Anisotropic x16 LOD (ratio of anisotropy)

Percentage Accurate: 97.8% → 97.5%

Time: 1.6min

Alternatives: 8

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: 97.5% accurate, 1.0× speedup

Math

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

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_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))))
   (if (< t_9 1.0)
     (fmax 1.0 (* t_9 (if t_8 (floor maxAniso) t_7)))
     (if (> (/ t_4 (fabs (* dX.u (* (floor w) t_1)))) (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_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_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 * (floorf(w) * t_1)))) > 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_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_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(dX_46_u * Float32(floor(w) * t_1)))) > 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_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_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 * (floor(w) * t_1)))) > floor(maxAniso))
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_7;
	end
	tmp_5 = tmp_3;
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\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 98.0%

   \[\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* 98.0%

      \[\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|dX.u \cdot \color{blue}{\left(\left(dY.v \cdot \left\lfloorh\right\rfloor\right) \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 98.0%

   \[\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(\left(dY.v \cdot \left\lfloorh\right\rfloor\right) \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 98.0%

   \[\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:\\ \;\;\;\;\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} \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:\\ \;\;\;\;\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}\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|dX.u \cdot \left(\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\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} \]
7. Add Preprocessing

Alternative 2: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(\left\lfloorw\right\rfloor\right)}^{2}\\ t_1 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_2 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_3 := \left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\\ t_4 := \left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ t_5 := {\left(\left\lfloorh\right\rfloor\right)}^{2}\\ t_6 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_7 := \left|t\_3 \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\right)\right|\\ t_8 := \frac{\mathsf{max}\left(\mathsf{fma}\left({dX.u}^{2}, t\_0, {dX.v}^{2} \cdot t\_5\right), \mathsf{fma}\left({dY.u}^{2}, t\_0, t\_5 \cdot {dY.v}^{2}\right)\right)}{\left|dX.u \cdot \left(dY.v \cdot t\_3\right) - dX.v \cdot \left(\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot dY.u\right)\right)\right|}\\ t_9 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_10 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t\_1, t\_9\right)\right)}^{2}, {\left(\mathsf{hypot}\left(t\_6, t\_2\right)\right)}^{2}\right)\\ t_11 := \sqrt{t\_10}\\ t_12 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t\_9, t\_1\right)\right)}^{2}, {\left(\mathsf{hypot}\left(t\_2, t\_6\right)\right)}^{2}\right)\\ t_13 := \sqrt{t\_12}\\ t_14 := \frac{t\_10}{t\_4}\\ t_15 := t\_14 > \left\lfloormaxAniso\right\rfloor\\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{t\_12}{t\_7} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{t\_13}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;t\_7 \cdot \frac{1}{t\_13}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t\_15:\\ \;\;\;\;\frac{t\_11}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_4}{t\_11}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t\_15:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t\_14\\ \end{array}\right)\\ \mathbf{elif}\;t\_8 > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\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 (pow (floor w) 2.0))
        (t_1 (* (floor h) dX.v))
        (t_2 (* (floor w) dY.u))
        (t_3 (* (floor w) (floor h)))
        (t_4 (* (floor h) (* (floor w) (- (* dX.u dY.v) (* dX.v dY.u)))))
        (t_5 (pow (floor h) 2.0))
        (t_6 (* (floor h) dY.v))
        (t_7 (fabs (* t_3 (- (* dX.v dY.u) (* dX.u dY.v)))))
        (t_8
         (/
          (fmax
           (fma (pow dX.u 2.0) t_0 (* (pow dX.v 2.0) t_5))
           (fma (pow dY.u 2.0) t_0 (* t_5 (pow dY.v 2.0))))
          (fabs
           (-
