp_4 = max(single(1.0), (tmp_5 * t_10));
	else
		tmp_4 = t_10;
	end
	tmp_6 = tmp_4;
end

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in dX.u around inf 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\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\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]
4. Step-by-step derivation

   1. associate-*r* 98.7%

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

5. Simplified 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(dX.u \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\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\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

6. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(dX.u \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\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\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]
7. Add Preprocessing

Alternative 3: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := dX.u \cdot dY.v - dX.v \cdot dY.u\\ t_1 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_2 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_3 := \left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\\ t_4 := \frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right), dX.v \cdot \left(dX.v \cdot t\_3\right)\right), \mathsf{fma}\left(\left\lfloorw\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right), t\_3 \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloorw\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloorh\right\rfloor, dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left(-dX.v\right)\right)\right)\right|}\\ t_5 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_6 := {\left(\mathsf{hypot}\left(t\_2, t\_5\right)\right)}^{2}\\ t_7 := t\_0 \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\\ t_8 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_9 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t\_1, t\_8\right)\right)}^{2}, t\_6\right)\\ t_10 := {\left(\mathsf{hypot}\left(t\_8, t\_1\right)\right)}^{2}\\ t_11 := \mathsf{max}\left(t\_10, {\left(\mathsf{hypot}\left(t\_5, t\_2\right)\right)}^{2}\right)\\ t_12 := \frac{t\_9}{t\_7}\\ t_13 := t\_12 > \left\lfloormaxAniso\right\rfloor\\ t_14 := \sqrt{t\_9}\\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(t\_10, t\_6\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot t\_0\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{t\_11}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \left(dX.u \cdot dY.v\right) - \left\lfloorh\right\rfloor \cdot \left(dX.v \cdot dY.u\right)\right)\right| \cdot \sqrt{\frac{1}{t\_11}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t\_13:\\ \;\;\;\;\frac{t\_14}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_7}{t\_14}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t\_13:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t\_12\\ \end{array}\right)\\ \mathbf{elif}\;t\_4 > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (- (* dX.u dY.v) (* dX.v dY.u)))
        (t_1 (* (floor h) dX.v))
        (t_2 (* (floor h) dY.v))
        (t_3 (* (floor h) (floor h)))
        (t_4
         (/
          (fmax
           (fma (floor w) (* (floor w) (* dX.u dX.u)) (* dX.v (* dX.v t_3)))
           (fma (floor w) (* (floor w) (* dY.u dY.u)) (* t_3 (* dY.v dY.v))))
          (fabs
           (*
            (floor w)
            (fma dY.v (* dX.u (floor h)) (* dY.u (* (floor h) (- dX.v))))))))
        (t_5 (* (floor w) dY.u))
        (t_6 (pow (hypot t_2 t_5) 2.0))
        (t_7 (* t_0 (* (floor w) (floor h))))
        (t_8 (* (floor w) dX.u))
        (t_9 (fmax (pow (hypot t_1 t_8) 2.0) t_6))
        (t_10 (pow (hypot t_8 t_1) 2.0))
        (t_11 (fmax t_10 (pow (hypot t_5 t_2) 2.0)))
        (t_12 (/ t_9 t_7))
        (t_13 (> t_12 (floor maxAniso)))
        (t_14 (sqrt t_9)))
   (if (<
        (if (>
             (/ (fmax t_10 t_6) (fabs (* (floor h) (* (floor w) t_0))))
             (floor maxAniso))
          (/ (sqrt t_11) (floor maxAniso))
          (*
           (fabs
            (*
             (floor w)
             (- (* (floor h) (* dX.u dY.v)) (* (floor h) (* dX.v dY.u)))))
           (sqrt (/ 1.0 t_11))))
        1.0)
     (fmax
      1.0
      (*
       (if t_13 (/ t_14 (floor maxAniso)) (/ t_7 t_14))
       (if t_13 (floor maxAniso) t_12)))
     (if (> t_4 (floor maxAniso)) (floor maxAniso) t_4))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = (dX_46_u * dY_46_v) - (dX_46_v * dY_46_u);
	float t_1 = floorf(h) * dX_46_v;
	float t_2 = floorf(h) * dY_46_v;
	float t_3 = floorf(h) * floorf(h);
	float t_4 = fmaxf(fmaf(floorf(w), (floorf(w) * (dX_46_u * dX_46_u)), (dX_46_v * (dX_46_v * t_3))), fmaf(floorf(w), (floorf(w) * (dY_46_u * dY_46_u)), (t_3 * (dY_46_v * dY_46_v)))) / fabsf((floorf(w) * fmaf(dY_46_v, (dX_46_u * floorf(h)), (dY_46_u * (floorf(h) * -dX_46_v)))));
	float t_5 = floorf(w) * dY_46_u;
	float t_6 = powf(hypotf(t_2, t_5), 2.0f);
	float t_7 = t_0 * (floorf(w) * floorf(h));
	float t_8 = floorf(w) * dX_46_u;
	float t_9 = fmaxf(powf(hypotf(t_1, t_8), 2.0f), t_6);
	float t_10 = powf(hypotf(t_8, t_1), 2.0f);
	float t_11 = fmaxf(t_10, powf(hypotf(t_5, t_2), 2.0f));
	float t_12 = t_9 / t_7;
	int t_13 = t_12 > floorf(maxAniso);
	float t_14 = sqrtf(t_9);
	float tmp;
	if ((fmaxf(t_10, t_6) / fabsf((floorf(h) * (floorf(w) * t_0)))) > floorf(maxAniso)) {
		tmp = sqrtf(t_11) / floorf(maxAniso);
	} else {
		tmp = fabsf((floorf(w) * ((floorf(h) * (dX_46_u * dY_46_v)) - (floorf(h) * (dX_46_v * dY_46_u))))) * sqrtf((1.0f / t_11));
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_13) {
			tmp_4 = t_14 / floorf(maxAniso);
		} else {
			tmp_4 = t_7 / t_14;
		}
		float tmp_5;
		if (t_13) {
			tmp_5 = floorf(maxAniso);
		} else {
			tmp_5 = t_12;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_4 > floorf(maxAniso)) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_4;
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))
	t_1 = Float32(floor(h) * dX_46_v)
	t_2 = Float32(floor(h) * dY_46_v)
	t_3 = Float32(floor(h) * floor(h))
	t_4 = Float32(((fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(dX_46_v * Float32(dX_46_v * t_3))) != fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(dX_46_v * Float32(dX_46_v * t_3)))) ? fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(t_3 * Float32(dY_46_v * dY_46_v))) : ((fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(t_3 * Float32(dY_46_v * dY_46_v))) != fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(t_3 * Float32(dY_46_v * dY_46_v)))) ? fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(dX_46_v * Float32(dX_46_v * t_3))) : max(fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(dX_46_v * Float32(dX_46_v * t_3))), fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(t_3 * Float32(dY_46_v * dY_46_v)))))) / abs(Float32(floor(w) * fma(dY_46_v, Float32(dX_46_u * floor(h)), Float32(dY_46_u * Float32(floor(h) * Float32(-dX_46_v)))))))
	t_5 = Float32(floor(w) * dY_46_u)
	t_6 = hypot(t_2, t_5) ^ Float32(2.0)
	t_7 = Float32(t_0 * Float32(floor(w) * floor(h)))
	t_8 = Float32(floor(w) * dX_46_u)
	t_9 = ((hypot(t_1, t_8) ^ Float32(2.0)) != (hypot(t_1, t_8) ^ Float32(2.0))) ? t_6 : ((t_6 != t_6) ? (hypot(t_1, t_8) ^ Float32(2.0)) : max((hypot(t_1, t_8) ^ Float32(2.0)), t_6))
	t_10 = hypot(t_8, t_1) ^ Float32(2.0)
	t_11 = (t_10 != t_10) ? (hypot(t_5, t_2) ^ Float32(2.0)) : (((hypot(t_5, t_2) ^ Float32(2.0)) != (hypot(t_5, t_2) ^ Float32(2.0))) ? t_10 : max(t_10, (hypot(t_5, t_2) ^ Float32(2.0))))
	t_12 = Float32(t_9 / t_7)
	t_13 = t_12 > floor(maxAniso)
	t_14 = sqrt(t_9)
	tmp = Float32(0.0)
	if (Float32(((t_10 != t_10) ? t_6 : ((t_6 != t_6) ? t_10 : max(t_10, t_6))) / abs(Float32(floor(h) * Float32(floor(w) * t_0)))) > floor(maxAniso))
		tmp = Float32(sqrt(t_11) / floor(maxAniso));
	else
		tmp = Float32(abs(Float32(floor(w) * Float32(Float32(floor(h) * Float32(dX_46_u * dY_46_v)) - Float32(floor(h) * Float32(dX_46_v * dY_46_u))))) * sqrt(Float32(Float32(1.0) / t_11)));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_13)
			tmp_4 = Float32(t_14 / floor(maxAniso));
		else
			tmp_4 = Float32(t_7 / t_14);
		end
		tmp_5 = Float32(0.0)
		if (t_13)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = t_12;
		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_4 > floor(maxAniso))
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_4;
	end
	return tmp_3
end

