Anisotropic x16 LOD (line direction, v)

Percentage Accurate: 76.4% → 76.5%

Time: 27.6s

Alternatives: 4

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

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

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) dY.u))
        (t_2 (* (floor w) dX.u))
        (t_3 (+ (* t_2 t_2) (* t_0 t_0)))
        (t_4 (* (floor h) dY.v))
        (t_5 (+ (* t_1 t_1) (* t_4 t_4)))
        (t_6 (/ 1.0 (sqrt (fmax t_3 t_5)))))
   (if (>= t_3 t_5) (* t_6 t_0) (* t_6 t_4))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(h) * dX_46_v;
	float t_1 = floorf(w) * dY_46_u;
	float t_2 = floorf(w) * dX_46_u;
	float t_3 = (t_2 * t_2) + (t_0 * t_0);
	float t_4 = floorf(h) * dY_46_v;
	float t_5 = (t_1 * t_1) + (t_4 * t_4);
	float t_6 = 1.0f / sqrtf(fmaxf(t_3, t_5));
	float tmp;
	if (t_3 >= t_5) {
		tmp = t_6 * t_0;
	} else {
		tmp = t_6 * t_4;
	}
	return tmp;
}

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) * dY_46_u)
	t_2 = Float32(floor(w) * dX_46_u)
	t_3 = Float32(Float32(t_2 * t_2) + Float32(t_0 * t_0))
	t_4 = Float32(floor(h) * dY_46_v)
	t_5 = Float32(Float32(t_1 * t_1) + Float32(t_4 * t_4))
	t_6 = Float32(Float32(1.0) / sqrt(((t_3 != t_3) ? t_5 : ((t_5 != t_5) ? t_3 : max(t_3, t_5)))))
	tmp = Float32(0.0)
	if (t_3 >= t_5)
		tmp = Float32(t_6 * t_0);
	else
		tmp = Float32(t_6 * t_4);
	end
	return tmp
end

MATLAB

function tmp_2 = 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) * dY_46_u;
	t_2 = floor(w) * dX_46_u;
	t_3 = (t_2 * t_2) + (t_0 * t_0);
	t_4 = floor(h) * dY_46_v;
	t_5 = (t_1 * t_1) + (t_4 * t_4);
	t_6 = single(1.0) / sqrt(max(t_3, t_5));
	tmp = single(0.0);
	if (t_3 >= t_5)
		tmp = t_6 * t_0;
	else
		tmp = t_6 * t_4;
	end
	tmp_2 = tmp;
end

Initial Program: 76.4% accurate, 1.0× speedup

Math

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

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) dY.u))
        (t_2 (* (floor w) dX.u))
        (t_3 (+ (* t_2 t_2) (* t_0 t_0)))
        (t_4 (* (floor h) dY.v))
        (t_5 (+ (* t_1 t_1) (* t_4 t_4)))
        (t_6 (/ 1.0 (sqrt (fmax t_3 t_5)))))
   (if (>= t_3 t_5) (* t_6 t_0) (* t_6 t_4))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(h) * dX_46_v;
	float t_1 = floorf(w) * dY_46_u;
	float t_2 = floorf(w) * dX_46_u;
	float t_3 = (t_2 * t_2) + (t_0 * t_0);
	float t_4 = floorf(h) * dY_46_v;
	float t_5 = (t_1 * t_1) + (t_4 * t_4);
	float t_6 = 1.0f / sqrtf(fmaxf(t_3, t_5));
	float tmp;
	if (t_3 >= t_5) {
		tmp = t_6 * t_0;
	} else {
		tmp = t_6 * t_4;
	}
	return tmp;
}

