Anisotropic x16 LOD (ratio of anisotropy)

Percentage Accurate: 97.7% → 98.2%

Time: 53.8s

Alternatives: 6

Speedup: 1.0×

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

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

FPCore

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

C

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

Julia

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

MATLAB

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

MATLAB

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0
         (pow
          (fmax
           (pow (hypot (* (floor w) dX.u) (* (floor h) dX.v)) 2.0)
           (pow (hypot (* (floor w) dY.u) (* (floor h) dY.v)) 2.0))
          -0.5))
        (t_1 (- (* dX.u dY.v) (* dX.v dY.u)))
        (t_2
         (fmax
          (fma
           (floor w)
           (* (floor w) (* dX.u dX.u))
           (* (floor h) (* (floor h) (* dX.v dX.v))))
          (fma
           (floor w)
           (* (floor w) (* dY.u dY.u))
           (* (* (floor h) (floor h)) (* dY.v dY.v)))))
        (t_3 (/ (sqrt t_2) (floor maxAniso)))
        (t_4 (/ t_2 (fabs (* (floor h) (* (floor w) t_1)))))
        (t_5 (> t_4 (floor maxAniso)))
        (t_6 (if t_5 (floor maxAniso) t_4)))
   (if (<
        (if t_5
          t_3
          (log (pow (exp (fabs (* (floor w) (* (floor h) t_1)))) t_0)))
        1.0)
     (fmax
      1.0
      (*
       (if t_5
         t_3
         (*
          t_0
          (fabs
           (* (* (floor w) (floor h)) (fma dX.u dY.v (* dX.v (- dY.u)))))))
       t_6))
     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 = powf(fmaxf(powf(hypotf((floorf(w) * dX_46_u), (floorf(h) * dX_46_v)), 2.0f), powf(hypotf((floorf(w) * dY_46_u), (floorf(h) * dY_46_v)), 2.0f)), -0.5f);
	float t_1 = (dX_46_u * dY_46_v) - (dX_46_v * dY_46_u);
	float t_2 = fmaxf(fmaf(floorf(w), (floorf(w) * (dX_46_u * dX_46_u)), (floorf(h) * (floorf(h) * (dX_46_v * dX_46_v)))), fmaf(floorf(w), (floorf(w) * (dY_46_u * dY_46_u)), ((floorf(h) * floorf(h)) * (dY_46_v * dY_46_v))));
	float t_3 = sqrtf(t_2) / floorf(maxAniso);
	float t_4 = t_2 / fabsf((floorf(h) * (floorf(w) * t_1)));
	int t_5 = t_4 > floorf(maxAniso);
	float tmp;
	if (t_5) {
		tmp = floorf(maxAniso);
	} else {
		tmp = t_4;
	}
	float t_6 = tmp;
	float tmp_1;
	if (t_5) {
		tmp_1 = t_3;
	} else {
		tmp_1 = logf(powf(expf(fabsf((floorf(w) * (floorf(h) * t_1)))), t_0));
	}
	float tmp_3;
	if (tmp_1 < 1.0f) {
		float tmp_4;
		if (t_5) {
			tmp_4 = t_3;
		} else {
			tmp_4 = t_0 * fabsf(((floorf(w) * floorf(h)) * fmaf(dX_46_u, dY_46_v, (dX_46_v * -dY_46_u))));
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * t_6));
	} 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 = (((hypot(Float32(floor(w) * dX_46_u), Float32(floor(h) * dX_46_v)) ^ Float32(2.0)) != (hypot(Float32(floor(w) * dX_46_u), Float32(floor(h) * dX_46_v)) ^ Float32(2.0))) ? (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0)) : (((hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0)) != (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0))) ? (hypot(Float32(floor(w) * dX_46_u), Float32(floor(h) * dX_46_v)) ^ Float32(2.0)) : max((hypot(Float32(floor(w) * dX_46_u), Float32(floor(h) * dX_46_v)) ^ Float32(2.0)), (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0))))) ^ Float32(-0.5)
	t_1 = Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))
	t_2 = (fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) != fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v))))) ? fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(Float32(floor(h) * floor(h)) * Float32(dY_46_v * dY_46_v))) : ((fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(Float32(floor(h) * floor(h)) * Float32(dY_46_v * dY_46_v))) != fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(Float32(floor(h) * floor(h)) * Float32(dY_46_v * dY_46_v)))) ? fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) : max(fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))), fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(Float32(floor(h) * floor(h)) * Float32(dY_46_v * dY_46_v)))))