Derivation

1. Initial program 98.0%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\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\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 98.0%

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

6. Applied egg-rr 98.0%

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

8. Simplified 98.0%

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

9. Taylor expanded in w around 0 98.0%

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

11. Simplified 98.0%

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

12. Taylor expanded in dX.u around 0 98.0%

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

14. Simplified 98.0%

    \[\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\lfloorw\right\rfloor, dX.v \cdot \left\lfloorh\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloorw\right\rfloor, dX.v \cdot \left\lfloorh\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \left(dX.u \cdot dY.v\right) - \left\lfloorh\right\rfloor \cdot \left(dX.v \cdot dY.u\right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloorw\right\rfloor, dX.v \cdot \left\lfloorh\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, dX.v \cdot \left(dX.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\right)\right), \mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloorw\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloorh\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, dX.v \cdot \left(dX.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\right)\right), \mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloorw\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloorh\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|}\\ \end{array} \]

15. Final simplification 98.0%

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

Alternative 4: 61.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_1 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_2 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_3 := {\left(\mathsf{hypot}\left(t\_1, t\_2\right)\right)}^{2}\\ t_4 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_5 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t\_4, t\_0\right)\right)}^{2}, t\_3\right)\\ t_6 := dX.u \cdot dY.v - dX.v \cdot dY.u\\ t_7 := t\_6 \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\\ t_8 := \frac{t\_5}{t\_7}\\ t_9 := t\_8 > \left\lfloormaxAniso\right\rfloor\\ t_10 := \begin{array}{l} \mathbf{if}\;t\_9:\\ \;\;\;\;\frac{\sqrt{t\_5}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;t\_7 \cdot \sqrt{\frac{1}{t\_5}}\\ \end{array}\\ \mathbf{if}\;t\_10 < 1:\\ \;\;\;\;\mathsf{max}\left(1, t\_10 \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({t\_4}^{2}, t\_3\right)}{t\_7} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(t\_0, t\_4\right)\right)}^{2}, {\left(\mathsf{hypot}\left(t\_2, t\_1\right)\right)}^{2}\right)}{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot t\_6\right)}\right)\right)\\ \end{array}\right)\\ \mathbf{elif}\;t\_9:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t\_8\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (* (floor w) dX.u))
        (t_1 (* (floor h) dY.v))
        (t_2 (* (floor w) dY.u))
        (t_3 (pow (hypot t_1 t_2) 2.0))
        (t_4 (* (floor h) dX.v))
        (t_5 (fmax (pow (hypot t_4 t_0) 2.0) t_3))
        (t_6 (- (* dX.u dY.v) (* dX.v dY.u)))
        (t_7 (* t_6 (* (floor w) (floor h))))
        (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 (> (/ (fmax (pow t_4 2.0) t_3) t_7) (floor maxAniso))
         (floor maxAniso)
         (expm1
          (log1p
           (/
            (fmax (pow (hypot t_0 t_4) 2.0) (pow (hypot t_2 t_1) 2.0))
            (* (floor h) (* (floor w) t_6))))))))
     (if t_9 (floor maxAniso) t_8))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(w) * dX_46_u;
	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 = floorf(h) * dX_46_v;
	float t_5 = fmaxf(powf(hypotf(t_4, t_0), 2.0f), t_3);
	float t_6 = (dX_46_u * dY_46_v) - (dX_46_v * dY_46_u);
	float t_7 = t_6 * (floorf(w) * floorf(h));
	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 ((fmaxf(powf(t_4, 2.0f), t_3) / t_7) > floorf(maxAniso)) {
			tmp_3 = floorf(maxAniso);
		} else {
			tmp_3 = expm1f(log1pf((fmaxf(powf(hypotf(t_0, t_4), 2.0f), powf(hypotf(t_2, t_1), 2.0f)) / (floorf(h) * (floorf(w) * t_6)))));
		}
		tmp_2 = fmaxf(1.0f, (t_10 * tmp_3));
	} else if (t_9) {
		tmp_2 = floorf(maxAniso);
	} else {
		tmp_2 = t_8;
	}
	return tmp_2;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(w) * dX_46_u)
	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(floor(h) * dX_46_v)
	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(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))
	t_7 = Float32(t_6 * Float32(floor(w) * floor(h)))
	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 (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) > floor(maxAniso))
			tmp_3 = floor(maxAniso);
		else
			tmp_3 = expm1(log1p(Float32((((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))))) / Float32(floor(h) * Float32(floor(w) * t_6)))));
		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