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) * dY_46_u)
	t_2 = Float32(floor(w) * dX_46_u)
	t_3 = Float32(Float32(t_2 * t_2) + Float32(t_0 * t_0))
	t_4 = Float32(floor(h) * dY_46_v)
	t_5 = Float32(Float32(t_1 * t_1) + Float32(t_4 * t_4))
	t_6 = Float32(Float32(1.0) / sqrt(((t_3 != t_3) ? t_5 : ((t_5 != t_5) ? t_3 : max(t_3, t_5)))))
	tmp = Float32(0.0)
	if (t_3 >= t_5)
		tmp = Float32(t_6 * t_0);
	else
		tmp = Float32(t_6 * t_4);
	end
	return tmp
end

MATLAB

function tmp_2 = 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) * dY_46_u;
	t_2 = floor(w) * dX_46_u;
	t_3 = (t_2 * t_2) + (t_0 * t_0);
	t_4 = floor(h) * dY_46_v;
	t_5 = (t_1 * t_1) + (t_4 * t_4);
	t_6 = single(1.0) / sqrt(max(t_3, t_5));
	tmp = single(0.0);
	if (t_3 >= t_5)
		tmp = t_6 * t_0;
	else
		tmp = t_6 * t_4;
	end
	tmp_2 = tmp;
end

Alternative 1: 76.5% accurate, 0.9× speedup

Math

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

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 (* (floor w) dX.u))
        (t_3 (* (floor h) dY.v))
        (t_4
         (sqrt (fmax (pow (hypot t_2 t_1) 2.0) (pow (hypot t_0 t_3) 2.0)))))
   (if (>=
        (fma t_2 t_2 (pow t_1 2.0))
        (fma t_0 t_0 (* (floor h) (* dY.v t_3))))
     (/ t_1 t_4)
     (* dY.v (/ (floor h) t_4)))))

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(w) * dY_46_u;
	float t_1 = floorf(h) * dX_46_v;
	float t_2 = floorf(w) * dX_46_u;
	float t_3 = floorf(h) * dY_46_v;
	float t_4 = sqrtf(fmaxf(powf(hypotf(t_2, t_1), 2.0f), powf(hypotf(t_0, t_3), 2.0f)));
	float tmp;
	if (fmaf(t_2, t_2, powf(t_1, 2.0f)) >= fmaf(t_0, t_0, (floorf(h) * (dY_46_v * t_3)))) {
		tmp = t_1 / t_4;
	} else {
		tmp = dY_46_v * (floorf(h) / t_4);
	}
	return tmp;
}

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 = Float32(floor(w) * dX_46_u)
	t_3 = Float32(floor(h) * dY_46_v)
	t_4 = sqrt((((hypot(t_2, t_1) ^ Float32(2.0)) != (hypot(t_2, 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_2, t_1) ^ Float32(2.0)) : max((hypot(t_2, t_1) ^ Float32(2.0)), (hypot(t_0, t_3) ^ Float32(2.0))))))
	tmp = Float32(0.0)
	if (fma(t_2, t_2, (t_1 ^ Float32(2.0))) >= fma(t_0, t_0, Float32(floor(h) * Float32(dY_46_v * t_3))))
		tmp = Float32(t_1 / t_4);
	else
		tmp = Float32(dY_46_v * Float32(floor(h) / t_4));
	end
	return tmp
end

Derivation

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

Alternative 2: 76.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(w) * dX_46_u;
	float t_1 = t_0 * t_0;
	float t_2 = floorf(w) * dY_46_u;
	float t_3 = floorf(h) * dY_46_v;
	float t_4 = t_3 * t_3;
	float t_5 = floorf(h) * dX_46_v;
	float tmp;
	if ((powf(t_5, 2.0f) + t_1) >= (powf(t_2, 2.0f) + t_4)) {
		tmp = t_5 * (1.0f / sqrtf(fmaxf((t_1 + (t_5 * t_5)), (t_4 + (t_2 * t_2)))));
	} else {
		tmp = t_3 * (1.0f / powf(fmaxf(powf(hypotf(t_0, t_5), 2.0f), powf(hypotf(t_2, t_3), 2.0f)), 0.5f));
	}
	return tmp;
}