            (* dX.u (* dY.v t_3))
            (* dX.v (* (floor w) (* (floor h) dY.u)))))))
        (t_9 (* (floor w) dX.u))
        (t_10 (fmax (pow (hypot t_1 t_9) 2.0) (pow (hypot t_6 t_2) 2.0)))
        (t_11 (sqrt t_10))
        (t_12 (fmax (pow (hypot t_9 t_1) 2.0) (pow (hypot t_2 t_6) 2.0)))
        (t_13 (sqrt t_12))
        (t_14 (/ t_10 t_4))
        (t_15 (> t_14 (floor maxAniso))))
   (if (<
        (if (> (/ t_12 t_7) (floor maxAniso))
          (/ t_13 (floor maxAniso))
          (* t_7 (/ 1.0 t_13)))
        1.0)
     (fmax
      1.0
      (*
       (if t_15 (/ t_11 (floor maxAniso)) (/ t_4 t_11))
       (if t_15 (floor maxAniso) t_14)))
     (if (> t_8 (floor maxAniso)) (floor maxAniso) t_8))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = powf(floorf(w), 2.0f);
	float t_1 = floorf(h) * dX_46_v;
	float t_2 = floorf(w) * dY_46_u;
	float t_3 = floorf(w) * floorf(h);
	float t_4 = floorf(h) * (floorf(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)));
	float t_5 = powf(floorf(h), 2.0f);
	float t_6 = floorf(h) * dY_46_v;
	float t_7 = fabsf((t_3 * ((dX_46_v * dY_46_u) - (dX_46_u * dY_46_v))));
	float t_8 = fmaxf(fmaf(powf(dX_46_u, 2.0f), t_0, (powf(dX_46_v, 2.0f) * t_5)), fmaf(powf(dY_46_u, 2.0f), t_0, (t_5 * powf(dY_46_v, 2.0f)))) / fabsf(((dX_46_u * (dY_46_v * t_3)) - (dX_46_v * (floorf(w) * (floorf(h) * dY_46_u)))));
	float t_9 = floorf(w) * dX_46_u;
	float t_10 = fmaxf(powf(hypotf(t_1, t_9), 2.0f), powf(hypotf(t_6, t_2), 2.0f));
	float t_11 = sqrtf(t_10);
	float t_12 = fmaxf(powf(hypotf(t_9, t_1), 2.0f), powf(hypotf(t_2, t_6), 2.0f));
	float t_13 = sqrtf(t_12);
	float t_14 = t_10 / t_4;
	int t_15 = t_14 > floorf(maxAniso);
	float tmp;
	if ((t_12 / t_7) > floorf(maxAniso)) {
		tmp = t_13 / floorf(maxAniso);
	} else {
		tmp = t_7 * (1.0f / t_13);
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_15) {
			tmp_4 = t_11 / floorf(maxAniso);
		} else {
			tmp_4 = t_4 / t_11;
		}
		float tmp_5;
		if (t_15) {
			tmp_5 = floorf(maxAniso);
		} else {
			tmp_5 = t_14;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_8 > floorf(maxAniso)) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_8;
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = floor(w) ^ Float32(2.0)
	t_1 = Float32(floor(h) * dX_46_v)
	t_2 = Float32(floor(w) * dY_46_u)
	t_3 = Float32(floor(w) * floor(h))
	t_4 = Float32(floor(h) * Float32(floor(w) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))))
	t_5 = floor(h) ^ Float32(2.0)
	t_6 = Float32(floor(h) * dY_46_v)
	t_7 = abs(Float32(t_3 * Float32(Float32(dX_46_v * dY_46_u) - Float32(dX_46_u * dY_46_v))))
	t_8 = Float32(((fma((dX_46_u ^ Float32(2.0)), t_0, Float32((dX_46_v ^ Float32(2.0)) * t_5)) != fma((dX_46_u ^ Float32(2.0)), t_0, Float32((dX_46_v ^ Float32(2.0)) * t_5))) ? fma((dY_46_u ^ Float32(2.0)), t_0, Float32(t_5 * (dY_46_v ^ Float32(2.0)))) : ((fma((dY_46_u ^ Float32(2.0)), t_0, Float32(t_5 * (dY_46_v ^ Float32(2.0)))) != fma((dY_46_u ^ Float32(2.0)), t_0, Float32(t_5 * (dY_46_v ^ Float32(2.0))))) ? fma((dX_46_u ^ Float32(2.0)), t_0, Float32((dX_46_v ^ Float32(2.0)) * t_5)) : max(fma((dX_46_u ^ Float32(2.0)), t_0, Float32((dX_46_v ^ Float32(2.0)) * t_5)), fma((dY_46_u ^ Float32(2.0)), t_0, Float32(t_5 * (dY_46_v ^ Float32(2.0))))))) / abs(Float32(Float32(dX_46_u * Float32(dY_46_v * t_3)) - Float32(dX_46_v * Float32(floor(w) * Float32(floor(h) * dY_46_u))))))
	t_9 = Float32(floor(w) * dX_46_u)
	t_10 = ((hypot(t_1, t_9) ^ Float32(2.0)) != (hypot(t_1, t_9) ^ 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_1, t_9) ^ Float32(2.0)) : max((hypot(t_1, t_9) ^ Float32(2.0)), (hypot(t_6, t_2) ^ Float32(2.0))))
	t_11 = sqrt(t_10)
	t_12 = ((hypot(t_9, t_1) ^ Float32(2.0)) != (hypot(t_9, t_1) ^ Float32(2.0))) ? (hypot(t_2, t_6) ^ Float32(2.0)) : (((hypot(t_2, t_6) ^ Float32(2.0)) != (hypot(t_2, t_6) ^ Float32(2.0))) ? (hypot(t_9, t_1) ^ Float32(2.0)) : max((hypot(t_9, t_1) ^ Float32(2.0)), (hypot(t_2, t_6) ^ Float32(2.0))))
	t_13 = sqrt(t_12)
	t_14 = Float32(t_10 / t_4)
	t_15 = t_14 > floor(maxAniso)
	tmp = Float32(0.0)
	if (Float32(t_12 / t_7) > floor(maxAniso))
		tmp = Float32(t_13 / floor(maxAniso));
	else
		tmp = Float32(t_7 * Float32(Float32(1.0) / t_13));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_15)
			tmp_4 = Float32(t_11 / floor(maxAniso));
		else
			tmp_4 = Float32(t_4 / t_11);
		end
		tmp_5 = Float32(0.0)
		if (t_15)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = t_14;
		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_8 > floor(maxAniso))
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_8;
	end
	return tmp_3
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\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

