\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]
Math FPCore C Julia Wolfram TeX \[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}
\]
↓
\[\begin{array}{l}
t_0 := \frac{\frac{x \cdot y}{\mathsf{fma}\left(z, z, z\right)}}{z}\\
\mathbf{if}\;x \cdot y \leq -\infty:\\
\;\;\;\;\frac{\frac{y}{z} \cdot \frac{x}{z}}{z}\\
\mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-270}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-314}:\\
\;\;\;\;\frac{\frac{x}{\mathsf{fma}\left(z, z, z\right)}}{\frac{z}{y}}\\
\mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+179}:\\
\;\;\;\;t_0\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{z}}{z \cdot \frac{z + 1}{y}}\\
\end{array}
\]
(FPCore (x y z) :precision binary64 (/ (* x y) (* (* z z) (+ z 1.0)))) ↓
(FPCore (x y z)
:precision binary64
(let* ((t_0 (/ (/ (* x y) (fma z z z)) z)))
(if (<= (* x y) (- INFINITY))
(/ (* (/ y z) (/ x z)) z)
(if (<= (* x y) -1e-270)
t_0
(if (<= (* x y) 4e-314)
(/ (/ x (fma z z z)) (/ z y))
(if (<= (* x y) 2e+179) t_0 (/ (/ x z) (* z (/ (+ z 1.0) y))))))))) double code(double x, double y, double z) {
return (x * y) / ((z * z) * (z + 1.0));
}
↓
double code(double x, double y, double z) {
double t_0 = ((x * y) / fma(z, z, z)) / z;
double tmp;
if ((x * y) <= -((double) INFINITY)) {
tmp = ((y / z) * (x / z)) / z;
} else if ((x * y) <= -1e-270) {
tmp = t_0;
} else if ((x * y) <= 4e-314) {
tmp = (x / fma(z, z, z)) / (z / y);
} else if ((x * y) <= 2e+179) {
tmp = t_0;
} else {
tmp = (x / z) / (z * ((z + 1.0) / y));
}
return tmp;
}
function code(x, y, z)
return Float64(Float64(x * y) / Float64(Float64(z * z) * Float64(z + 1.0)))
end
↓
function code(x, y, z)
t_0 = Float64(Float64(Float64(x * y) / fma(z, z, z)) / z)
tmp = 0.0
if (Float64(x * y) <= Float64(-Inf))
tmp = Float64(Float64(Float64(y / z) * Float64(x / z)) / z);
elseif (Float64(x * y) <= -1e-270)
tmp = t_0;
elseif (Float64(x * y) <= 4e-314)
tmp = Float64(Float64(x / fma(z, z, z)) / Float64(z / y));
elseif (Float64(x * y) <= 2e+179)
tmp = t_0;
else
tmp = Float64(Float64(x / z) / Float64(z * Float64(Float64(z + 1.0) / y)));
end
return tmp
end
code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] / N[(N[(z * z), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x * y), $MachinePrecision] / N[(z * z + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(N[(N[(y / z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-270], t$95$0, If[LessEqual[N[(x * y), $MachinePrecision], 4e-314], N[(N[(x / N[(z * z + z), $MachinePrecision]), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+179], t$95$0, N[(N[(x / z), $MachinePrecision] / N[(z * N[(N[(z + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]
\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}
↓
\begin{array}{l}
t_0 := \frac{\frac{x \cdot y}{\mathsf{fma}\left(z, z, z\right)}}{z}\\
\mathbf{if}\;x \cdot y \leq -\infty:\\
\;\;\;\;\frac{\frac{y}{z} \cdot \frac{x}{z}}{z}\\
\mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-270}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-314}:\\
\;\;\;\;\frac{\frac{x}{\mathsf{fma}\left(z, z, z\right)}}{\frac{z}{y}}\\
\mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+179}:\\