Derivation

1. Initial program 98.0%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\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\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 98.0%

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

5. Taylor expanded in w around 0 98.0%

   \[\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\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{1}{\left\lfloormaxAniso\right\rfloor} \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\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\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{1}{\left\lfloormaxAniso\right\rfloor} \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.8%

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

   1. expm1-log1p-u 60.7%

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

9. Applied egg-rr 60.7%

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

10. Taylor expanded in dX.v around inf 60.7%

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

11. Final simplification 60.7%

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

Alternative 5: 58.2% accurate, 1.3× speedup

Math

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

FPCore

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

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 = powf(floorf(h), 2.0f);
	float t_2 = floorf(h) * dY_46_v;
	float t_3 = floorf(w) * floorf(h);
	float t_4 = floorf(w) * dX_46_u;
	float t_5 = powf(floorf(w), 2.0f);
	float t_6 = floorf(w) * dY_46_u;
	float t_7 = powf(hypotf(t_2, t_6), 2.0f);
	float t_8 = fmaxf(powf(hypotf(t_0, t_4), 2.0f), t_7);
	float t_9 = sqrtf(t_8) / floorf(maxAniso);
	float t_10 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * t_3;
	float t_11 = t_8 / t_10;
	float t_12 = t_10 * sqrtf((1.0f / t_8));
	float tmp;
	if ((fmaxf(powf(hypotf(t_4, t_0), 2.0f), powf(hypotf(t_6, t_2), 2.0f)) / (floorf(h) * (dY_46_v * t_4))) > floorf(maxAniso)) {
		tmp = t_9;
	} else {
		tmp = t_12;
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_11 > floorf(maxAniso)) {
			tmp_4 = floorf(maxAniso);
		} else {
			tmp_4 = t_11;
		}
		float tmp_5;
		if ((fmaxf(powf(t_4, 2.0f), t_7) / t_10) > floorf(maxAniso)) {
			tmp_5 = t_9;
		} else {
			tmp_5 = t_12;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if ((fmaxf(fmaf(powf(dX_46_u, 2.0f), t_5, (powf(dX_46_v, 2.0f) * t_1)), fmaf(powf(dY_46_u, 2.0f), t_5, (t_1 * powf(dY_46_v, 2.0f)))) / (dX_46_u * (dY_46_v * t_3))) > floorf(maxAniso)) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_11;
	}
	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) * dX_46_v)
	t_1 = floor(h) ^ Float32(2.0)
	t_2 = Float32(floor(h) * dY_46_v)
	t_3 = Float32(floor(w) * floor(h))
	t_4 = Float32(floor(w) * dX_46_u)
	t_5 = floor(w) ^ Float32(2.0)
	t_6 = Float32(floor(w) * dY_46_u)
	t_7 = hypot(t_2, t_6) ^ Float32(2.0)
	t_8 = ((hypot(t_0, t_4) ^ Float32(2.0)) != (hypot(t_0, t_4) ^ Float32(2.0))) ? t_7 : ((t_7 != t_7) ? (hypot(t_0, t_4) ^ Float32(2.0)) : max((hypot(t_0, t_4) ^ Float32(2.0)), t_7))
	t_9 = Float32(sqrt(t_8) / floor(maxAniso))
	t_10 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * t_3)
	t_11 = Float32(t_8 / t_10)
	t_12 = Float32(t_10 * sqrt(Float32(Float32(1.0) / t_8)))
	tmp = Float32(0.0)
	if (Float32((((hypot(t_4, t_0) ^ Float32(2.0)) != (hypot(t_4, t_0) ^ Float32(2.0))) ? (hypot(t_6, t_2) ^ Float32(2.0)) : (((hypot(t_6, t_2) ^ Float32(2.0)) != (hypot(t_6, t_2) ^ Float32(2.0))) ? (hypot(t_4, t_0) ^ Float32(2.0)) : max((hypot(t_4, t_0) ^ Float32(2.0)), (hypot(t_6, t_2) ^ Float32(2.0))))) / Float32(floor(h) * Float32(dY_46_v * t_4))) > floor(maxAniso))
		tmp = t_9;
	else
		tmp = t_12;
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_11 > floor(maxAniso))
			tmp_4 = floor(maxAniso);
		else
			tmp_4 = t_11;
		end
		tmp_5 = Float32(0.0)
		if (Float32((((t_4 ^ Float32(2.0)) != (t_4 ^ Float32(2.0))) ? t_7 : ((t_7 != t_7) ? (t_4 ^ Float32(2.0)) : max((t_4 ^ Float32(2.0)), t_7))) / t_10) > floor(maxAniso))
			tmp_5 = t_9;
		else
			tmp_5 = t_12;
		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(((fma((dX_46_u ^ Float32(2.0)), t_5, Float32((dX_46_v ^ Float32(2.0)) * t_1)) != fma((dX_46_u ^ Float32(2.0)), t_5, Float32((dX_46_v ^ Float32(2.0)) * t_1))) ? fma((dY_46_u ^ Float32(2.0)), t_5, Float32(t_1 * (dY_46_v ^ Float32(2.0)))) : ((fma((dY_46_u ^ Float32(2.0)), t_5, Float32(t_1 * (dY_46_v ^ Float32(2.0)))) != fma((dY_46_u ^ Float32(2.0)), t_5, Float32(t_1 * (dY_46_v ^ Float32(2.0))))) ? fma((dX_46_u ^ Float32(2.0)), t_5, Float32((dX_46_v ^ Float32(2.0)) * t_1)) : max(fma((dX_46_u ^ Float32(2.0)), t_5, Float32((dX_46_v ^ Float32(2.0)) * t_1)), fma((dY_46_u ^ Float32(2.0)), t_5, Float32(t_1 * (dY_46_v ^ Float32(2.0))))))) / Float32(dX_46_u * Float32(dY_46_v * t_3))) > floor(maxAniso))
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_11;
	end
	return tmp_3
end