4. Applied egg-rr 97.2%

   \[\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:\\ \;\;\;\;\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 \left(dX.u \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right) - \left\lfloorh\right\rfloor \cdot \left(dX.v \cdot \left(\left\lfloorw\right\rfloor \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 \left(dX.u \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right) - \left\lfloorh\right\rfloor \cdot \left(dX.v \cdot \left(\left\lfloorw\right\rfloor \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 \left(dX.u \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right) - \left\lfloorh\right\rfloor \cdot \left(dX.v \cdot \left(\left\lfloorw\right\rfloor \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 \left(dX.u \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right) - \left\lfloorh\right\rfloor \cdot \left(dX.v \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\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. Simplified 97.2%

   \[\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:\\ \;\;\;\;\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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} \]

7. Taylor expanded in w around 0 97.2%

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

9. Simplified 97.2%

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

10. Taylor expanded in w around 0 97.3%

    \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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}:\\ \;\;\;\;\frac{1}{\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)}} \cdot \left|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \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({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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right)\right|}\\ \end{array} \]

12. Simplified 97.3%

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

13. Final simplification 97.3%

    \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\right)\right| \cdot \frac{1}{\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)}}\\ \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\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)}{\left|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\right) - dX.v \cdot \left(\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot dY.u\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\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)}{\left|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)\right) - dX.v \cdot \left(\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot dY.u\right)\right)\right|}\\ \end{array} \]
14. Add Preprocessing