	t_3 = Float32(sqrt(t_2) / floor(maxAniso))
	t_4 = Float32(t_2 / abs(Float32(floor(h) * Float32(floor(w) * t_1))))
	t_5 = t_4 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_5)
		tmp = floor(maxAniso);
	else
		tmp = t_4;
	end
	t_6 = tmp
	tmp_1 = Float32(0.0)
	if (t_5)
		tmp_1 = t_3;
	else
		tmp_1 = log((exp(abs(Float32(floor(w) * Float32(floor(h) * t_1)))) ^ t_0));
	end
	tmp_3 = Float32(0.0)
	if (tmp_1 < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_5)
			tmp_4 = t_3;
		else
			tmp_4 = Float32(t_0 * abs(Float32(Float32(floor(w) * floor(h)) * fma(dX_46_u, dY_46_v, Float32(dX_46_v * Float32(-dY_46_u))))));
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * t_6) : ((Float32(tmp_4 * t_6) != Float32(tmp_4 * t_6)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * t_6)));
	else
		tmp_3 = t_6;
	end
	return tmp_3
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 98.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0
         (fmax
          (fma
           (floor w)
           (* (floor w) (* dX.u dX.u))
           (* (floor h) (* (floor h) (* dX.v dX.v))))
          (fma
           (floor w)
           (* (floor w) (* dY.u dY.u))
           (* (* (floor h) (floor h)) (* dY.v dY.v)))))
        (t_1 (/ (sqrt t_0) (floor maxAniso)))
        (t_2
         (pow
          (fmax
           (pow (hypot (* (floor w) dX.u) (* (floor h) dX.v)) 2.0)
           (pow (hypot (* (floor w) dY.u) (* (floor h) dY.v)) 2.0))
          -0.5))
        (t_3
         (/
          t_0
          (fabs (* (floor h) (* (floor w) (- (* dX.u dY.v) (* dX.v dY.u)))))))
        (t_4 (> t_3 (floor maxAniso)))
        (t_5 (if t_4 (floor maxAniso) t_3))
        (t_6 (fma dX.u dY.v (* dX.v (- dY.u)))))
   (if (< (if t_4 t_1 (* (floor w) (* t_2 (* (floor h) (fabs t_6))))) 1.0)
     (fmax
      1.0
      (* (if t_4 t_1 (* t_2 (fabs (* (* (floor w) (floor h)) t_6)))) t_5))
     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 = fmaxf(fmaf(floorf(w), (floorf(w) * (dX_46_u * dX_46_u)), (floorf(h) * (floorf(h) * (dX_46_v * dX_46_v)))), fmaf(floorf(w), (floorf(w) * (dY_46_u * dY_46_u)), ((floorf(h) * floorf(h)) * (dY_46_v * dY_46_v))));
	float t_1 = sqrtf(t_0) / floorf(maxAniso);
	float t_2 = powf(fmaxf(powf(hypotf((floorf(w) * dX_46_u), (floorf(h) * dX_46_v)), 2.0f), powf(hypotf((floorf(w) * dY_46_u), (floorf(h) * dY_46_v)), 2.0f)), -0.5f);
	float t_3 = t_0 / fabsf((floorf(h) * (floorf(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)))));
	int t_4 = t_3 > floorf(maxAniso);
	float tmp;
	if (t_4) {
		tmp = floorf(maxAniso);
	} else {
		tmp = t_3;
	}
	float t_5 = tmp;
	float t_6 = fmaf(dX_46_u, dY_46_v, (dX_46_v * -dY_46_u));
	float tmp_1;
	if (t_4) {
		tmp_1 = t_1;
	} else {
		tmp_1 = floorf(w) * (t_2 * (floorf(h) * fabsf(t_6)));
	}
	float tmp_3;
	if (tmp_1 < 1.0f) {
		float tmp_4;
		if (t_4) {
			tmp_4 = t_1;
		} else {
			tmp_4 = t_2 * fabsf(((floorf(w) * floorf(h)) * t_6));
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * t_5));
	} 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 = (fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) != fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v))))) ? fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(Float32(floor(h) * floor(h)) * Float32(dY_46_v * dY_46_v))) : ((fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(Float32(floor(h) * floor(h)) * Float32(dY_46_v * dY_46_v))) != fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(Float32(floor(h) * floor(h)) * Float32(dY_46_v * dY_46_v)))) ? fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))) : max(fma(floor(w), Float32(floor(w) * Float32(dX_46_u * dX_46_u)), Float32(floor(h) * Float32(floor(h) * Float32(dX_46_v * dX_46_v)))), fma(floor(w), Float32(floor(w) * Float32(dY_46_u * dY_46_u)), Float32(Float32(floor(h) * floor(h)) * Float32(dY_46_v * dY_46_v)))))