Derivation

1. Initial program 98.0%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\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\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 98.0%

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

5. Taylor expanded in w around 0 98.0%

   \[\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\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{1}{\left\lfloormaxAniso\right\rfloor} \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\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\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{1}{\left\lfloormaxAniso\right\rfloor} \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.8%

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

8. Taylor expanded in dX.v around 0 50.2%

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

10. Simplified 50.2%

    \[\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\lfloorw\right\rfloor, dX.v \cdot \left\lfloorh\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloorh\right\rfloor \cdot \left(dY.v \cdot \left(dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

11. Taylor expanded in dX.v around 0 50.4%

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

12. Taylor expanded in dX.v around 0 59.6%

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

    1. fma-define 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\lfloorw\right\rfloor, dX.v \cdot \left\lfloorh\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloorh\right\rfloor \cdot \left(dY.v \cdot \left(dX.u \cdot \left\lfloorw\right\rfloor\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(dX.u \cdot \left\lfloorw\right\rfloor\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\color{blue}{\mathsf{fma}\left({dX.u}^{2}, {\left(\left\lfloorw\right\rfloor\right)}^{2}, {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

    2. fma-define 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\lfloorw\right\rfloor, dX.v \cdot \left\lfloorh\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloorh\right\rfloor \cdot \left(dY.v \cdot \left(dX.u \cdot \left\lfloorw\right\rfloor\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(dX.u \cdot \left\lfloorw\right\rfloor\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left({dX.u}^{2}, {\left(\left\lfloorw\right\rfloor\right)}^{2}, {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right), \color{blue}{\mathsf{fma}\left({dY.u}^{2}, {\left(\left\lfloorw\right\rfloor\right)}^{2}, {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}\right)}{dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

    3. *-commutative 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\lfloorw\right\rfloor, dX.v \cdot \left\lfloorh\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloorh\right\rfloor \cdot \left(dY.v \cdot \left(dX.u \cdot \left\lfloorw\right\rfloor\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(dX.u \cdot \left\lfloorw\right\rfloor\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left({dX.u}^{2}, {\left(\left\lfloorw\right\rfloor\right)}^{2}, {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right), \mathsf{fma}\left({dY.u}^{2}, {\left(\left\lfloorw\right\rfloor\right)}^{2}, \color{blue}{{\left(\left\lfloorh\right\rfloor\right)}^{2} \cdot {dY.v}^{2}}\right)\right)}{dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

    4. *-commutative 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\lfloorw\right\rfloor, dX.v \cdot \left\lfloorh\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloorh\right\rfloor \cdot \left(dY.v \cdot \left(dX.u \cdot \left\lfloorw\right\rfloor\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(dX.u \cdot \left\lfloorw\right\rfloor\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left({dX.u}^{2}, {\left(\left\lfloorw\right\rfloor\right)}^{2}, {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right), \mathsf{fma}\left({dY.u}^{2}, {\left(\left\lfloorw\right\rfloor\right)}^{2}, {\left(\left\lfloorh\right\rfloor\right)}^{2} \cdot {dY.v}^{2}\right)\right)}{dX.u \cdot \left(dY.v \cdot \color{blue}{\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)}\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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\lfloorw\right\rfloor, dX.v \cdot \left\lfloorh\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloorh\right\rfloor \cdot \left(dY.v \cdot \left(dX.u \cdot \left\lfloorw\right\rfloor\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(dX.u \cdot \left\lfloorw\right\rfloor\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\color{blue}{\frac{\mathsf{max}\left(\mathsf{fma}\left({dX.u}^{2}, {\left(\left\lfloorw\right\rfloor\right)}^{2}, {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right), \mathsf{fma}\left({dY.u}^{2}, {\left(\left\lfloorw\right\rfloor\right)}^{2}, {\left(\left\lfloorh\right\rfloor\right)}^{2} \cdot {dY.v}^{2}\right)\right)}{dX.u \cdot \left(dY.v \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\right)}} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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(\left\lfloorw\right\rfloor \cdot dX.u, \left\lfloorh\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloorh\right\rfloor \cdot \left(dY.v \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\left\lfloorw\right\rfloor \cdot dX.u\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left({dX.u}^{2}, {\left(\left\lfloorw\right\rfloor\right)}^{2}, {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right), \mathsf{fma}\left({dY.u}^{2}, {\left(\left\lfloorw\right\rfloor\right)}^{2}, {\left(\left\lfloorh\right\rfloor\right)}^{2} \cdot {dY.v}^{2}\right)\right)}{dX.u \cdot \left(dY.v \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)}\\ \end{array} \]
16. Add Preprocessing