\;\;\;\;t_0\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{z}}{z \cdot \frac{z + 1}{y}}\\
\end{array}
Alternatives Alternative 1 Error 0.8 Cost 8016
\[\begin{array}{l}
t_0 := \frac{\frac{x \cdot y}{\mathsf{fma}\left(z, z, z\right)}}{z}\\
t_1 := \frac{y}{z} \cdot \frac{x}{z}\\
\mathbf{if}\;x \cdot y \leq -\infty:\\
\;\;\;\;\frac{t_1}{z}\\
\mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-280}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-314}:\\
\;\;\;\;t_1\\
\mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+179}:\\
\;\;\;\;t_0\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{z}}{z \cdot \frac{z + 1}{y}}\\
\end{array}
\]
Alternative 2 Error 2.8 Cost 1224
\[\begin{array}{l}
t_0 := \frac{\frac{x}{z}}{z \cdot \frac{z + 1}{y}}\\
\mathbf{if}\;x \cdot y \leq 10^{-57}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+179}:\\
\;\;\;\;\frac{x \cdot y}{\left(z + 1\right) \cdot \left(z \cdot z\right)}\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\]
Alternative 3 Error 5.2 Cost 840
\[\begin{array}{l}
t_0 := \frac{x \cdot \frac{\frac{y}{z}}{z}}{z}\\
\mathbf{if}\;z \leq -2718407729970204700:\\
\;\;\;\;t_0\\
\mathbf{elif}\;z \leq 1:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{z}{y}}\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\]
Alternative 4 Error 5.0 Cost 840
\[\begin{array}{l}
\mathbf{if}\;z \leq -2718407729970204700:\\
\;\;\;\;\frac{\frac{y}{z} \cdot \frac{x}{z}}{z}\\
\mathbf{elif}\;z \leq 1:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{z}{y}}\\
\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \frac{\frac{y}{z}}{z}}{z}\\
\end{array}
\]
Alternative 5 Error 4.7 Cost 840
\[\begin{array}{l}
\mathbf{if}\;z \leq -2718407729970204700:\\
\;\;\;\;\frac{\frac{y}{z} \cdot \frac{x}{z}}{z}\\
\mathbf{elif}\;z \leq 0.01:\\
\;\;\;\;\frac{\frac{x}{z} - x}{\frac{z}{y}}\\
\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \frac{\frac{y}{z}}{z}}{z}\\
\end{array}
\]
Alternative 6 Error 3.3 Cost 704
\[\frac{\frac{x}{z}}{z \cdot \frac{z + 1}{y}}
\]
Alternative 7 Error 17.0 Cost 580
\[\begin{array}{l}
\mathbf{if}\;x \leq -1.7430456274312792 \cdot 10^{-44}:\\
\;\;\;\;x \cdot \frac{\frac{y}{z}}{z}\\
\mathbf{else}:\\
\;\;\;\;y \cdot \frac{\frac{x}{z}}{z}\\
\end{array}
\]
Alternative 8 Error 16.9 Cost 580
\[\begin{array}{l}
\mathbf{if}\;x \leq -7.175635036983987 \cdot 10^{-127}:\\
\;\;\;\;\frac{x}{\frac{z}{\frac{y}{z}}}\\
\mathbf{else}:\\
\;\;\;\;y \cdot \frac{\frac{x}{z}}{z}\\
\end{array}
\]
Alternative 9 Error 42.4 Cost 452
\[\begin{array}{l}
\mathbf{if}\;x \leq -1 \cdot 10^{+36}:\\
\;\;\;\;x \cdot \frac{y}{z}\\
\mathbf{else}:\\
\;\;\;\;y \cdot \frac{x}{z}\\
\end{array}
\]
Alternative 10 Error 42.1 Cost 452
\[\begin{array}{l}
\mathbf{if}\;y \leq 3.8826789787260356 \cdot 10^{-81}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\
\mathbf{else}:\\
\;\;\;\;y \cdot \frac{x}{z}\\
\end{array}
\]
Alternative 11 Error 41.7 Cost 452
\[\begin{array}{l}
\mathbf{if}\;y \leq 3.8826789787260356 \cdot 10^{-81}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\
\mathbf{else}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\
\end{array}
\]
Alternative 12 Error 22.3 Cost 448
\[y \cdot \frac{\frac{x}{z}}{z}
\]
Alternative 13 Error 45.3 Cost 320
\[y \cdot \frac{x}{z}
\]