	t_1 = Float32(sqrt(t_0) / floor(maxAniso))
	t_2 = (((hypot(Float32(floor(w) * dX_46_u), Float32(floor(h) * dX_46_v)) ^ Float32(2.0)) != (hypot(Float32(floor(w) * dX_46_u), Float32(floor(h) * dX_46_v)) ^ Float32(2.0))) ? (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0)) : (((hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0)) != (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0))) ? (hypot(Float32(floor(w) * dX_46_u), Float32(floor(h) * dX_46_v)) ^ Float32(2.0)) : max((hypot(Float32(floor(w) * dX_46_u), Float32(floor(h) * dX_46_v)) ^ Float32(2.0)), (hypot(Float32(floor(w) * dY_46_u), Float32(floor(h) * dY_46_v)) ^ Float32(2.0))))) ^ Float32(-0.5)
	t_3 = Float32(t_0 / abs(Float32(floor(h) * Float32(floor(w) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u))))))
	t_4 = t_3 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_4)
		tmp = floor(maxAniso);
	else
		tmp = t_3;
	end
	t_5 = tmp
	t_6 = fma(dX_46_u, dY_46_v, Float32(dX_46_v * Float32(-dY_46_u)))
	tmp_1 = Float32(0.0)
	if (t_4)
		tmp_1 = t_1;
	else
		tmp_1 = Float32(floor(w) * Float32(t_2 * Float32(floor(h) * abs(t_6))));
	end
	tmp_3 = Float32(0.0)
	if (tmp_1 < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_4)
			tmp_4 = t_1;
		else
			tmp_4 = Float32(t_2 * abs(Float32(Float32(floor(w) * floor(h)) * t_6)));
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * t_5) : ((Float32(tmp_4 * t_5) != Float32(tmp_4 * t_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * t_5)));
	else
		tmp_3 = t_5;
	end
	return tmp_3
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_1 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_2 := {\left(\left\lfloorw\right\rfloor\right)}^{2}\\ t_3 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_4 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_5 := \mathsf{max}\left(t_4 \cdot t_4 + t_1 \cdot t_1, t_0 \cdot t_0 + t_3 \cdot t_3\right)\\ t_6 := \sqrt{t_5}\\ t_7 := \frac{t_6}{\left\lfloormaxAniso\right\rfloor}\\ t_8 := \left|t_3 \cdot t_4 - t_0 \cdot t_1\right|\\ t_9 := \frac{t_5}{t_8}\\ t_10 := t_9 > \left\lfloormaxAniso\right\rfloor\\ t_11 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t_4, t_1\right)\right)}^{2}, {\left(\mathsf{hypot}\left(t_0, t_3\right)\right)}^{2}\right)\\ t_12 := \left|\left\lfloorh\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right|\\ t_13 := \left\lfloorw\right\rfloor \cdot t_12\\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;\frac{t_11}{t_13} > \left\lfloormaxAniso\right\rfloor:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;\frac{t_13}{\sqrt{t_11}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t_10:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_9\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t_10:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;\frac{t_8}{t_6}\\ \end{array}\right)\\ \mathbf{elif}\;t_10:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{max}\left(\mathsf{fma}\left({dX.u}^{2}, t_2, {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right), \mathsf{fma}\left(t_2, {dY.u}^{2}, {t_3}^{2}\right)\right)}{t_12}}{\left\lfloorw\right\rfloor}\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 97.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(\left\lfloorw\right\rfloor\right)}^{2}\\ t_1 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_2 := \left\lfloorw\right\rfloor \cdot \left|\left\lfloorh\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right|\\ t_3 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_4 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_5 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_6 := \mathsf{max}\left(t_3 \cdot t_3 + t_1 \cdot t_1, t_4 \cdot t_4 + t_5 \cdot t_5\right)\\ t_7 := \sqrt{t_6}\\ t_8 := \frac{t_7}{\left\lfloormaxAniso\right\rfloor}\\ t_9 := \left|t_5 \cdot t_3 - t_4 \cdot t_1\right|\\ t_10 := \frac{t_6}{t_9}\\ t_11 := t_10 > \left\lfloormaxAniso\right\rfloor\\ t_12 