Alternative 6: 50.2% accurate, 1.3× speedup

Math

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

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

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(w) * floorf(h);
	float t_2 = floorf(w) * dX_46_u;
	float t_3 = floorf(w) * dY_46_u;
	float t_4 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * t_1;
	float t_5 = floorf(h) * dY_46_v;
	float t_6 = powf(hypotf(t_5, t_3), 2.0f);
	float t_7 = fmaxf(powf(hypotf(t_0, t_2), 2.0f), t_6);
	float t_8 = sqrtf(t_7) / floorf(maxAniso);
	float t_9 = t_7 / t_4;
	int t_10 = t_9 > floorf(maxAniso);
	float t_11 = t_4 * sqrtf((1.0f / t_7));
	float t_12 = fmaxf(powf(hypotf(t_2, t_0), 2.0f), powf(hypotf(t_3, t_5), 2.0f));
	float tmp;
	if ((t_12 / (floorf(h) * (dY_46_v * t_2))) > floorf(maxAniso)) {
		tmp = t_8;
	} else {
		tmp = t_11;
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_10) {
			tmp_4 = floorf(maxAniso);
		} else {
			tmp_4 = t_9;
		}
		float tmp_5;
		if ((fmaxf(powf(t_2, 2.0f), t_6) / t_4) > floorf(maxAniso)) {
			tmp_5 = t_8;
		} else {
			tmp_5 = t_11;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_10) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = fmaf(dX_46_v, ((t_12 / (dY_46_v * powf(dX_46_u, 2.0f))) * (dY_46_u / t_1)), (t_12 / (dX_46_u * t_1))) / dY_46_v;
	}
	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) * dX_46_v)
	t_1 = Float32(floor(w) * floor(h))
	t_2 = Float32(floor(w) * dX_46_u)
	t_3 = Float32(floor(w) * dY_46_u)
	t_4 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * t_1)
	t_5 = Float32(floor(h) * dY_46_v)
	t_6 = hypot(t_5, t_3) ^ Float32(2.0)
	t_7 = ((hypot(t_0, t_2) ^ Float32(2.0)) != (hypot(t_0, t_2) ^ Float32(2.0))) ? t_6 : ((t_6 != t_6) ? (hypot(t_0, t_2) ^ Float32(2.0)) : max((hypot(t_0, t_2) ^ Float32(2.0)), t_6))
	t_8 = Float32(sqrt(t_7) / floor(maxAniso))
	t_9 = Float32(t_7 / t_4)
	t_10 = t_9 > floor(maxAniso)
	t_11 = Float32(t_4 * sqrt(Float32(Float32(1.0) / t_7)))
	t_12 = ((hypot(t_2, t_0) ^ Float32(2.0)) != (hypot(t_2, t_0) ^ Float32(2.0))) ? (hypot(t_3, t_5) ^ Float32(2.0)) : (((hypot(t_3, t_5) ^ Float32(2.0)) != (hypot(t_3, t_5) ^ Float32(2.0))) ? (hypot(t_2, t_0) ^ Float32(2.0)) : max((hypot(t_2, t_0) ^ Float32(2.0)), (hypot(t_3, t_5) ^ Float32(2.0))))
	tmp = Float32(0.0)
	if (Float32(t_12 / Float32(floor(h) * Float32(dY_46_v * t_2))) > floor(maxAniso))
		tmp = t_8;
	else
		tmp = t_11;
	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 = t_9;
		end
		tmp_5 = Float32(0.0)
		if (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_4) > floor(maxAniso))
			tmp_5 = t_8;
		else
			tmp_5 = t_11;
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_10)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = Float32(fma(dX_46_v, Float32(Float32(t_12 / Float32(dY_46_v * (dX_46_u ^ Float32(2.0)))) * Float32(dY_46_u / t_1)), Float32(t_12 / Float32(dX_46_u * t_1))) / dY_46_v);
	end
	return tmp_3
end

Derivation

1. Initial program 98.0%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\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\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 98.0%

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

5. Taylor expanded in w around 0 98.0%

   \[\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\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{1}{\left\lfloormaxAniso\right\rfloor} \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\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\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{1}{\left\lfloormaxAniso\right\rfloor} \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.8%

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

8. Taylor expanded in dX.v around 0 50.2%

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

10. Simplified 50.2%

    \[\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\lfloorw\right\rfloor, dX.v \cdot \left\lfloorh\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloorh\right\rfloor \cdot \left(dY.v \cdot \left(dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

11. Taylor expanded in dX.v around 0 50.4%

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

12. Taylor expanded in dY.v around inf 51.0%

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

14. Simplified 51.0%

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

15. Final simplification 51.0%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dX.u, \left\lfloorh\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloorh\right\rfloor \cdot \left(dY.v \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\left\lfloorw\right\rfloor \cdot dX.u\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(dX.u \cdot dY.v - dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(dX.v, \frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dX.u, \left\lfloorh\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{dY.v \cdot {dX.u}^{2}} \cdot \frac{dY.u}{\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor}, \frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dX.u, \left\lfloorh\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{dX.u \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)}\right)}{dY.v}\\ \end{array} \]
16. Add Preprocessing