Alternative 3: 97.6% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

MATLAB

function tmp_7 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = floor(h) * (floor(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)));
	t_1 = floor(w) * dY_46_u;
	t_2 = floor(w) * dX_46_u;
	t_3 = floor(h) * dX_46_v;
	t_4 = floor(h) * dY_46_v;
	t_5 = max(((t_2 * t_2) + (t_3 * t_3)), ((t_1 * t_1) + (t_4 * t_4))) / abs(((t_2 * t_4) - (t_3 * t_1)));
	t_6 = hypot(t_4, t_1) ^ single(2.0);
	t_7 = max((hypot(t_3, t_2) ^ single(2.0)), t_6);
	t_8 = sqrt(t_7);
	t_9 = max((hypot(t_2, t_3) ^ single(2.0)), (hypot(t_1, t_4) ^ single(2.0)));
	t_10 = sqrt(t_9);
	t_11 = abs(((floor(w) * floor(h)) * ((dX_46_v * dY_46_u) - (dX_46_u * dY_46_v))));
	t_12 = (t_7 / t_0) > floor(maxAniso);
	tmp = single(0.0);
	if ((t_9 / t_11) > floor(maxAniso))
		tmp = t_10 / floor(maxAniso);
	else
		tmp = t_11 * (single(1.0) / t_10);
	end
	tmp_4 = single(0.0);
	if (tmp < single(1.0))
		tmp_5 = single(0.0);
		if (t_12)
			tmp_5 = t_8 / floor(maxAniso);
		else
			tmp_5 = t_0 / t_8;
		end
		tmp_6 = single(0.0);
		if (t_12)
			tmp_6 = floor(maxAniso);
		else
			tmp_6 = max((t_3 ^ single(2.0)), t_6) / t_0;
		end
		tmp_4 = max(single(1.0), (tmp_5 * tmp_6));
	elseif (t_5 > floor(maxAniso))
		tmp_4 = floor(maxAniso);
	else
		tmp_4 = t_5;
	end
	tmp_7 = tmp_4;
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\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

4. Applied egg-rr 97.2%

   \[\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:\\ \;\;\;\;\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 \left(dX.u \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right) - \left\lfloorh\right\rfloor \cdot \left(dX.v \cdot \left(\left\lfloorw\right\rfloor \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 \left(dX.u \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right) - \left\lfloorh\right\rfloor \cdot \left(dX.v \cdot \left(\left\lfloorw\right\rfloor \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 \left(dX.u \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right) - \left\lfloorh\right\rfloor \cdot \left(dX.v \cdot \left(\left\lfloorw\right\rfloor \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 \left(dX.u \cdot \left(\left\lfloorh\right\rfloor \cdot dY.v\right)\right) - \left\lfloorh\right\rfloor \cdot \left(dX.v \cdot \left(\left\lfloorw\right\rfloor \cdot dY.u\right)\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. Simplified 97.2%

   \[\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:\\ \;\;\;\;\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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} \]

7. Taylor expanded in w around 0 97.2%

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

9. Simplified 97.2%

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

10. Taylor expanded in dX.v around inf 97.2%

    \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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}:\\ \;\;\;\;\frac{1}{\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)}} \cdot \left|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.v}^{2} \cdot {\left(\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\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} \]
11. Step-by-step derivation

    1. *-commutative 97.2%

       \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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}:\\ \;\;\;\;\frac{1}{\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)}} \cdot \left|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloorh\right\rfloor\right)}^{2} \cdot {dX.v}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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. unpow2 97.2%

       \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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}:\\ \;\;\;\;\frac{1}{\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)}} \cdot \left|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot {dX.v}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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. unpow2 97.2%

       \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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}:\\ \;\;\;\;\frac{1}{\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)}} \cdot \left|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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. swap-sqr 97.2%

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

    5. unpow2 97.2%

       \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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}:\\ \;\;\;\;\frac{1}{\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)}} \cdot \left|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloorh\right\rfloor \cdot dX.v\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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. *-commutative 97.2%

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

12. Simplified 97.2%

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

13. Final simplification 97.2%

    \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\right)\right| \cdot \frac{1}{\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)}}\\ \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\left(\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} \]
14. Add Preprocessing

Alternative 4: 60.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

MATLAB

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

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\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 w around 0 97.3%

   \[\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \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({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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \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({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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right)\right|}\\ } \end{array}} \]