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t_3, t_1\right)\right)}^{2}, {\left(\mathsf{hypot}\left(t_4, t_5\right)\right)}^{2}\right)\\ t_13 := \frac{t_12}{t_2} > \left\lfloormaxAniso\right\rfloor\\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t_13:\\ \;\;\;\;t_8\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{\sqrt{t_12}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t_11:\\ \;\;\;\;t_8\\ \mathbf{else}:\\ \;\;\;\;\frac{t_9}{t_7}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t_13:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_10\\ \end{array}\right)\\ \mathbf{elif}\;t_11:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(\mathsf{fma}\left({dX.u}^{2}, t_0, {dX.v}^{2} \cdot {\left(\left\lfloorh\right\rfloor\right)}^{2}\right), \mathsf{fma}\left(t_0, {dY.u}^{2}, {t_5}^{2}\right)\right)}{t_2}\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 97.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_1 := \left\lfloorw\right\rfloor \cdot \left|\left\lfloorh\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right|\\ t_2 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_3 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_4 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_5 := \mathsf{max}\left(t_2 \cdot t_2 + t_0 \cdot t_0, t_3 \cdot t_3 + t_4 \cdot t_4\right)\\ t_6 := t_4 \cdot t_2\\ t_7 := \sqrt{t_5}\\ t_8 := \frac{t_7}{\left\lfloormaxAniso\right\rfloor}\\ t_9 := \left|t_6 - t_3 \cdot t_0\right|\\ t_10 := \frac{t_5}{t_9}\\ t_11 := t_10 > \left\lfloormaxAniso\right\rfloor\\ t_12 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t_2, t_0\right)\right)}^{2}, {\left(\mathsf{hypot}\left(t_3, t_4\right)\right)}^{2}\right)\\ t_13 := \frac{t_12}{t_1} > \left\lfloormaxAniso\right\rfloor\\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t_13:\\ \;\;\;\;t_8\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{\sqrt{t_12}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t_11:\\ \;\;\;\;t_8\\ \mathbf{else}:\\ \;\;\;\;\frac{t_9}{t_7}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t_13:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_10\\ \end{array}\right)\\ \mathbf{elif}\;t_11:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.v \cdot dY.u\right)\right) - t_6\right|}{t_12}\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(h) * dX_46_v)
	t_1 = Float32(floor(w) * abs(Float32(floor(h) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)))))
	t_2 = Float32(floor(w) * dX_46_u)
	t_3 = Float32(floor(w) * dY_46_u)
	t_4 = Float32(floor(h) * dY_46_v)
	t_5 = (Float32(Float32(t_2 * t_2) + Float32(t_0 * t_0)) != Float32(Float32(t_2 * t_2) + Float32(t_0 * t_0))) ? 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_2 * t_2) + Float32(t_0 * t_0)) : max(Float32(Float32(t_2 * t_2) + Float32(t_0 * t_0)), Float32(Float32(t_3 * t_3) + Float32(t_4 * t_4))))
	t_6 = Float32(t_4 * t_2)
	t_7 = sqrt(t_5)
	t_8 = Float32(t_7 / floor(maxAniso))
	t_9 = abs(Float32(t_6 - Float32(t_3 * t_0)))
	t_10 = Float32(t_5 / t_9)
	t_11 = t_10 > floor(maxAniso)
	t_12 = ((hypot(t_2, t_0) ^ Float32(2.0)) != (hypot(t_2, t_0) ^ Float32(2.0))) ? (hypot(t_3, t_4) ^ Float32(2.0)) : (((hypot(t_3, t_4) ^ Float32(2.0)) != (hypot(t_3, t_4) ^ Float32(2.0))) ? (hypot(t_2, t_0) ^ Float32(2.0)) : max((hypot(t_2, t_0) ^ Float32(2.0)), (hypot(t_3, t_4) ^ Float32(2.0))))
	t_13 = Float32(t_12 / t_1) > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_13)
		tmp = t_8;
	else
		tmp = Float32(t_1 / sqrt(t_12));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_11)
			tmp_4 = t_8;
		else
			tmp_4 = Float32(t_9 / t_7);
		end
		tmp_5 = Float32(0.0)
		if (t_13)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = t_10;
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_11)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = Float32(abs(Float32(Float32(floor(h) * Float32(floor(w) * Float32(dX_46_v * dY_46_u))) - t_6)) / t_12) ^ Float32(-1.0);
	end
	return tmp_3
end

