Anisotropic x16 LOD (ratio of anisotropy)

Percentage Accurate: 97.7% → 97.7%

Time: 1.5min

Alternatives: 7

Speedup: N/A×

• Could not converge on a ground truth

  1. w = 2.158085823059082
  2. h = 827.0936279296875
  3. dX.u = 1.3374518506581445e-11
  4. dX.v = -2.8966391255380586e-5
  5. dY.u = 1.6998606048922643e-18
  6. dY.v = 15355440.0
  7. maxAniso = 16.0

Specification

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

Math

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

FPCore

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

C

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

Julia

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

MATLAB

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

MATLAB

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

Alternative 1: 97.7% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Derivation

1. Initial program 98.7%

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

3. Simplified 98.8%

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

6. Applied egg-rr 98.8%

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

8. Simplified 98.8%

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

9. Taylor expanded in w around 0 98.8%

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

11. Simplified 98.8%

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

12. Final simplification 98.8%

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

Alternative 2: 97.7% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

MATLAB

function tmp_7 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = (dX_46_u * dY_46_v) - (dX_46_v * dY_46_u);
	t_1 = dX_46_v * floor(h);
	t_2 = floor(h) * (floor(w) * t_0);
	t_3 = floor(w) * dY_46_u;
	t_4 = floor(h) * dY_46_v;
	t_5 = abs((floor(w) * (floor(h) * t_0)));
	t_6 = dX_46_u * floor(w);
	t_7 = max((hypot(t_1, t_6) ^ single(2.0)), (hypot(t_4, t_3) ^ single(2.0)));
	t_8 = sqrt(t_7);
	t_9 = max(((t_6 * t_6) + (t_1 * t_1)), ((t_3 * t_3) + (t_4 * t_4))) / abs(((t_6 * t_4) - (t_3 * t_1)));
	t_10 = max((hypot(t_6, t_1) ^ single(2.0)), (hypot(t_3, t_4) ^ single(2.0)));
	t_11 = sqrt(t_10);
	t_12 = t_7 / t_2;
	t_13 = t_12 > floor(maxAniso);
	tmp = single(0.0);
	if ((t_10 / t_5) > floor(maxAniso))
		tmp = t_11 / floor(maxAniso);
	else
		tmp = t_5 * (single(1.0) / t_11);
	end
	tmp_4 = single(0.0);
	if (tmp < single(1.0))
		tmp_5 = single(0.0);
		if (t_13)
			tmp_5 = t_8 / floor(maxAniso);
		else
			tmp_5 = t_2 / t_8;
		end
		tmp_6 = single(0.0);
		if (t_13)
			tmp_6 = floor(maxAniso);
		else
			tmp_6 = t_12;
		end
		tmp_4 = max(single(1.0), (tmp_5 * tmp_6));
	elseif (t_9 > floor(maxAniso))
		tmp_4 = floor(maxAniso);
	else
		tmp_4 = t_9;
	end
	tmp_7 = tmp_4;
end