5. Simplified 58.7%

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

6. Taylor expanded in dX.v around 0 59.5%

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

8. Simplified 59.5%

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

9. Taylor expanded in dX.v around inf 60.9%

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

11. Simplified 60.9%

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

12. Final simplification 60.9%

    \[\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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}:\\ \;\;\;\;dX.v \cdot \left(\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)}} \cdot \left(\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(-dY.u\right)\right)\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(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array} \]
13. Add Preprocessing

Alternative 5: 60.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_1 := \left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\\ t_2 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_3 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_4 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_5 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t\_0, t\_2\right)\right)}^{2}, {\left(\mathsf{hypot}\left(t\_4, t\_3\right)\right)}^{2}\right)\\ t_6 := {\left(\mathsf{hypot}\left(t\_3, t\_4\right)\right)}^{2}\\ t_7 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t\_2, t\_0\right)\right)}^{2}, t\_6\right)\\ t_8 := \frac{\sqrt{t\_7}}{\left\lfloormaxAniso\right\rfloor}\\ t_9 := \frac{t\_7}{t\_1}\\ t_10 := t\_9 > \left\lfloormaxAniso\right\rfloor\\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t\_10:\\ \;\;\;\;t\_8\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \sqrt{\frac{1}{t\_7}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t\_10:\\ \;\;\;\;t\_8\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \sqrt[3]{{\left(\frac{1}{t\_5}\right)}^{1.5}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{t\_5}{\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({t\_0}^{2}, t\_6\right)}{t\_1}\\ \end{array}\right)\\ \mathbf{elif}\;t\_10:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t\_9\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

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

Derivation

1. Initial program 97.2%

   \[\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 w around 0 97.3%

   \[\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \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({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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \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({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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right)\right|}\\ } \end{array}} \]

5. Simplified 58.7%

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

6. Taylor expanded in dX.v around 0 59.5%

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

8. Simplified 59.5%

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

   1. add-cbrt-cube 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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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[3]{\left(\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 \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)}}\right) \cdot \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\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\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array} \]

   2. add-sqr-sqrt 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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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[3]{\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 \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\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\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array} \]

   3. pow1 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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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[3]{{\left(\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)}\right)}^{1} \cdot \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\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\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array} \]

10. 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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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[3]{{\left(\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)}\right)}^{1.5}} \cdot \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)\\ \end{array} \cdot \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(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array} \]

11. Taylor expanded in dX.v around 0 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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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[3]{{\left(\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)}\right)}^{1.5}} \cdot \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)\\ \end{array} \cdot \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(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\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}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \end{array} \]
12. Step-by-step derivation

    1. unpow2 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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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[3]{{\left(\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)}\right)}^{1.5}} \cdot \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)\\ \end{array} \cdot \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(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.u \cdot dX.u\right) \cdot {\left(\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array} \]

    2. unpow2 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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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[3]{{\left(\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)}\right)}^{1.5}} \cdot \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)\\ \end{array} \cdot \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(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.u \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorw\right\rfloor\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \end{array} \]

    3. swap-sqr 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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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[3]{{\left(\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)}\right)}^{1.5}} \cdot \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)\\ \end{array} \cdot \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(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.u \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot \left\lfloorw\right\rfloor\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \end{array} \]

    4. unpow2 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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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[3]{{\left(\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)}\right)}^{1.5}} \cdot \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)\\ \end{array} \cdot \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(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array} \]

13. Simplified 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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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[3]{{\left(\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)}\right)}^{1.5}} \cdot \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)\\ \end{array} \cdot \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(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array} \]

14. 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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right) \cdot \sqrt{\frac{1}{\mathsf{max}\left({\left(\mathsf{hypot}\left(\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right) \cdot \sqrt[3]{{\left(\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)}\right)}^{1.5}}\\ \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(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array} \]
15. Add Preprocessing

Alternative 6: 59.2% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\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 w around 0 97.3%

   \[\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \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({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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \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({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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right)\right|}\\ } \end{array}} \]

