Anisotropic x16 LOD (ratio of anisotropy)

Percentage Accurate: 97.7% → 97.7%
Time: 56.4s
Alternatives: 1
Speedup: N/A×

Specification

?
\[\left(\left(\left(\left(\left(\left(1 \leq w \land w \leq 16384\right) \land \left(1 \leq h \land h \leq 16384\right)\right) \land \left(10^{-20} \leq \left|dX.u\right| \land \left|dX.u\right| \leq 10^{+20}\right)\right) \land \left(10^{-20} \leq \left|dX.v\right| \land \left|dX.v\right| \leq 10^{+20}\right)\right) \land \left(10^{-20} \leq \left|dY.u\right| \land \left|dY.u\right| \leq 10^{+20}\right)\right) \land \left(10^{-20} \leq \left|dY.v\right| \land \left|dY.v\right| \leq 10^{+20}\right)\right) \land maxAniso = 16\]
\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left\lfloorh\right\rfloor \cdot dX.v\\ t_1 := \left\lfloorh\right\rfloor \cdot dY.v\\ t_2 := \left\lfloorw\right\rfloor \cdot dY.u\\ t_3 := \left\lfloorw\right\rfloor \cdot dX.u\\ t_4 := \mathsf{max}\left(t_3 \cdot t_3 + t_0 \cdot t_0, t_2 \cdot t_2 + t_1 \cdot t_1\right)\\ t_5 := \sqrt{t_4}\\ t_6 := \left|t_3 \cdot t_1 - t_0 \cdot t_2\right|\\ t_7 := \frac{t_4}{t_6}\\ t_8 := t_7 > \left\lfloormaxAniso\right\rfloor\\ t_9 := \begin{array}{l} \mathbf{if}\;t_8:\\ \;\;\;\;\frac{t_5}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_6}{t_5}\\ \end{array}\\ t_10 := \begin{array}{l} \mathbf{if}\;t_8:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array}\\ \mathbf{if}\;t_9 < 1:\\ \;\;\;\;\mathsf{max}\left(1, t_10 \cdot t_9\right)\\ \mathbf{else}:\\ \;\;\;\;t_10\\ \end{array} \end{array} \]
(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:

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Accuracy vs Speed?

Herbie found 1 alternatives:

AlternativeAccuracySpeedup
The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Initial Program: 97.7% accurate, 1.0× speedup?