Alternative 7: 51.0% accurate, 1.3× speedup

Math

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

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) dX.u))
        (t_3 (* (floor w) dY.u))
        (t_4 (pow (hypot t_1 t_3) 2.0))
        (t_5 (fmax (pow (hypot t_0 t_2) 2.0) t_4))
        (t_6 (/ (sqrt t_5) (floor maxAniso)))
        (t_7 (* (- (* dX.u dY.v) (* dX.v dY.u)) (* (floor w) (floor h))))
        (t_8 (/ t_5 t_7))
        (t_9 (* t_7 (sqrt (/ 1.0 t_5))))
        (t_10 (if (> t_8 (floor maxAniso)) (floor maxAniso) t_8)))
   (if (<
        (if (>
             (/
              (fmax (pow (hypot t_2 t_0) 2.0) (pow (hypot t_3 t_1) 2.0))
              (* (floor h) (* dY.v t_2)))
             (floor maxAniso))
          t_6
          t_9)
        1.0)
     (fmax
      1.0
      (*
       t_10
       (if (>
            (/
             (fmax (pow t_2 2.0) t_4)
             (* (* dX.v dY.u) (* (floor w) (- (floor h)))))
            (floor maxAniso))
         t_6
         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) * dX_46_u;
	float t_3 = floorf(w) * dY_46_u;
	float t_4 = powf(hypotf(t_1, t_3), 2.0f);
	float t_5 = fmaxf(powf(hypotf(t_0, t_2), 2.0f), t_4);
	float t_6 = sqrtf(t_5) / floorf(maxAniso);
	float t_7 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floorf(w) * floorf(h));
	float t_8 = t_5 / t_7;
	float t_9 = t_7 * sqrtf((1.0f / t_5));
	float tmp;
	if (t_8 > floorf(maxAniso)) {
		tmp = floorf(maxAniso);
	} else {
		tmp = t_8;
	}
	float t_10 = tmp;
	float tmp_1;
	if ((fmaxf(powf(hypotf(t_2, t_0), 2.0f), powf(hypotf(t_3, t_1), 2.0f)) / (floorf(h) * (dY_46_v * t_2))) > floorf(maxAniso)) {
		tmp_1 = t_6;
	} else {
		tmp_1 = t_9;
	}
	float tmp_3;
	if (tmp_1 < 1.0f) {
		float tmp_4;
		if ((fmaxf(powf(t_2, 2.0f), t_4) / ((dX_46_v * dY_46_u) * (floorf(w) * -floorf(h)))) > floorf(maxAniso)) {
			tmp_4 = t_6;
		} else {
			tmp_4 = t_9;
		}
		tmp_3 = fmaxf(1.0f, (t_10 * tmp_4));
	} else {
		tmp_3 = t_10;
	}
	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) * dX_46_v)
	t_1 = Float32(floor(h) * dY_46_v)
	t_2 = Float32(floor(w) * dX_46_u)
	t_3 = Float32(floor(w) * dY_46_u)
	t_4 = hypot(t_1, t_3) ^ Float32(2.0)
	t_5 = ((hypot(t_0, t_2) ^ Float32(2.0)) != (hypot(t_0, t_2) ^ Float32(2.0))) ? t_4 : ((t_4 != t_4) ? (hypot(t_0, t_2) ^ Float32(2.0)) : max((hypot(t_0, t_2) ^ Float32(2.0)), t_4))
	t_6 = Float32(sqrt(t_5) / floor(maxAniso))
	t_7 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * Float32(floor(w) * floor(h)))
	t_8 = Float32(t_5 / t_7)
	t_9 = Float32(t_7 * sqrt(Float32(Float32(1.0) / t_5)))
	tmp = Float32(0.0)
	if (t_8 > floor(maxAniso))
		tmp = floor(maxAniso);
	else
		tmp = t_8;
	end
	t_10 = tmp
	tmp_1 = Float32(0.0)
	if (Float32((((hypot(t_2, t_0) ^ Float32(2.0)) != (hypot(t_2, t_0) ^ Float32(2.0))) ? (hypot(t_3, t_1) ^ Float32(2.0)) : (((hypot(t_3, t_1) ^ Float32(2.0)) != (hypot(t_3, t_1) ^ Float32(2.0))) ? (hypot(t_2, t_0) ^ Float32(2.0)) : max((hypot(t_2, t_0) ^ Float32(2.0)), (hypot(t_3, t_1) ^ Float32(2.0))))) / Float32(floor(h) * Float32(dY_46_v * t_2))) > floor(maxAniso))
		tmp_1 = t_6;
	else
		tmp_1 = t_9;
	end
	tmp_3 = Float32(0.0)
	if (tmp_1 < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (Float32((((t_2 ^ Float32(2.0)) != (t_2 ^ Float32(2.0))) ? t_4 : ((t_4 != t_4) ? (t_2 ^ Float32(2.0)) : max((t_2 ^ Float32(2.0)), t_4))) / Float32(Float32(dX_46_v * dY_46_u) * Float32(floor(w) * Float32(-floor(h))))) > floor(maxAniso))
			tmp_4 = t_6;
		else
			tmp_4 = t_9;
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(t_10 * tmp_4) : ((Float32(t_10 * tmp_4) != Float32(t_10 * tmp_4)) ? Float32(1.0) : max(Float32(1.0), Float32(t_10 * tmp_4)));
	else
		tmp_3 = t_10;
	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 = floor(h) * dX_46_v;
	t_1 = floor(h) * dY_46_v;
	t_2 = floor(w) * dX_46_u;
	t_3 = floor(w) * dY_46_u;
	t_4 = hypot(t_1, t_3) ^ single(2.0);
	t_5 = max((hypot(t_0, t_2) ^ single(2.0)), t_4);
	t_6 = sqrt(t_5) / floor(maxAniso);
	t_7 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floor(w) * floor(h));
	t_8 = t_5 / t_7;
	t_9 = t_7 * sqrt((single(1.0) / t_5));
	tmp = single(0.0);
	if (t_8 > floor(maxAniso))
		tmp = floor(maxAniso);
	else
		tmp = t_8;
	end
	t_10 = tmp;
	tmp_2 = single(0.0);
	if ((max((hypot(t_2, t_0) ^ single(2.0)), (hypot(t_3, t_1) ^ single(2.0))) / (floor(h) * (dY_46_v * t_2))) > floor(maxAniso))
		tmp_2 = t_6;
	else
		tmp_2 = t_9;
	end
	tmp_4 = single(0.0);
	if (tmp_2 < single(1.0))
		tmp_5 = single(0.0);
		if ((max((t_2 ^ single(2.0)), t_4) / ((dX_46_v * dY_46_u) * (floor(w) * -floor(h)))) > floor(maxAniso))
			tmp_5 = t_6;
		else
			tmp_5 = t_9;
		end
		tmp_4 = max(single(1.0), (t_10 * tmp_5));
	else
		tmp_4 = t_10;
	end
	tmp_6 = tmp_4;
end

Derivation

1. Initial program 98.0%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\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\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 98.0%

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

5. Taylor expanded in w around 0 98.0%

   \[\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\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{1}{\left\lfloormaxAniso\right\rfloor} \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\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\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{1}{\left\lfloormaxAniso\right\rfloor} \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.8%

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

8. Taylor expanded in dX.v around 0 50.2%

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

10. Simplified 50.2%

    \[\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\lfloorw\right\rfloor, dX.v \cdot \left\lfloorh\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloorh\right\rfloor \cdot \left(dY.v \cdot \left(dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