Derivation

1. Initial program 98.7%

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

4. Applied egg-rr 98.7%

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

6. Simplified 98.7%

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

7. Taylor expanded in w around 0 98.7%

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

9. Simplified 98.7%

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

10. Final simplification 98.7%

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

Alternative 3: 97.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := dX.u \cdot dY.v - dX.v \cdot dY.u\\ t_1 := \left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot t\_0\right)\\ t_2 := \left\lfloor w\right\rfloor \cdot dY.u\\ t_3 := dX.u \cdot \left\lfloor w\right\rfloor \\ t_4 := dX.u \cdot \left\lfloor h\right\rfloor \\ t_5 := dX.v \cdot \left\lfloor h\right\rfloor \\ t_6 := {\left(\mathsf{hypot}\left(t\_3, t\_5\right)\right)}^{2}\\ t_7 := \left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \\ t_8 := \left\lfloor h\right\rfloor \cdot dY.v\\ t_9 := {\left(\mathsf{hypot}\left(t\_8, t\_2\right)\right)}^{2}\\ t_10 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t\_5, t\_3\right)\right)}^{2}, t\_9\right)\\ t_11 := \sqrt{t\_10}\\ t_12 := \mathsf{max}\left(t\_6, {\left(\mathsf{hypot}\left(t\_2, t\_8\right)\right)}^{2}\right)\\ t_13 := \sqrt{t\_12}\\ t_14 := \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot t\_0\right)\right|\\ t_15 := \frac{t\_10}{t\_1} > \left\lfloor maxAniso\right\rfloor \\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{t\_12}{t\_14} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{t\_13}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;t\_14 \cdot \frac{1}{t\_13}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t\_15:\\ \;\;\;\;\frac{t\_11}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{t\_11}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t\_15:\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({t\_5}^{2}, t\_9\right)}{t\_1}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dX.u\right), dX.v \cdot \left(dX.v \cdot t\_7\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left\lfloor w\right\rfloor \cdot \left(dY.u \cdot dY.u\right), t\_7 \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, t\_4, dY.u \cdot \left(dX.v \cdot \left(-\left\lfloor h\right\rfloor \right)\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left(t\_6, t\_9\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, t\_4, \left\lfloor h\right\rfloor \cdot \left(-dX.v \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \end{array} \]

