Result for Anisotropic x16 LOD (ratio of anisotropy)

Specification

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

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

(FPCore (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)))

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;
}

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

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

\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}

Sampling outcomes in binary32 precision:

Initial Program: 97.8% accurate, 1.0× speedup?

(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)))

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;
}

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

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

\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}

Alternative 1: 98.2% accurate, 1.1× speedup?

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

(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0 (fabs (- (* dX.u dY.v) (* dX.v dY.u))))
        (t_1 (* dX.v (floor h)))
        (t_2 (* dX.u (floor w)))
        (t_3 (* (floor w) dY.u))
        (t_4 (* (floor h) dY.v))
        (t_5 (fmax (+ (* t_2 t_2) (* t_1 t_1)) (+ (* 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_1))))
        (t_9 (/ t_5 t_8))
        (t_10 (> t_9 (floor maxAniso)))
        (t_11 (fmax (pow (hypot t_2 t_1) 2.0) (pow (hypot t_3 t_4) 2.0)))
        (t_12 (> (/ t_11 (* (floor h) (* (floor w) t_0))) (floor maxAniso))))
   (if (< (if t_12 t_7 (* (floor h) (* t_0 (/ (floor w) (sqrt t_11))))) 1.0)
     (fmax 1.0 (* (if t_12 (floor maxAniso) t_9) (if t_10 t_7 (/ t_8 t_6))))
     (if t_10 (floor maxAniso) t_9))))

float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = fabsf(((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)));
	float t_1 = dX_46_v * floorf(h);
	float t_2 = dX_46_u * floorf(w);
	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_1 * t_1)), ((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_1)));
	float t_9 = t_5 / t_8;
	int t_10 = t_9 > floorf(maxAniso);
	float t_11 = fmaxf(powf(hypotf(t_2, t_1), 2.0f), powf(hypotf(t_3, t_4), 2.0f));
	int t_12 = (t_11 / (floorf(h) * (floorf(w) * t_0))) > floorf(maxAniso);
	float tmp;
	if (t_12) {
		tmp = t_7;
	} else {
		tmp = floorf(h) * (t_0 * (floorf(w) / sqrtf(t_11)));
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_12) {
			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 = t_9;
	}
	return tmp_3;
}

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = abs(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(dX_46_u * floor(w))
	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_1 * t_1)) != Float32(Float32(t_2 * t_2) + 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_2 * t_2) + Float32(t_1 * t_1)) : max(Float32(Float32(t_2 * t_2) + Float32(t_1 * t_1)), 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_1)))
	t_9 = Float32(t_5 / t_8)
	t_10 = t_9 > floor(maxAniso)
	t_11 = ((hypot(t_2, t_1) ^ Float32(2.0)) != (hypot(t_2, 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_2, t_1) ^ Float32(2.0)) : max((hypot(t_2, t_1) ^ Float32(2.0)), (hypot(t_3, t_4) ^ Float32(2.0))))
	t_12 = Float32(t_11 / Float32(floor(h) * Float32(floor(w) * t_0))) > floor(maxAniso)
	tmp = Float32(0.0)
	if (t_12)
		tmp = t_7;
	else
		tmp = Float32(floor(h) * Float32(t_0 * Float32(floor(w) / sqrt(t_11))));
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_12)
			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 = t_9;
	end
	return tmp_3
end

function tmp_7 = code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = abs(((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)));
	t_1 = dX_46_v * floor(h);
	t_2 = dX_46_u * floor(w);
	t_3 = floor(w) * dY_46_u;
	t_4 = floor(h) * dY_46_v;
	t_5 = max(((t_2 * t_2) + (t_1 * t_1)), ((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_1)));
	t_9 = t_5 / t_8;
	t_10 = t_9 > floor(maxAniso);
	t_11 = max((hypot(t_2, t_1) ^ single(2.0)), (hypot(t_3, t_4) ^ single(2.0)));
	t_12 = (t_11 / (floor(h) * (floor(w) * t_0))) > floor(maxAniso);
	tmp = single(0.0);
	if (t_12)
		tmp = t_7;
	else
		tmp = floor(h) * (t_0 * (floor(w) / sqrt(t_11)));
	end
	tmp_4 = single(0.0);
	if (tmp < single(1.0))
		tmp_5 = single(0.0);
		if (t_12)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = t_9;
		end
		tmp_6 = single(0.0);
		if (t_10)
			tmp_6 = t_7;
		else
			tmp_6 = t_8 / t_6;
		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

\begin{array}{l}

\\
\begin{array}{l}
t_0 := \left|dX.u \cdot dY.v - dX.v \cdot dY.u\right|\\
t_1 := dX.v \cdot \left\lfloorh\right\rfloor\\
t_2 := dX.u \cdot \left\lfloorw\right\rfloor\\
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_1 \cdot t_1, 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_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_2, t_1\right)\right)}^{2}, {\left(\mathsf{hypot}\left(t_3, t_4\right)\right)}^{2}\right)\\
t_12 := \frac{t_11}{\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot t_0\right)} > \left\lfloormaxAniso\right\rfloor\\
\mathbf{if}\;\begin{array}{l}
\mathbf{if}\;t_12:\\
\;\;\;\;t_7\\

\mathbf{else}:\\
\;\;\;\;\left\lfloorh\right\rfloor \cdot \left(t_0 \cdot \frac{\left\lfloorw\right\rfloor}{\sqrt{t_11}}\right)\\


\end{array} < 1:\\
\;\;\;\;\mathsf{max}\left(1, \begin{array}{l}
\mathbf{if}\;t_12:\\
\;\;\;\;\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}:\\
\;\;\;\;t_9\\


\end{array}
\end{array}

Derivation

&prev;&pcontext;&pcontext2;&ctx;

Add Preprocessing

Reproduce

herbie shell --seed 2024008 
(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))))))))

Anisotropic x16 LOD (ratio of anisotropy)

Specification

Local Percentage Accuracy vs ?

Accuracy vs Speed?

Initial Program: 97.8% accurate, 1.0× speedup?

Alternative 1: 98.2% accurate, 1.1× speedup?

Reproduce

Specification

Local Percentage Accuracy vs ?

Accuracy vs Speed?

Initial Program: 97.8% accurate, 1.0× speedupMathFPCoreCJuliaMATLABTeX?

Alternative 1: 98.2% accurate, 1.1× speedupMathFPCoreCJuliaMATLABTeX?

Reproduce

Initial Program: 97.8% accurate, 1.0× speedup?

Alternative 1: 98.2% accurate, 1.1× speedup?