Julia

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

MATLAB

function tmp_2 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = floor(w) * dX_46_u;
	t_1 = t_0 * t_0;
	t_2 = floor(w) * dY_46_u;
	t_3 = floor(h) * dY_46_v;
	t_4 = t_3 * t_3;
	t_5 = floor(h) * dX_46_v;
	tmp = single(0.0);
	if (((t_5 ^ single(2.0)) + t_1) >= ((t_2 ^ single(2.0)) + t_4))
		tmp = t_5 * (single(1.0) / sqrt(max((t_1 + (t_5 * t_5)), (t_4 + (t_2 * t_2)))));
	else
		tmp = t_3 * (single(1.0) / (max((hypot(t_0, t_5) ^ single(2.0)), (hypot(t_2, t_3) ^ single(2.0))) ^ single(0.5)));
	end
	tmp_2 = tmp;
end

Derivation

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

Alternative 3: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_1 := t_0 \cdot t_0\\ t_2 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_3 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_4 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_5 := \frac{1}{\sqrt{\mathsf{max}\left(t_1 + t_4 \cdot t_4, t_3 \cdot t_3 + t_2 \cdot t_2\right)}}\\ \mathbf{if}\;{t_4}^{2} + t_1 \geq {t_2}^{2} + {t_3}^{2}:\\ \;\;\;\;t_4 \cdot t_5\\ \mathbf{else}:\\ \;\;\;\;t_3 \cdot t_5\\ \end{array} \end{array} \]

FPCore

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

C

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = floorf(w) * dX_46_u;
	float t_1 = t_0 * t_0;
	float t_2 = floorf(w) * dY_46_u;
	float t_3 = floorf(h) * dY_46_v;
	float t_4 = floorf(h) * dX_46_v;
	float t_5 = 1.0f / sqrtf(fmaxf((t_1 + (t_4 * t_4)), ((t_3 * t_3) + (t_2 * t_2))));
	float tmp;
	if ((powf(t_4, 2.0f) + t_1) >= (powf(t_2, 2.0f) + powf(t_3, 2.0f))) {
		tmp = t_4 * t_5;
	} else {
		tmp = t_3 * t_5;
	}
	return tmp;
}

Julia

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = Float32(floor(w) * dX_46_u)
	t_1 = Float32(t_0 * t_0)
	t_2 = Float32(floor(w) * dY_46_u)
	t_3 = Float32(floor(h) * dY_46_v)
	t_4 = Float32(floor(h) * dX_46_v)
	t_5 = Float32(Float32(1.0) / sqrt(((Float32(t_1 + Float32(t_4 * t_4)) != Float32(t_1 + Float32(t_4 * t_4))) ? Float32(Float32(t_3 * t_3) + Float32(t_2 * t_2)) : ((Float32(Float32(t_3 * t_3) + Float32(t_2 * t_2)) != Float32(Float32(t_3 * t_3) + Float32(t_2 * t_2))) ? Float32(t_1 + Float32(t_4 * t_4)) : max(Float32(t_1 + Float32(t_4 * t_4)), Float32(Float32(t_3 * t_3) + Float32(t_2 * t_2)))))))
	tmp = Float32(0.0)
	if (Float32((t_4 ^ Float32(2.0)) + t_1) >= Float32((t_2 ^ Float32(2.0)) + (t_3 ^ Float32(2.0))))
		tmp = Float32(t_4 * t_5);
	else
		tmp = Float32(t_3 * t_5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = floor(w) * dX_46_u;
	t_1 = t_0 * t_0;
	t_2 = floor(w) * dY_46_u;
	t_3 = floor(h) * dY_46_v;
	t_4 = floor(h) * dX_46_v;
	t_5 = single(1.0) / sqrt(max((t_1 + (t_4 * t_4)), ((t_3 * t_3) + (t_2 * t_2))));
	tmp = single(0.0);
	if (((t_4 ^ single(2.0)) + t_1) >= ((t_2 ^ single(2.0)) + (t_3 ^ single(2.0))))
		tmp = t_4 * t_5;
	else
		tmp = t_3 * t_5;
	end
	tmp_2 = tmp;
end