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (- (* dX.u dY.v) (* dX.v dY.u)))
        (t_1 (* (floor h) (* (floor w) t_0)))
        (t_2 (* (floor w) dY.u))
        (t_3 (* dX.u (floor w)))
        (t_4 (* dX.u (floor h)))
        (t_5 (* dX.v (floor h)))
        (t_6 (pow (hypot t_3 t_5) 2.0))
        (t_7 (* (floor h) (floor h)))
        (t_8 (* (floor h) dY.v))
        (t_9 (pow (hypot t_8 t_2) 2.0))
        (t_10 (fmax (pow (hypot t_5 t_3) 2.0) t_9))
        (t_11 (sqrt t_10))
        (t_12 (fmax t_6 (pow (hypot t_2 t_8) 2.0)))
        (t_13 (sqrt t_12))
        (t_14 (fabs (* (floor w) (* (floor h) t_0))))
        (t_15 (> (/ t_10 t_1) (floor maxAniso))))
   (if (<
        (if (> (/ t_12 t_14) (floor maxAniso))
          (/ t_13 (floor maxAniso))
          (* t_14 (/ 1.0 t_13)))
        1.0)
     (fmax
      1.0
      (*
       (if t_15 (/ t_11 (floor maxAniso)) (/ t_1 t_11))
       (if t_15 (floor maxAniso) (/ (fmax (pow t_5 2.0) t_9) t_1))))
     (if (>
          (/
           (fmax
            (fma (floor w) (* (floor w) (* dX.u dX.u)) (* dX.v (* dX.v t_7)))
            (fma (floor w) (* (floor w) (* dY.u dY.u)) (* t_7 (* dY.v dY.v))))
           (fabs (* (floor w) (fma dY.v t_4 (* dY.u (* dX.v (- (floor h))))))))
          (floor maxAniso))
       (floor maxAniso)
       (pow
        (pow
         (/
          (fmax t_6 t_9)
          (fabs (* (floor w) (fma dY.v t_4 (* (floor h) (- (* dX.v dY.u)))))))
         3.0)
        0.3333333333333333)))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = (dX_46_u * dY_46_v) - (dX_46_v * dY_46_u);
	float t_1 = floorf(h) * (floorf(w) * t_0);
	float t_2 = floorf(w) * dY_46_u;
	float t_3 = dX_46_u * floorf(w);
	float t_4 = dX_46_u * floorf(h);
	float t_5 = dX_46_v * floorf(h);
	float t_6 = powf(hypotf(t_3, t_5), 2.0f);
	float t_7 = floorf(h) * floorf(h);
	float t_8 = floorf(h) * dY_46_v;
	float t_9 = powf(hypotf(t_8, t_2), 2.0f);
	float t_10 = fmaxf(powf(hypotf(t_5, t_3), 2.0f), t_9);
	float t_11 = sqrtf(t_10);
	float t_12 = fmaxf(t_6, powf(hypotf(t_2, t_8), 2.0f));
	float t_13 = sqrtf(t_12);
	float t_14 = fabsf((floorf(w) * (floorf(h) * t_0)));
	int t_15 = (t_10 / t_1) > floorf(maxAniso);
	float tmp;
	if ((t_12 / t_14) > floorf(maxAniso)) {
		tmp = t_13 / floorf(maxAniso);
	} else {
		tmp = t_14 * (1.0f / t_13);
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_15) {
			tmp_4 = t_11 / floorf(maxAniso);
		} else {
			tmp_4 = t_1 / t_11;
		}
		float tmp_5;
		if (t_15) {
			tmp_5 = floorf(maxAniso);
		} else {
			tmp_5 = fmaxf(powf(t_5, 2.0f), t_9) / t_1;
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if ((fmaxf(fmaf(floorf(w), (floorf(w) * (dX_46_u * dX_46_u)), (dX_46_v * (dX_46_v * t_7))), fmaf(floorf(w), (floorf(w) * (dY_46_u * dY_46_u)), (t_7 * (dY_46_v * dY_46_v)))) / fabsf((floorf(w) * fmaf(dY_46_v, t_4, (dY_46_u * (dX_46_v * -floorf(h))))))) > floorf(maxAniso)) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = powf(powf((fmaxf(t_6, t_9) / fabsf((floorf(w) * fmaf(dY_46_v, t_4, (floorf(h) * -(dX_46_v * dY_46_u)))))), 3.0f), 0.3333333333333333f);
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))
	t_1 = Float32(floor(h) * Float32(floor(w) * t_0))
	t_2 = Float32(floor(w) * dY_46_u)
	t_3 = Float32(dX_46_u * floor(w))
	t_4 = Float32(dX_46_u * floor(h))
	t_5 = Float32(dX_46_v * floor(h))
	t_6 = hypot(t_3, t_5) ^ Float32(2.0)
	t_7 = Float32(floor(h) * floor(h))
	t_8 = Float32(floor(h) * dY_46_v)
	t_9 = hypot(t_8, t_2) ^ Float32(2.0)
	t_10 = ((hypot(t_5, t_3) ^ Float32(2.0)) != (hypot(t_5, t_3) ^ Float32(2.0))) ? t_9 : ((t_9 != t_9) ? (hypot(t_5, t_3) ^ Float32(2.0)) : max((hypot(t_5, t_3) ^ Float32(2.0)), t_9))
	t_11 = sqrt(t_10)
	t_12 = (t_6 != t_6) ? (hypot(t_2, t_8) ^ Float32(2.0)) : (((hypot(t_2, t_8) ^ Float32(2.0)) != (hypot(t_2, t_8) ^ Float32(2.0))) ? t_6 : max(t_6, (hypot(t_2, t_8) ^ Float32(2.0))))
	t_13 = sqrt(t_12)
	t_14 = abs(Float32(floor(w) * Float32(floor(h) * t_0)))
	t_15 = Float32(t_10 / t_1) > floor(maxAniso)
	tmp = Float32(0.0)
	if (Float32(t_12 / t_14) > floor(maxAniso))
		tmp = Float32(t_13 / floor(maxAniso));
	else
		tmp = Float32(t_14 * Float32(Float32(1.0) / t_13));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_15)
			tmp_4 = Float32(t_11 / floor(maxAniso));
		else
			tmp_4 = Float32(t_1 / t_11);
		end
		tmp_5 = Float32(0.0)
		if (t_15)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = Float32((((t_5 ^ Float32(2.0)) != (t_5 ^ Float32(2.0))) ? t_9 : ((t_9 != t_9) ? (t_5 ^ Float32(2.0)) : max((t_5 ^ Float32(2.0)), t_9))) / t_1);
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (Float32(((fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(dX_46_v * Float32(dX_46_v * t_7))) != fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(dX_46_v * Float32(dX_46_v * t_7)))) ? fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(t_7 * Float32(dY_46_v * dY_46_v))) : ((fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(t_7 * Float32(dY_46_v * dY_46_v))) != fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(t_7 * Float32(dY_46_v * dY_46_v)))) ? fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(dX_46_v * Float32(dX_46_v * t_7))) : max(fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(dX_46_v * Float32(dX_46_v * t_7))), fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(t_7 * Float32(dY_46_v * dY_46_v)))))) / abs(Float32(floor(w) * fma(dY_46_v, t_4, Float32(dY_46_u * Float32(dX_46_v * Float32(-floor(h)))))))) > floor(maxAniso))
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = (Float32(((t_6 != t_6) ? t_9 : ((t_9 != t_9) ? t_6 : max(t_6, t_9))) / abs(Float32(floor(w) * fma(dY_46_v, t_4, Float32(floor(h) * Float32(-Float32(dX_46_v * dY_46_u))))))) ^ Float32(3.0)) ^ Float32(0.3333333333333333);
	end
	return tmp_3
end