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

Alternative 1: 97.7% accurate, 1.1× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\ t_1 := \mathsf{fma}\left(dX.v, dY.u, dX.u \cdot dY.v\right)\\ t_2 := \mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)\\ t_3 := \mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right), \left\lfloorh\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot \left(dX.v \cdot dX.v\right)\right)\right), \mathsf{fma}\left(\left\lfloorw\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(dY.u \cdot dY.u\right), \left(\left\lfloorh\right\rfloor \cdot \left\lfloorh\right\rfloor\right) \cdot \left(dY.v \cdot dY.v\right)\right)\right)\\ t_4 := \frac{t_3}{t_0}\\ t_5 := t_4 > \left\lfloormaxAniso\right\rfloor\\ t_6 := \sqrt{t_3}\\ t_7 := \frac{t_6}{\left\lfloormaxAniso\right\rfloor}\\ \mathbf{if}\;\begin{array}{l} \mathbf{if}\;t_5:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{t_6}\\ \end{array} < 1:\\ \;\;\;\;\mathsf{max}\left(1, \begin{array}{l} \mathbf{if}\;t_5:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;\left(\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot t_1\right)\right) \cdot {t_2}^{-0.5}\\ \end{array} \cdot \begin{array}{l} \mathbf{if}\;t_5:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot t_1\right)}\\ \end{array}\right)\\ \mathbf{elif}\;t_5:\\ \;\;\;\;\left\lfloormaxAniso\right\rfloor\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]
(FPCore (w h dX.u dX.v dY.u dY.v maxAniso)
 :precision binary32
 (let* ((t_0
         (fabs (* (floor h) (* (floor w) (- (* dX.u dY.v) (* dX.v dY.u))))))
        (t_1 (fma dX.v dY.u (* dX.u dY.v)))
        (t_2
         (fmax
          (pow (hypot (* (floor h) dX.v) (* (floor w) dX.u)) 2.0)
          (pow (hypot (* (floor h) dY.v) (* (floor w) dY.u)) 2.0)))
        (t_3
         (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_4 (/ t_3 t_0))
        (t_5 (> t_4 (floor maxAniso)))
        (t_6 (sqrt t_3))
        (t_7 (/ t_6 (floor maxAniso))))
   (if (< (if t_5 t_7 (/ t_0 t_6)) 1.0)
     (fmax
      1.0
      (*
       (if t_5 t_7 (* (* (floor h) (* (floor w) t_1)) (pow t_2 -0.5)))
       (if t_5 (floor maxAniso) (/ t_2 (* (floor w) (* (floor h) t_1))))))
     (if t_5 (floor maxAniso) t_4))))
float code(float w, float h, float dX_46_u, float dX_46_v, float dY_46_u, float dY_46_v, float maxAniso) {
	float t_0 = fabsf((floorf(h) * (floorf(w) * ((dX_46_u * dY_46_v) - (dX_46_v * dY_46_u)))));
	float t_1 = fmaf(dX_46_v, dY_46_u, (dX_46_u * dY_46_v));
	float t_2 = fmaxf(powf(hypotf((floorf(h) * dX_46_v), (floorf(w) * dX_46_u)), 2.0f), powf(hypotf((floorf(h) * dY_46_v), (floorf(w) * dY_46_u)), 2.0f));
	float t_3 = fmaxf(fmaf(floorf(w), (floorf(w) * (dX_46_u * dX_46_u)), (floorf(h) * (floorf(h) * (dX_46_v * dX_46_v)))), fmaf(floorf(w), (floorf(w) * (dY_46_u * dY_46_u)), ((floorf(h) * floorf(h)) * (dY_46_v * dY_46_v))));
	float t_4 = t_3 / t_0;
	int t_5 = t_4 > floorf(maxAniso);
	float t_6 = sqrtf(t_3);
	float t_7 = t_6 / floorf(maxAniso);
	float tmp;
	if (t_5) {
		tmp = t_7;
	} else {
		tmp = t_0 / t_6;
	}
	float tmp_3;
	if (tmp < 1.0f) {
		float tmp_4;
		if (t_5) {
			tmp_4 = t_7;
		} else {
			tmp_4 = (floorf(h) * (floorf(w) * t_1)) * powf(t_2, -0.5f);
		}
		float tmp_5;
		if (t_5) {
			tmp_5 = floorf(maxAniso);
		} else {
			tmp_5 = t_2 / (floorf(w) * (floorf(h) * t_1));
		}
		tmp_3 = fmaxf(1.0f, (tmp_4 * tmp_5));
	} else if (t_5) {
		tmp_3 = floorf(maxAniso);
	} else {
		tmp_3 = t_4;
	}
	return tmp_3;
}