5. Simplified 58.7%

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

6. Taylor expanded in dX.v around 0 59.5%

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

8. Simplified 59.5%

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

9. Taylor expanded in h around 0 59.5%

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

    1. fma-define 59.5%

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

    2. fma-define 59.5%

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

    3. *-commutative 59.5%

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

11. Simplified 59.5%

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

12. Taylor expanded in dX.v around inf 60.1%

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

    1. *-commutative 97.2%

       \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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}:\\ \;\;\;\;\frac{1}{\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)}} \cdot \left|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloorh\right\rfloor\right)}^{2} \cdot {dX.v}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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. unpow2 97.2%

       \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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}:\\ \;\;\;\;\frac{1}{\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)}} \cdot \left|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot {dX.v}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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. unpow2 97.2%

       \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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}:\\ \;\;\;\;\frac{1}{\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)}} \cdot \left|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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. swap-sqr 97.2%

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

    5. unpow2 97.2%

       \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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}:\\ \;\;\;\;\frac{1}{\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)}} \cdot \left|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloorh\right\rfloor \cdot dX.v\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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. *-commutative 97.2%

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

14. Simplified 60.1%

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

15. Final simplification 60.1%

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

Alternative 7: 59.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(w) * dX_46_u)
	t_1 = Float32(floor(w) * floor(h))
	t_2 = Float32(floor(h) * dX_46_v)
	t_3 = Float32(floor(h) * dY_46_v)
	t_4 = Float32(floor(w) * dY_46_u)
	t_5 = hypot(t_3, t_4) ^ Float32(2.0)
	t_6 = ((hypot(t_2, t_0) ^ Float32(2.0)) != (hypot(t_2, t_0) ^ Float32(2.0))) ? t_5 : ((t_5 != t_5) ? (hypot(t_2, t_0) ^ Float32(2.0)) : max((hypot(t_2, t_0) ^ Float32(2.0)), t_5))
	t_7 = Float32(sqrt(t_6) / floor(maxAniso))
	t_8 = Float32(floor(h) * Float32(floor(w) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))))
	t_9 = Float32(t_6 / t_8)
	t_10 = t_9 > floor(maxAniso)
	t_11 = ((hypot(t_0, t_2) ^ Float32(2.0)) != (hypot(t_0, t_2) ^ Float32(2.0))) ? (hypot(t_4, t_3) ^ Float32(2.0)) : (((hypot(t_4, t_3) ^ Float32(2.0)) != (hypot(t_4, t_3) ^ Float32(2.0))) ? (hypot(t_0, t_2) ^ Float32(2.0)) : max((hypot(t_0, t_2) ^ Float32(2.0)), (hypot(t_4, t_3) ^ Float32(2.0))))
	tmp = Float32(0.0)
	if (t_10)
		tmp = t_7;
	else
		tmp = Float32(dX_46_u * Float32(t_1 * Float32(dY_46_v * 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_10)
			tmp_4 = t_7;
		else
			tmp_4 = Float32(t_8 * sqrt(Float32(Float32(1.0) / t_6)));
		end
		tmp_5 = Float32(0.0)
		if (Float32(t_11 / Float32(t_1 * Float32(dX_46_u * dY_46_v))) > floor(maxAniso))
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = Float32((((t_2 ^ Float32(2.0)) != (t_2 ^ Float32(2.0))) ? t_5 : ((t_5 != t_5) ? (t_2 ^ Float32(2.0)) : max((t_2 ^ Float32(2.0)), t_5))) / t_8);
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_10)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_9;
	end
	return tmp_3
end