Derivation

1. Initial program 98.7%

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

3. Simplified 98.8%

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

6. Applied egg-rr 98.8%

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

8. Simplified 98.8%

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

9. Taylor expanded in w around 0 98.8%

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

11. Simplified 98.8%

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

13. Applied egg-rr 98.7%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} \cdot \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(-dX.v\right) \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

14. Taylor expanded in dX.v around inf 98.7%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} \cdot \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({dX.v}^{2} \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(-dX.v\right) \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]
15. Step-by-step derivation

    1. unpow2 98.7%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} \cdot \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.v \cdot dX.v\right) \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(-dX.v\right) \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

    2. unpow2 98.7%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} \cdot \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.v \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(-dX.v\right) \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

    3. swap-sqr 98.7%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} \cdot \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.v \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dX.v \cdot \left\lfloor h\right\rfloor \right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(-dX.v\right) \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

    4. unpow2 98.7%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} \cdot \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.v \cdot \left\lfloor h\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(-dX.v\right) \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

16. Simplified 98.7%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} \cdot \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.v \cdot \left\lfloor h\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(-dX.v\right) \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

17. Final simplification 98.7%

    \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right| \cdot \frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.v \cdot \left\lfloor h\right\rfloor , dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.v \cdot \left\lfloor h\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dX.u\right), dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left\lfloor w\right\rfloor \cdot \left(dY.u \cdot dY.u\right), \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , dY.u \cdot \left(dX.v \cdot \left(-\left\lfloor h\right\rfloor \right)\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(-dX.v \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]
18. Add Preprocessing

Alternative 4: 60.5% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(dX_46_u * floor(w))
	t_1 = Float32(floor(h) * Float32(floor(w) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))))
	t_2 = hypot(Float32(floor(h) * dY_46_v), Float32(floor(w) * dY_46_u)) ^ Float32(2.0)
	t_3 = ((hypot(Float32(dX_46_v * floor(h)), t_0) ^ Float32(2.0)) != (hypot(Float32(dX_46_v * floor(h)), t_0) ^ Float32(2.0))) ? t_2 : ((t_2 != t_2) ? (hypot(Float32(dX_46_v * floor(h)), t_0) ^ Float32(2.0)) : max((hypot(Float32(dX_46_v * floor(h)), t_0) ^ Float32(2.0)), t_2))
	t_4 = Float32(sqrt(t_3) / floor(maxAniso))
	t_5 = Float32(t_3 / t_1)
	t_6 = t_5 > floor(maxAniso)
	t_7 = sqrt(Float32(Float32(1.0) / t_3))
	tmp = Float32(0.0)
	if (t_6)
		tmp = t_4;
	else
		tmp = Float32(t_1 * t_7);
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_6)
			tmp_4 = t_4;
		else
			tmp_4 = Float32(dX_46_v * Float32(t_7 * Float32(dY_46_u * Float32(floor(w) * Float32(-floor(h))))));
		end
		tmp_5 = Float32(0.0)
		if (t_6)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = Float32((((t_0 ^ Float32(2.0)) != (t_0 ^ Float32(2.0))) ? t_2 : ((t_2 != t_2) ? (t_0 ^ Float32(2.0)) : max((t_0 ^ Float32(2.0)), t_2))) / Float32(Float32(dX_46_u * dY_46_v) * 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_6)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_5;
	end
	return tmp_3
end