function code(w, h, dX_46_u, dX_46_v, dY_46_u, dY_46_v, maxAniso)
	t_0 = abs(Float32(floor(h) * Float32(floor(w) * Float32(Float32(dX_46_u * dY_46_v) - Float32(dX_46_v * dY_46_u)))))
	t_1 = fma(dX_46_v, dY_46_u, Float32(dX_46_u * dY_46_v))
	t_2 = ((hypot(Float32(floor(h) * dX_46_v), Float32(floor(w) * dX_46_u)) ^ Float32(2.0)) != (hypot(Float32(floor(h) * dX_46_v), Float32(floor(w) * dX_46_u)) ^ Float32(2.0))) ? (hypot(Float32(floor(h) * dY_46_v), Float32(floor(w) * dY_46_u)) ^ Float32(2.0)) : (((hypot(Float32(floor(h) * dY_46_v), Float32(floor(w) * dY_46_u)) ^ Float32(2.0)) != (hypot(Float32(floor(h) * dY_46_v), Float32(floor(w) * dY_46_u)) ^ Float32(2.0))) ? (hypot(Float32(floor(h) * dX_46_v), Float32(floor(w) * dX_46_u)) ^ Float32(2.0)) : max((hypot(Float32(floor(h) * dX_46_v), Float32(floor(w) * dX_46_u)) ^ Float32(2.0)), (hypot(Float32(floor(h) * dY_46_v), Float32(floor(w) * dY_46_u)) ^ Float32(2.0))))
	t_3 = (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_4 = Float32(t_3 / t_0)
	t_5 = t_4 > floor(maxAniso)
	t_6 = sqrt(t_3)
	t_7 = Float32(t_6 / floor(maxAniso))
	tmp = Float32(0.0)
	if (t_5)
		tmp = t_7;
	else
		tmp = Float32(t_0 / t_6);
	end
	tmp_3 = Float32(0.0)
	if (tmp < Float32(1.0))
		tmp_4 = Float32(0.0)
		if (t_5)
			tmp_4 = t_7;
		else
			tmp_4 = Float32(Float32(floor(h) * Float32(floor(w) * t_1)) * (t_2 ^ Float32(-0.5)));
		end
		tmp_5 = Float32(0.0)
		if (t_5)
			tmp_5 = floor(maxAniso);
		else
			tmp_5 = Float32(t_2 / Float32(floor(w) * Float32(floor(h) * t_1)));
		end
		tmp_3 = (Float32(1.0) != Float32(1.0)) ? Float32(tmp_4 * tmp_5) : ((Float32(tmp_4 * tmp_5) != Float32(tmp_4 * tmp_5)) ? Float32(1.0) : max(Float32(1.0), Float32(tmp_4 * tmp_5)));
	elseif (t_5)
		tmp_3 = floor(maxAniso);
	else
		tmp_3 = t_4;
	end
	return tmp_3
end

\begin{array}{l}

\\
\begin{array}{l}
t_0 := \left|\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dY.v - dX.v \cdot dY.u\right)\right)\right|\\
t_1 := \mathsf{fma}\left(dX.v, dY.u, dX.u \cdot dY.v\right)\\
t_2 := \mathsf{max}\left({\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dX.v, \left\lfloorw\right\rfloor \cdot dX.u\right)\right)}^{2}, {\left(\mathsf{hypot}\left(\left\lfloorh\right\rfloor \cdot dY.v, \left\lfloorw\right\rfloor \cdot dY.u\right)\right)}^{2}\right)\\
t_3 := \mathsf{max}\left(\mathsf{fma}\left(\left\lfloorw\right\rfloor, \left\lfloorw\right\rfloor \cdot \left(dX.u \cdot dX.u\right), \left\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_4 := \frac{t_3}{t_0}\\
t_5 := t_4 > \left\lfloormaxAniso\right\rfloor\\
t_6 := \sqrt{t_3}\\
t_7 := \frac{t_6}{\left\lfloormaxAniso\right\rfloor}\\
\mathbf{if}\;\begin{array}{l}
\mathbf{if}\;t_5:\\
\;\;\;\;t_7\\

\mathbf{else}:\\
\;\;\;\;\frac{t_0}{t_6}\\


\end{array} < 1:\\
\;\;\;\;\mathsf{max}\left(1, \begin{array}{l}
\mathbf{if}\;t_5:\\
\;\;\;\;t_7\\

\mathbf{else}:\\
\;\;\;\;\left(\left\lfloorh\right\rfloor \cdot \left(\left\lfloorw\right\rfloor \cdot t_1\right)\right) \cdot {t_2}^{-0.5}\\


\end{array} \cdot \begin{array}{l}
\mathbf{if}\;t_5:\\
\;\;\;\;\left\lfloormaxAniso\right\rfloor\\

\mathbf{else}:\\
\;\;\;\;\frac{t_2}{\left\lfloorw\right\rfloor \cdot \left(\left\lfloorh\right\rfloor \cdot t_1\right)}\\


\end{array}\right)\\

\mathbf{elif}\;t_5:\\
\;\;\;\;\left\lfloormaxAniso\right\rfloor\\

\mathbf{else}:\\
\;\;\;\;t_4\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Reproduce

?
herbie shell --seed 2023347 
(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))))))))