MATLAB

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 97.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_1 := \left\lfloorw\right\rfloor \cdot \left|\left\lfloorh\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right|\\ t_2 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_3 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_4 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_5 := \mathsf{max}\left(t_2 \cdot t_2 + t_0 \cdot t_0, t_3 \cdot t_3 + t_4 \cdot t_4\right)\\ t_6 := \sqrt{t_5}\\ t_7 := \frac{t_6}{\left\lfloormaxAniso\right\rfloor}\\ t_8 := \left|t_4 \cdot t_2 - t_3 \cdot t_0\right|\\ t_9 := \frac{t_5}{t_8}\\ t_10 := t_9 > \left\lfloormaxAniso\right\rfloor\\ t_11 := \mathsf{max}\left({\left(\mathsf{hypot}\left(t_2, t_0\right)\right)}^{2}, {\left(\mathsf{hypot}\left(t_3, t_4\right)\right)}^{2}\right)\\ t_12 := \frac{t_11}{t_1}\\ t_13 := t_12 > \left\lfloormaxAniso\right\rfloor\\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t_13:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{\sqrt{t_11}}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t_10:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;\frac{t_8}{t_6}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t_13:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_12\\ \end{array}\right)\\ \mathbf{elif}\;t_10:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_9\\ \end{array} \end{array} \]