MATLAB

function tmp_7 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = floor(w) * dX_46_u;
	t_1 = floor(w) * floor(h);
	t_2 = floor(h) * dX_46_v;
	t_3 = floor(h) * dY_46_v;
	t_4 = floor(w) * dY_46_u;
	t_5 = hypot(t_3, t_4) ^ single(2.0);
	t_6 = max((hypot(t_2, t_0) ^ single(2.0)), t_5);
	t_7 = sqrt(t_6) / floor(maxAniso);
	t_8 = floor(h) * (floor(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)));
	t_9 = t_6 / t_8;
	t_10 = t_9 > floor(maxAniso);
	t_11 = max((hypot(t_0, t_2) ^ single(2.0)), (hypot(t_4, t_3) ^ single(2.0)));
	tmp = single(0.0);
	if (t_10)
		tmp = t_7;
	else
		tmp = dX_46_u * (t_1 * (dY_46_v * sqrt((single(1.0) / t_11))));
	end
	tmp_4 = single(0.0);
	if (tmp < single(1.0))
		tmp_5 = single(0.0);
		if (t_10)
			tmp_5 = t_7;
		else
			tmp_5 = t_8 * sqrt((single(1.0) / t_6));
		end
		tmp_6 = single(0.0);
		if ((t_11 / (t_1 * (dX_46_u * dY_46_v))) > floor(maxAniso))
			tmp_6 = floor(maxAniso);
		else
			tmp_6 = max((t_2 ^ single(2.0)), t_5) / t_8;
		end
		tmp_4 = max(single(1.0), (tmp_5 * tmp_6));
	elseif (t_10)
		tmp_4 = floor(maxAniso);
	else
		tmp_4 = t_9;
	end
	tmp_7 = tmp_4;
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\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 w around 0 97.3%

   \[\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \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({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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \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({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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right)\right|}\\ } \end{array}} \]

5. Simplified 58.7%

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

6. Taylor expanded in dX.v around 0 59.5%

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

8. Simplified 59.5%

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

9. Taylor expanded in dX.v around 0 59.2%

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

11. Simplified 59.4%

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

12. Taylor expanded in dX.v around inf 60.0%

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

    1. *-commutative 97.2%

       \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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}:\\ \;\;\;\;\frac{1}{\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)}} \cdot \left|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloorh\right\rfloor\right)}^{2} \cdot {dX.v}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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. unpow2 97.2%

       \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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}:\\ \;\;\;\;\frac{1}{\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)}} \cdot \left|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot {dX.v}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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. unpow2 97.2%

       \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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}:\\ \;\;\;\;\frac{1}{\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)}} \cdot \left|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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. swap-sqr 97.2%

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

    5. unpow2 97.2%

       \[\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|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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}:\\ \;\;\;\;\frac{1}{\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)}} \cdot \left|\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dY.u - dX.u \cdot dY.v\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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}:\\ \;\;\;\;\frac{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloorh\right\rfloor \cdot dX.v\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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. *-commutative 97.2%

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

14. Simplified 60.0%

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

15. Final simplification 60.0%

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

Alternative 8: 58.9% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(w) * dX_46_u)
	t_1 = Float32(floor(w) * floor(h))
	t_2 = Float32(floor(h) * dX_46_v)
	t_3 = Float32(floor(h) * dY_46_v)
	t_4 = Float32(floor(w) * dY_46_u)
	t_5 = hypot(t_3, t_4) ^ Float32(2.0)
	t_6 = ((hypot(t_2, t_0) ^ Float32(2.0)) != (hypot(t_2, t_0) ^ Float32(2.0))) ? t_5 : ((t_5 != t_5) ? (hypot(t_2, t_0) ^ Float32(2.0)) : max((hypot(t_2, t_0) ^ Float32(2.0)), t_5))
	t_7 = Float32(sqrt(t_6) / floor(maxAniso))
	t_8 = Float32(floor(h) * Float32(floor(w) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))))
	t_9 = Float32(t_6 / t_8)
	t_10 = t_9 > floor(maxAniso)
	t_11 = ((hypot(t_0, t_2) ^ Float32(2.0)) != (hypot(t_0, t_2) ^ Float32(2.0))) ? (hypot(t_4, t_3) ^ Float32(2.0)) : (((hypot(t_4, t_3) ^ Float32(2.0)) != (hypot(t_4, t_3) ^ Float32(2.0))) ? (hypot(t_0, t_2) ^ Float32(2.0)) : max((hypot(t_0, t_2) ^ Float32(2.0)), (hypot(t_4, t_3) ^ Float32(2.0))))
	tmp = Float32(0.0)
	if (t_10)
		tmp = t_7;
	else
		tmp = Float32(dX_46_u * Float32(t_1 * Float32(dY_46_v * 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_10)
			tmp_4 = t_7;
		else
			tmp_4 = Float32(t_8 * sqrt(Float32(Float32(1.0) / t_6)));
		end
		tmp_5 = Float32(0.0)
		if (Float32(t_11 / Float32(t_1 * Float32(dX_46_u * dY_46_v))) > floor(maxAniso))
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = Float32((((t_0 ^ Float32(2.0)) != (t_0 ^ Float32(2.0))) ? t_5 : ((t_5 != t_5) ? (t_0 ^ Float32(2.0)) : max((t_0 ^ Float32(2.0)), t_5))) / t_8);
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_10)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_9;
	end
	return tmp_3
end