Derivation

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

Alternative 4: 57.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_1 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_2 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_3 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_4 := {\left(\mathsf{hypot}\left(t_3, t_0\right)\right)}^{2}\\ \mathbf{if}\;t_3 \cdot t_3 + t_0 \cdot t_0 \geq t_1 \cdot t_1 + t_2 \cdot t_2:\\ \;\;\;\;t_0 \cdot \frac{1}{{\left({\left(\mathsf{max}\left(t_4, {t_2}^{2}\right)\right)}^{1.5}\right)}^{0.3333333333333333}}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \frac{1}{\sqrt{\mathsf{max}\left(t_4, {\left(\mathsf{hypot}\left(t_2, t_1\right)\right)}^{2}\right)}}\\ \end{array} \end{array} \]

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 (pow (hypot t_3 t_0) 2.0)))
   (if (>= (+ (* t_3 t_3) (* t_0 t_0)) (+ (* t_1 t_1) (* t_2 t_2)))
     (*
      t_0
      (/ 1.0 (pow (pow (fmax t_4 (pow t_2 2.0)) 1.5) 0.3333333333333333)))
     (* t_1 (/ 1.0 (sqrt (fmax t_4 (pow (hypot t_2 t_1) 2.0))))))))

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(h) * dY_46_v;
	float t_2 = floorf(w) * dY_46_u;
	float t_3 = floorf(w) * dX_46_u;
	float t_4 = powf(hypotf(t_3, t_0), 2.0f);
	float tmp;
	if (((t_3 * t_3) + (t_0 * t_0)) >= ((t_1 * t_1) + (t_2 * t_2))) {
		tmp = t_0 * (1.0f / powf(powf(fmaxf(t_4, powf(t_2, 2.0f)), 1.5f), 0.3333333333333333f));
	} else {
		tmp = t_1 * (1.0f / sqrtf(fmaxf(t_4, powf(hypotf(t_2, t_1), 2.0f))));
	}
	return tmp;
}

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 = hypot(t_3, t_0) ^ Float32(2.0)
	tmp = Float32(0.0)
	if (Float32(Float32(t_3 * t_3) + Float32(t_0 * t_0)) >= Float32(Float32(t_1 * t_1) + Float32(t_2 * t_2)))
		tmp = Float32(t_0 * Float32(Float32(1.0) / ((((t_4 != t_4) ? (t_2 ^ Float32(2.0)) : (((t_2 ^ Float32(2.0)) != (t_2 ^ Float32(2.0))) ? t_4 : max(t_4, (t_2 ^ Float32(2.0))))) ^ Float32(1.5)) ^ Float32(0.3333333333333333))));
	else
		tmp = Float32(t_1 * Float32(Float32(1.0) / sqrt(((t_4 != t_4) ? (hypot(t_2, t_1) ^ Float32(2.0)) : (((hypot(t_2, t_1) ^ Float32(2.0)) != (hypot(t_2, t_1) ^ Float32(2.0))) ? t_4 : max(t_4, (hypot(t_2, t_1) ^ Float32(2.0))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = 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 = hypot(t_3, t_0) ^ single(2.0);
	tmp = single(0.0);
	if (((t_3 * t_3) + (t_0 * t_0)) >= ((t_1 * t_1) + (t_2 * t_2)))
		tmp = t_0 * (single(1.0) / ((max(t_4, (t_2 ^ single(2.0))) ^ single(1.5)) ^ single(0.3333333333333333)));
	else
		tmp = t_1 * (single(1.0) / sqrt(max(t_4, (hypot(t_2, t_1) ^ single(2.0)))));
	end
	tmp_2 = tmp;
end

Derivation

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

Reproduce

herbie shell --seed 2023350 
(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
  :name "Anisotropic x16 LOD (line direction, v)"
  :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 (>= (+ (* (* (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 (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 h) dX.v)) (* (/ 1.0 (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 h) dY.v))))