FPCore

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

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(h) * dX_46_v;
	float t_1 = floorf(w) * fabsf((floorf(h) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u))));
	float t_2 = floorf(w) * dX_46_u;
	float t_3 = floorf(w) * dY_46_u;
	float t_4 = floorf(h) * dY_46_v;
	float t_5 = fmaxf(((t_2 * t_2) + (t_0 * t_0)), ((t_3 * t_3) + (t_4 * t_4)));
	float t_6 = sqrtf(t_5);
	float t_7 = t_6 / floorf(maxAniso);
	float t_8 = fabsf(((t_4 * t_2) - (t_3 * t_0)));
	float t_9 = t_5 / t_8;
	int t_10 = t_9 > floorf(maxAniso);
	float t_11 = fmaxf(powf(hypotf(t_2, t_0), 2.0f), powf(hypotf(t_3, t_4), 2.0f));
	float t_12 = t_11 / t_1;
	int t_13 = t_12 > floorf(maxAniso);
	float tmp;
	if (t_13) {
		tmp = t_7;
	} else {
		tmp = t_1 / sqrtf(t_11);
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_10) {
			tmp_4 = t_7;
		} else {
			tmp_4 = t_8 / t_6;
		}
		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_10) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_9;
	}
	return tmp_3;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(h) * dX_46_v)
	t_1 = Float32(floor(w) * abs(Float32(floor(h) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)))))
	t_2 = Float32(floor(w) * dX_46_u)
	t_3 = Float32(floor(w) * dY_46_u)
	t_4 = Float32(floor(h) * dY_46_v)
	t_5 = (Float32(Float32(t_2 * t_2) + Float32(t_0 * t_0)) != Float32(Float32(t_2 * t_2) + Float32(t_0 * t_0))) ? 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_2 * t_2) + Float32(t_0 * t_0)) : max(Float32(Float32(t_2 * t_2) + Float32(t_0 * t_0)), Float32(Float32(t_3 * t_3) + Float32(t_4 * t_4))))
	t_6 = sqrt(t_5)
	t_7 = Float32(t_6 / floor(maxAniso))
	t_8 = abs(Float32(Float32(t_4 * t_2) - Float32(t_3 * t_0)))
	t_9 = Float32(t_5 / t_8)
	t_10 = t_9 > floor(maxAniso)
	t_11 = ((hypot(t_2, t_0) ^ Float32(2.0)) != (hypot(t_2, t_0) ^ Float32(2.0))) ? (hypot(t_3, t_4) ^ Float32(2.0)) : (((hypot(t_3, t_4) ^ Float32(2.0)) != (hypot(t_3, t_4) ^ Float32(2.0))) ? (hypot(t_2, t_0) ^ Float32(2.0)) : max((hypot(t_2, t_0) ^ Float32(2.0)), (hypot(t_3, t_4) ^ Float32(2.0))))
	t_12 = Float32(t_11 / t_1)
	t_13 = t_12 > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_13)
		tmp = t_7;
	else
		tmp = Float32(t_1 / sqrt(t_11));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_10)
			tmp_4 = t_7;
		else
			tmp_4 = Float32(t_8 / t_6);
		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_10)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_9;
	end
	return tmp_3
end

MATLAB

function tmp_7 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = floor(h) * dX_46_v;
	t_1 = floor(w) * abs((floor(h) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u))));
	t_2 = floor(w) * dX_46_u;
	t_3 = floor(w) * dY_46_u;
	t_4 = floor(h) * dY_46_v;
	t_5 = max(((t_2 * t_2) + (t_0 * t_0)), ((t_3 * t_3) + (t_4 * t_4)));
	t_6 = sqrt(t_5);
	t_7 = t_6 / floor(maxAniso);
	t_8 = abs(((t_4 * t_2) - (t_3 * t_0)));
	t_9 = t_5 / t_8;
	t_10 = t_9 > floor(maxAniso);
	t_11 = max((hypot(t_2, t_0) ^ single(2.0)), (hypot(t_3, t_4) ^ single(2.0)));
	t_12 = t_11 / t_1;
	t_13 = t_12 > floor(maxAniso);
	tmp = single(0.0);
	if (t_13)
		tmp = t_7;
	else
		tmp = t_1 / sqrt(t_11);
	end
	tmp_4 = single(0.0);
	if (tmp < single(1.0))
		tmp_5 = single(0.0);
		if (t_10)
			tmp_5 = t_7;
		else
			tmp_5 = t_8 / t_6;
		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_10)
		tmp_4 = floor(maxAniso);
	else
		tmp_4 = t_9;
	end
	tmp_7 = tmp_4;
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023348 
(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))))))))