MATLAB

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

Derivation

1. Initial program 98.7%

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

3. Taylor expanded in w around 0 98.7%

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

5. Simplified 56.6%

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

6. Taylor expanded in dX.v around 0 57.2%

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

   1. unpow2 57.2%

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

   2. unpow2 57.2%

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

   3. swap-sqr 57.2%

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

   4. unpow2 57.2%

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

8. Simplified 57.2%

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

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

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

11. Simplified 59.2%

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

12. Taylor expanded in dX.u around inf 59.4%

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

14. Simplified 59.4%

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

15. Final simplification 59.4%

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

Alternative 5: 60.6% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(dX_46_u * floor(w))
	t_1 = hypot(Float32(floor(h) * dY_46_v), Float32(floor(w) * dY_46_u)) ^ Float32(2.0)
	t_2 = ((hypot(Float32(dX_46_v * floor(h)), t_0) ^ Float32(2.0)) != (hypot(Float32(dX_46_v * floor(h)), t_0) ^ Float32(2.0))) ? t_1 : ((t_1 != t_1) ? (hypot(Float32(dX_46_v * floor(h)), t_0) ^ Float32(2.0)) : max((hypot(Float32(dX_46_v * floor(h)), t_0) ^ Float32(2.0)), t_1))
	t_3 = Float32(sqrt(t_2) / floor(maxAniso))
	t_4 = Float32(floor(h) * Float32(floor(w) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))))
	t_5 = Float32(t_2 / t_4)
	t_6 = t_5 > floor(maxAniso)
	t_7 = Float32(-floor(h))
	tmp = Float32(0.0)
	if (t_6)
		tmp = t_3;
	else
		tmp = Float32(t_4 * sqrt(Float32(Float32(1.0) / (((Float32(dX_46_v * t_7) ^ Float32(2.0)) != (Float32(dX_46_v * t_7) ^ Float32(2.0))) ? t_1 : ((t_1 != t_1) ? (Float32(dX_46_v * t_7) ^ Float32(2.0)) : max((Float32(dX_46_v * t_7) ^ Float32(2.0)), t_1))))));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_6)
			tmp_4 = t_3;
		else
			tmp_4 = Float32(dX_46_v * Float32(sqrt(Float32(Float32(1.0) / t_2)) * Float32(dY_46_u * Float32(floor(w) * t_7))));
		end
		tmp_5 = Float32(0.0)
		if (t_6)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = Float32((((t_0 ^ Float32(2.0)) != (t_0 ^ Float32(2.0))) ? t_1 : ((t_1 != t_1) ? (t_0 ^ Float32(2.0)) : max((t_0 ^ Float32(2.0)), t_1))) / t_4);
		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_6)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_5;
	end
	return tmp_3
end

MATLAB

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

Derivation

1. Initial program 98.7%

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

3. Taylor expanded in w around 0 98.7%

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

5. Simplified 56.6%

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

6. Taylor expanded in dX.v around 0 57.2%

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

   1. unpow2 57.2%

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

   2. unpow2 57.2%

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

   3. swap-sqr 57.2%

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

   4. unpow2 57.2%

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

8. Simplified 57.2%

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

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

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

11. Simplified 59.2%

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

12. Taylor expanded in dX.v around -inf 59.3%

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

    1. mul-1-neg 59.3%

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

    2. *-commutative 59.3%

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

    3. distribute-rgt-neg-in 59.3%

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

14. Simplified 59.3%

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

15. Final simplification 59.3%

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

Alternative 6: 60.4% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

MATLAB

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

Derivation

1. Initial program 98.7%

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

3. Taylor expanded in w around 0 98.7%

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

5. Simplified 56.6%

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

6. Taylor expanded in dX.v around 0 57.2%

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

   1. unpow2 57.2%

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

   2. unpow2 57.2%

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

   3. swap-sqr 57.2%

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

   4. unpow2 57.2%

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

8. Simplified 57.2%

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

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

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

11. Simplified 59.2%

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

12. Taylor expanded in dX.v around inf 59.2%

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

    1. unpow2 98.7%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} \cdot \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.v \cdot dX.v\right) \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(-dX.v\right) \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