MATLAB

function tmp_7 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = floor(w) * dX_46_u;
	t_1 = floor(w) * floor(h);
	t_2 = floor(h) * dX_46_v;
	t_3 = floor(h) * dY_46_v;
	t_4 = floor(w) * dY_46_u;
	t_5 = hypot(t_3, t_4) ^ single(2.0);
	t_6 = max((hypot(t_2, t_0) ^ single(2.0)), t_5);
	t_7 = sqrt(t_6) / floor(maxAniso);
	t_8 = floor(h) * (floor(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)));
	t_9 = t_6 / t_8;
	t_10 = t_9 > floor(maxAniso);
	t_11 = max((hypot(t_0, t_2) ^ single(2.0)), (hypot(t_4, t_3) ^ single(2.0)));
	tmp = single(0.0);
	if (t_10)
		tmp = t_7;
	else
		tmp = dX_46_u * (t_1 * (dY_46_v * sqrt((single(1.0) / t_11))));
	end
	tmp_4 = single(0.0);
	if (tmp < single(1.0))
		tmp_5 = single(0.0);
		if (t_10)
			tmp_5 = t_7;
		else
			tmp_5 = t_8 * sqrt((single(1.0) / t_6));
		end
		tmp_6 = single(0.0);
		if ((t_11 / (t_1 * (dX_46_u * dY_46_v))) > floor(maxAniso))
			tmp_6 = floor(maxAniso);
		else
			tmp_6 = max((t_0 ^ single(2.0)), t_5) / t_8;
		end
		tmp_4 = max(single(1.0), (tmp_5 * tmp_6));
	elseif (t_10)
		tmp_4 = floor(maxAniso);
	else
		tmp_4 = t_9;
	end
	tmp_7 = tmp_4;
end

Derivation

1. Initial program 97.2%

   \[\begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\left(\left\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 w around 0 97.3%

   \[\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \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({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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \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({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|dX.u \cdot \left(dY.v \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right) - dX.v \cdot \left(dY.u \cdot \left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right)\right)\right|}\\ } \end{array}} \]

5. Simplified 58.7%

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

6. Taylor expanded in dX.v around 0 59.5%

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

8. Simplified 59.5%

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

9. Taylor expanded in dX.v around 0 59.2%

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

11. Simplified 59.4%

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

    1. unpow2 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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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[3]{{\left(\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)}\right)}^{1.5}} \cdot \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)\\ \end{array} \cdot \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(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.u \cdot dX.u\right) \cdot {\left(\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array} \]

    2. unpow2 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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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[3]{{\left(\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)}\right)}^{1.5}} \cdot \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)\\ \end{array} \cdot \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(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.u \cdot dX.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorw\right\rfloor\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \end{array} \]

    3. swap-sqr 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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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[3]{{\left(\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)}\right)}^{1.5}} \cdot \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)\\ \end{array} \cdot \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(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.u \cdot \left\lfloorw\right\rfloor\right) \cdot \left(dX.u \cdot \left\lfloorw\right\rfloor\right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.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, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)}\\ \end{array} \]

    4. unpow2 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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right)\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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[3]{{\left(\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)}\right)}^{1.5}} \cdot \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)\\ \end{array} \cdot \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(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v\right)} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloorw\right\rfloor\right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot dY.u\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)} > \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\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array} \]

14. Simplified 59.6%

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

15. Final simplification 59.6%

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

Reproduce

herbie shell --seed 2024150 
(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))))))))