Anisotropic x16 LOD (ratio of anisotropy)

Percentage Accurate: 98.0% → 97.9%

Time: 2.3min

Alternatives: 1

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: 98.0% 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: 97.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ t_1 := \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\\ t_2 := \mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)\\ t_3 := \mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right), \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left\lfloorh\right\rfloor \cdot \left(dY.v \cdot dY.v\right), \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)\\ t_4 := \frac{t_3}{t_0}\\ t_5 := t_4 > \left\lfloormaxAniso\right\rfloor\\ t_6 := \sqrt{t_3}\\ t_7 := \frac{t_6}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t_5:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{t_6}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t_5:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;\left(\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot t_1\right)\right) \cdot {t_2}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t_5:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{t_1 \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)}\\ \end{array}\right)\\ \mathbf{elif}\;t_5:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

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

Derivation

1. Initial program 98.4%

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

3. Simplified 98.4%

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

5. Applied egg-rr 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right)\right) \cdot {\left(\mathsf{max}\left({\left(\left\lfloorw\right\rfloor\right)}^{2} \cdot {dX.u}^{2} + {\left(\left\lfloorh\right\rfloor \cdot dX.v\right)}^{2}, {\left(\left\lfloorh\right\rfloor\right)}^{2} \cdot {dY.v}^{2} + {\left(dY.u \cdot \left\lfloorw\right\rfloor\right)}^{2}\right)\right)}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]

7. Applied egg-rr 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;e^{\mathsf{log1p}\left(\left\lfloorh\right\rfloor \cdot \left(\left(\left\lfloorw\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right) \cdot {\left(\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\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)\right)}^{-0.5}\right)\right)} - 1\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]
8. Step-by-step derivation

   1. expm1-def 98.4%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{expm1}\left(\mathsf{log1p}\left(\left\lfloorh\right\rfloor \cdot \left(\left(\left\lfloorw\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right) \cdot {\left(\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\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)\right)}^{-0.5}\right)\right)\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]

   2. expm1-log1p 98.4%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left\lfloorh\right\rfloor \cdot \left(\left(\left\lfloorw\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right) \cdot {\left(\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\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)\right)}^{-0.5}\right)\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]

   3. associate-*r* 98.4%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right)\right) \cdot {\left(\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\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)\right)}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]

   4. associate-*r* 98.4%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left\lfloorh\right\rfloor \cdot \left\lfloorw\right\rfloor\right) \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right) \cdot {\left(\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\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)\right)}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]

   5. *-commutative 98.4%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right) \cdot {\left(\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\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)\right)}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]

   6. fma-def 98.4%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.u \cdot dY.v + dX.v \cdot dY.u\right)\right) \cdot {\left(\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\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)\right)}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]

   7. +-commutative 98.4%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\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 {\left(\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\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)\right)}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]

   8. fma-udef 98.4%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \mathsf{fma}\left(dX.v, dY.u, dX.u \cdot dY.v\right)\right) \cdot {\left(\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\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)\right)}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]

   9. associate-*r* 98.4%

      \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \mathsf{fma}\left(dX.v, dY.u, dX.u \cdot dY.v\right)\right)\right) \cdot {\left(\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\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)\right)}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]

9. Simplified 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right)\right) \cdot {\left(\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloorh\right\rfloor, dX.u \cdot \left\lfloorw\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)}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]

11. Applied egg-rr 98.4%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right)\right) \cdot {\left(\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloorh\right\rfloor, dX.u \cdot \left\lfloorw\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)}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left({\left(\left\lfloorw\right\rfloor\right)}^{2} \cdot {dX.u}^{2} + {\left(\left\lfloorh\right\rfloor \cdot dX.v\right)}^{2}, {\left(\left\lfloorh\right\rfloor\right)}^{2} \cdot {dY.v}^{2} + {\left(dY.u \cdot \left\lfloorw\right\rfloor\right)}^{2}\right) \cdot \frac{1}{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]
12. Step-by-step derivation

    1. un-div-inv 98.4%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right)\right) \cdot {\left(\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloorh\right\rfloor, dX.u \cdot \left\lfloorw\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)}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\left\lfloorw\right\rfloor\right)}^{2} \cdot {dX.u}^{2} + {\left(\left\lfloorh\right\rfloor \cdot dX.v\right)}^{2}, {\left(\left\lfloorh\right\rfloor\right)}^{2} \cdot {dY.v}^{2} + {\left(dY.u \cdot \left\lfloorw\right\rfloor\right)}^{2}\right)}{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]

    2. *-commutative 98.4%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right)\right) \cdot {\left(\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloorh\right\rfloor, dX.u \cdot \left\lfloorw\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)}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\color{blue}{\frac{\mathsf{max}\left({\left(\left\lfloorw\right\rfloor\right)}^{2} \cdot {dX.u}^{2} + {\left(\left\lfloorh\right\rfloor \cdot dX.v\right)}^{2}, {\left(\left\lfloorh\right\rfloor\right)}^{2} \cdot {dY.v}^{2} + {\left(dY.u \cdot \left\lfloorw\right\rfloor\right)}^{2}\right)}{\left(\left\lfloorw\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right) \cdot \left\lfloorh\right\rfloor}}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]

13. Applied egg-rr 98.4%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right)\right) \cdot {\left(\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloorh\right\rfloor, dX.u \cdot \left\lfloorw\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)}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\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\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left(dX.u \cdot dX.u\right) \cdot \left\lfloorw\right\rfloor, \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left(dY.v \cdot dY.v\right) \cdot \left\lfloorh\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(\left(dY.u \cdot dY.u\right) \cdot \left\lfloorw\right\rfloor\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v + dX.v \cdot \left(-dY.u\right)\right)\right)\right|}\\ \end{array} \]

14. Final simplification 98.4%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right), \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left\lfloorh\right\rfloor \cdot \left(dY.v \cdot dY.v\right), \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right), \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left\lfloorh\right\rfloor \cdot \left(dY.v \cdot dY.v\right), \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{\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|}{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right), \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left\lfloorh\right\rfloor \cdot \left(dY.v \cdot dY.v\right), \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right), \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left\lfloorh\right\rfloor \cdot \left(dY.v \cdot dY.v\right), \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right), \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left\lfloorh\right\rfloor \cdot \left(dY.v \cdot dY.v\right), \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)}}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\left(\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right)\right)\right) \cdot {\left(\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\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)\right)}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right), \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left\lfloorh\right\rfloor \cdot \left(dY.v \cdot dY.v\right), \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\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\lfloorw\right\rfloor \cdot dY.u, \left\lfloorh\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\mathsf{fma}\left(dX.u, dY.v, dX.v \cdot dY.u\right) \cdot \left(\left\lfloorw\right\rfloor \cdot \left\lfloorh\right\rfloor\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right), \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left\lfloorh\right\rfloor \cdot \left(dY.v \cdot dY.v\right), \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right), \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dX.v \cdot dX.v\right)\right), \mathsf{fma}\left(\left\lfloorh\right\rfloor, \left\lfloorh\right\rfloor \cdot \left(dY.v \cdot dY.v\right), \left\lfloorw\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right)\right)\right)\right)}{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|}\\ \end{array} \]

Reproduce

herbie shell --seed 2023312 
(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))))))))