11. Taylor expanded in dX.v around 0 50.4%

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

12. Taylor expanded in dX.u around 0 50.9%

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

    1. mul-1-neg 50.9%

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

    2. distribute-neg-frac2 50.9%

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

14. Simplified 50.9%

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

15. Final simplification 50.9%

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

Alternative 8: 50.8% accurate, 1.3× speedup

Math

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

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

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) * floorf(h);
	float t_3 = floorf(w) * dX_46_u;
	float t_4 = floorf(w) * dY_46_u;
	float t_5 = powf(hypotf(t_1, t_4), 2.0f);
	float t_6 = fmaxf(powf(hypotf(t_0, t_3), 2.0f), t_5);
	float t_7 = sqrtf(t_6) / floorf(maxAniso);
	float t_8 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * t_2;
	float t_9 = t_6 / t_8;
	float t_10 = t_8 * sqrtf((1.0f / t_6));
	float tmp;
	if (t_9 > floorf(maxAniso)) {
		tmp = floorf(maxAniso);
	} else {
		tmp = t_9;
	}
	float t_11 = tmp;
	float tmp_1;
	if ((fmaxf(powf(hypotf(t_3, t_0), 2.0f), powf(hypotf(t_4, t_1), 2.0f)) / (floorf(h) * (dY_46_v * t_3))) > floorf(maxAniso)) {
		tmp_1 = t_7;
	} else {
		tmp_1 = t_10;
	}
	float tmp_3;
	if (tmp_1 < 1.0f) {
		float tmp_4;
		if ((fmaxf(powf(t_3, 2.0f), t_5) / ((dX_46_u * dY_46_v) * t_2)) > floorf(maxAniso)) {
			tmp_4 = t_7;
		} else {
			tmp_4 = t_10;
		}
		tmp_3 = fmaxf(1.0f, (t_11 * tmp_4));
	} else {
		tmp_3 = t_11;
	}
	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) * dX_46_v)
	t_1 = Float32(floor(h) * dY_46_v)
	t_2 = Float32(floor(w) * floor(h))
	t_3 = Float32(floor(w) * dX_46_u)
	t_4 = Float32(floor(w) * dY_46_u)
	t_5 = hypot(t_1, t_4) ^ Float32(2.0)
	t_6 = ((hypot(t_0, t_3) ^ Float32(2.0)) != (hypot(t_0, t_3) ^ Float32(2.0))) ? t_5 : ((t_5 != t_5) ? (hypot(t_0, t_3) ^ Float32(2.0)) : max((hypot(t_0, t_3) ^ Float32(2.0)), t_5))
	t_7 = Float32(sqrt(t_6) / floor(maxAniso))
	t_8 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * t_2)
	t_9 = Float32(t_6 / t_8)
	t_10 = Float32(t_8 * sqrt(Float32(Float32(1.0) / t_6)))
	tmp = Float32(0.0)
	if (t_9 > floor(maxAniso))
		tmp = floor(maxAniso);
	else
		tmp = t_9;
	end
	t_11 = tmp
	tmp_1 = Float32(0.0)
	if (Float32((((hypot(t_3, t_0) ^ Float32(2.0)) != (hypot(t_3, t_0) ^ Float32(2.0))) ? (hypot(t_4, t_1) ^ Float32(2.0)) : (((hypot(t_4, t_1) ^ Float32(2.0)) != (hypot(t_4, t_1) ^ Float32(2.0))) ? (hypot(t_3, t_0) ^ Float32(2.0)) : max((hypot(t_3, t_0) ^ Float32(2.0)), (hypot(t_4, t_1) ^ Float32(2.0))))) / Float32(floor(h) * Float32(dY_46_v * t_3))) > floor(maxAniso))
		tmp_1 = t_7;
	else
		tmp_1 = t_10;
	end
	tmp_3 = Float32(0.0)
	if (tmp_1 < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (Float32((((t_3 ^ Float32(2.0)) != (t_3 ^ Float32(2.0))) ? t_5 : ((t_5 != t_5) ? (t_3 ^ Float32(2.0)) : max((t_3 ^ Float32(2.0)), t_5))) / Float32(Float32(dX_46_u * dY_46_v) * t_2)) > floor(maxAniso))
			tmp_4 = t_7;
		else
			tmp_4 = t_10;
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(t_11 * tmp_4) : ((Float32(t_11 * tmp_4) != Float32(t_11 * tmp_4)) ? Float32(1.0) : max(Float32(1.0), Float32(t_11 * tmp_4)));
	else
		tmp_3 = t_11;
	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 = floor(h) * dX_46_v;
	t_1 = floor(h) * dY_46_v;
	t_2 = floor(w) * floor(h);
	t_3 = floor(w) * dX_46_u;
	t_4 = floor(w) * dY_46_u;
	t_5 = hypot(t_1, t_4) ^ single(2.0);
	t_6 = max((hypot(t_0, t_3) ^ single(2.0)), t_5);
	t_7 = sqrt(t_6) / floor(maxAniso);
	t_8 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * t_2;
	t_9 = t_6 / t_8;
	t_10 = t_8 * sqrt((single(1.0) / t_6));
	tmp = single(0.0);
	if (t_9 > floor(maxAniso))
		tmp = floor(maxAniso);
	else
		tmp = t_9;
	end
	t_11 = tmp;
	tmp_2 = single(0.0);
	if ((max((hypot(t_3, t_0) ^ single(2.0)), (hypot(t_4, t_1) ^ single(2.0))) / (floor(h) * (dY_46_v * t_3))) > floor(maxAniso))
		tmp_2 = t_7;
	else
		tmp_2 = t_10;
	end
	tmp_4 = single(0.0);
	if (tmp_2 < single(1.0))
		tmp_5 = single(0.0);
		if ((max((t_3 ^ single(2.0)), t_5) / ((dX_46_u * dY_46_v) * t_2)) > floor(maxAniso))
			tmp_5 = t_7;
		else
			tmp_5 = t_10;
		end
		tmp_4 = max(single(1.0), (t_11 * tmp_5));
	else
		tmp_4 = t_11;
	end
	tmp_6 = tmp_4;
end

Derivation

1. Initial program 98.0%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\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\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 98.0%

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

5. Taylor expanded in w around 0 98.0%

   \[\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\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{1}{\left\lfloormaxAniso\right\rfloor} \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\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\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{1}{\left\lfloormaxAniso\right\rfloor} \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.8%

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

8. Taylor expanded in dX.v around 0 50.2%

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

10. Simplified 50.2%

    \[\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\lfloorw\right\rfloor, dX.v \cdot \left\lfloorh\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloorh\right\rfloor \cdot \left(dY.v \cdot \left(dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