    2. unpow2 98.7%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} \cdot \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.v \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(-dX.v\right) \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

    3. swap-sqr 98.7%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} \cdot \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.v \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dX.v \cdot \left\lfloor h\right\rfloor \right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(-dX.v\right) \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

    4. unpow2 98.7%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} \cdot \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.v \cdot \left\lfloor h\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(-dX.v\right) \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

14. Simplified 59.2%

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

15. Final simplification 59.2%

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

Alternative 7: 58.8% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

MATLAB

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

Derivation

1. Initial program 98.7%

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

3. Taylor expanded in w around 0 98.7%

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

5. Simplified 56.6%

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

6. Taylor expanded in dX.v around 0 57.2%

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

   1. unpow2 57.2%

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

   2. unpow2 57.2%

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

   3. swap-sqr 57.2%

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

   4. unpow2 57.2%

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

8. Simplified 57.2%

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

9. Taylor expanded in dX.v around 0 56.9%

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

11. Simplified 56.9%

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

12. Taylor expanded in dX.v around inf 56.9%

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

    1. unpow2 98.7%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} \cdot \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.v \cdot dX.v\right) \cdot {\left(\left\lfloor h\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(-dX.v\right) \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

    2. unpow2 98.7%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} \cdot \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.v \cdot dX.v\right) \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(-dX.v\right) \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

    3. swap-sqr 98.7%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} \cdot \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\left(dX.v \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dX.v \cdot \left\lfloor h\right\rfloor \right), {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(-dX.v\right) \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

    4. unpow2 98.7%

       \[\leadsto \begin{array}{l} \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(dX.u \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left\lfloor h\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dY.u, \left\lfloor h\right\rfloor \cdot dY.v\right)\right)}^{2}\right)}} \cdot \left|\left\lfloor w\right\rfloor \cdot \left(\left\lfloor h\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\frac{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}{\left\lfloor maxAniso\right\rfloor }\\ \mathbf{else}:\\ \;\;\;\;\frac{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}{\sqrt{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dX.v, dX.u \cdot \left\lfloor w\right\rfloor \right)\right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left({\left(dX.v \cdot \left\lfloor h\right\rfloor \right)}^{2}, {\left(\mathsf{hypot}\left(dY.v \cdot \left\lfloor h\right\rfloor , \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left\lfloor h\right\rfloor \cdot \left(\left\lfloor w\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)}\\ \end{array}\right)\\ \mathbf{elif}\;\frac{\mathsf{max}\left(\mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dX.u \cdot dX.u\right) \cdot \left\lfloor w\right\rfloor , dX.v \cdot \left(dX.v \cdot \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right)\right)\right), \mathsf{fma}\left(\left\lfloor w\right\rfloor , \left(dY.u \cdot dY.u\right) \cdot \left\lfloor w\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left\lfloor h\right\rfloor \right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left(\left\lfloor h\right\rfloor \cdot \left(-dX.v\right)\right) \cdot dY.u\right)\right|} > \left\lfloor maxAniso\right\rfloor :\\ \;\;\;\;\left\lfloor maxAniso\right\rfloor \\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloor w\right\rfloor \cdot dX.u, \left\lfloor h\right\rfloor \cdot dX.v\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloor h\right\rfloor \cdot dY.v, \left\lfloor w\right\rfloor \cdot dY.u\right)\right)}^{2}\right)}{\left|\left\lfloor w\right\rfloor \cdot \mathsf{fma}\left(dY.v, dX.u \cdot \left\lfloor h\right\rfloor , \left\lfloor h\right\rfloor \cdot \left(\left(-dX.v\right) \cdot dY.u\right)\right)\right|}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

14. Simplified 56.9%

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

15. Final simplification 56.9%

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

Reproduce

herbie shell --seed 2024191 
(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))))))))