11. Taylor expanded in dX.v around 0 50.4%

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

12. Taylor expanded in dX.u around inf 50.7%

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

14. Simplified 50.7%

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

15. Final simplification 50.7%

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

Alternative 9: 49.5% accurate, 1.3× speedup

Math

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

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) dX.u))
        (t_3 (* (floor w) dY.u))
        (t_4 (pow (hypot t_1 t_3) 2.0))
        (t_5 (fmax (pow (hypot t_0 t_2) 2.0) t_4))
        (t_6 (/ (sqrt t_5) (floor maxAniso)))
        (t_7
         (>
          (/
           (fmax (pow (hypot t_2 t_0) 2.0) (pow (hypot t_3 t_1) 2.0))
           (* (floor h) (* dY.v t_2)))
          (floor maxAniso)))
        (t_8 (* (- (* dX.u dY.v) (* dX.v dY.u)) (* (floor w) (floor h))))
        (t_9 (* t_8 (sqrt (/ 1.0 t_5))))
        (t_10 (/ t_5 t_8)))
   (if (< (if t_7 t_6 t_9) 1.0)
     (fmax
      1.0
      (*
       (if (> (/ (fmax (pow t_2 2.0) t_4) t_8) (floor maxAniso)) t_6 t_9)
       (if t_7 (floor maxAniso) t_10)))
     (if (> t_10 (floor maxAniso)) (floor maxAniso) 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) * dX_46_u;
	float t_3 = floorf(w) * dY_46_u;
	float t_4 = powf(hypotf(t_1, t_3), 2.0f);
	float t_5 = fmaxf(powf(hypotf(t_0, t_2), 2.0f), t_4);
	float t_6 = sqrtf(t_5) / floorf(maxAniso);
	int t_7 = (fmaxf(powf(hypotf(t_2, t_0), 2.0f), powf(hypotf(t_3, t_1), 2.0f)) / (floorf(h) * (dY_46_v * t_2))) > floorf(maxAniso);
	float t_8 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floorf(w) * floorf(h));
	float t_9 = t_8 * sqrtf((1.0f / t_5));
	float t_10 = t_5 / t_8;
	float tmp;
	if (t_7) {
		tmp = t_6;
	} else {
		tmp = t_9;
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if ((fmaxf(powf(t_2, 2.0f), t_4) / t_8) > floorf(maxAniso)) {
			tmp_4 = t_6;
		} else {
			tmp_4 = t_9;
		}
		float tmp_5;
		if (t_7) {
			tmp_5 = floorf(maxAniso);
		} else {
			tmp_5 = t_10;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_10 > floorf(maxAniso)) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_10;
	}
	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) * dX_46_v)
	t_1 = Float32(floor(h) * dY_46_v)
	t_2 = Float32(floor(w) * dX_46_u)
	t_3 = Float32(floor(w) * dY_46_u)
	t_4 = hypot(t_1, t_3) ^ Float32(2.0)
	t_5 = ((hypot(t_0, t_2) ^ Float32(2.0)) != (hypot(t_0, t_2) ^ Float32(2.0))) ? t_4 : ((t_4 != t_4) ? (hypot(t_0, t_2) ^ Float32(2.0)) : max((hypot(t_0, t_2) ^ Float32(2.0)), t_4))
	t_6 = Float32(sqrt(t_5) / floor(maxAniso))
	t_7 = Float32((((hypot(t_2, t_0) ^ Float32(2.0)) != (hypot(t_2, t_0) ^ Float32(2.0))) ? (hypot(t_3, t_1) ^ Float32(2.0)) : (((hypot(t_3, t_1) ^ Float32(2.0)) != (hypot(t_3, t_1) ^ Float32(2.0))) ? (hypot(t_2, t_0) ^ Float32(2.0)) : max((hypot(t_2, t_0) ^ Float32(2.0)), (hypot(t_3, t_1) ^ Float32(2.0))))) / Float32(floor(h) * Float32(dY_46_v * t_2))) > floor(maxAniso)
	t_8 = Float32(Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)) * Float32(floor(w) * floor(h)))
	t_9 = Float32(t_8 * sqrt(Float32(Float32(1.0) / t_5)))
	t_10 = Float32(t_5 / t_8)
	tmp = Float32(0.0)
	if (t_7)
		tmp = t_6;
	else
		tmp = t_9;
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (Float32((((t_2 ^ Float32(2.0)) != (t_2 ^ Float32(2.0))) ? t_4 : ((t_4 != t_4) ? (t_2 ^ Float32(2.0)) : max((t_2 ^ Float32(2.0)), t_4))) / t_8) > floor(maxAniso))
			tmp_4 = t_6;
		else
			tmp_4 = t_9;
		end
		tmp_5 = Float32(0.0)
		if (t_7)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = t_10;
		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 > floor(maxAniso))
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_10;
	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) * dX_46_v;
	t_1 = floor(h) * dY_46_v;
	t_2 = floor(w) * dX_46_u;
	t_3 = floor(w) * dY_46_u;
	t_4 = hypot(t_1, t_3) ^ single(2.0);
	t_5 = max((hypot(t_0, t_2) ^ single(2.0)), t_4);
	t_6 = sqrt(t_5) / floor(maxAniso);
	t_7 = (max((hypot(t_2, t_0) ^ single(2.0)), (hypot(t_3, t_1) ^ single(2.0))) / (floor(h) * (dY_46_v * t_2))) > floor(maxAniso);
	t_8 = ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)) * (floor(w) * floor(h));
	t_9 = t_8 * sqrt((single(1.0) / t_5));
	t_10 = t_5 / t_8;
	tmp = single(0.0);
	if (t_7)
		tmp = t_6;
	else
		tmp = t_9;
	end
	tmp_4 = single(0.0);
	if (tmp < single(1.0))
		tmp_5 = single(0.0);
		if ((max((t_2 ^ single(2.0)), t_4) / t_8) > floor(maxAniso))
			tmp_5 = t_6;
		else
			tmp_5 = t_9;
		end
		tmp_6 = single(0.0);
		if (t_7)
			tmp_6 = floor(maxAniso);
		else
			tmp_6 = t_10;
		end
		tmp_4 = max(single(1.0), (tmp_5 * tmp_6));
	elseif (t_10 > floor(maxAniso))
		tmp_4 = floor(maxAniso);
	else
		tmp_4 = t_10;
	end
	tmp_7 = tmp_4;
end

Derivation

1. Initial program 98.0%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\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\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}{\sqrt{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dX.u\right) + \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dX.v\right), \left(\left\lfloorw\right\rfloor \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right) + \left(\left\lfloorh\right\rfloor \cdot dY.v\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right)}{\left|\left(\left\lfloorw\right\rfloor \cdot dX.u\right) \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right) - \left(\left\lfloorh\right\rfloor \cdot dX.v\right) \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\right|}\\ \end{array} \]

3. Simplified 98.0%

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

5. Taylor expanded in w around 0 98.0%

   \[\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\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{1}{\left\lfloormaxAniso\right\rfloor} \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\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\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{1}{\left\lfloormaxAniso\right\rfloor} \cdot \sqrt{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right| \cdot \sqrt{\frac{1}{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}, {dY.u}^{2} \cdot {\left(\left\lfloorw\right\rfloor\right)}^{2} + {dY.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right)}{\left|\left\lfloorw\right\rfloor \cdot \left(-1 \cdot \left(dX.v \cdot \left(dY.u \cdot \left\lfloorh\right\rfloor\right)\right) + dX.u \cdot \left(dY.v \cdot \left\lfloorh\right\rfloor\right)\right)\right|}\\ } \end{array}} \]

7. Simplified 57.8%

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

8. Taylor expanded in dX.v around 0 50.2%

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

10. Simplified 50.2%

    \[\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\lfloorw\right\rfloor, dX.v \cdot \left\lfloorh\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left\lfloorh\right\rfloor \cdot \left(dY.v \cdot \left(dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}} \cdot \left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)}\\ \end{array} \]

11. Taylor expanded in dX.v around 0 50.4%

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

12. Taylor expanded in dX.v around 0 50.0%

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

14. Simplified 50.0%

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

15. Final simplification 50.0%

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

Reproduce

herbie shell --seed 2024129 
(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))))))))