\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]
Math FPCore C Julia Wolfram TeX \[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}
\]
↓
\[\begin{array}{l}
t_0 := \frac{\frac{x \cdot y}{\mathsf{fma}\left(z, z, z\right)}}{z}\\
\mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+303}:\\
\;\;\;\;\frac{\frac{y}{z}}{z \cdot \frac{z}{x}}\\
\mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-203}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-180}:\\
\;\;\;\;\frac{\frac{y}{z}}{\frac{\mathsf{fma}\left(z, z, z\right)}{x}}\\
\mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+132}:\\
\;\;\;\;t_0\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{y}{z}}{\frac{z}{\frac{x}{z}}}\\
\end{array}
\]
(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) -1e+303)
(/ (/ y z) (* z (/ z x)))
(if (<= (* x y) -1e-203)
t_0
(if (<= (* x y) 5e-180)
(/ (/ y z) (/ (fma z z z) x))
(if (<= (* x y) 2e+132) t_0 (/ (/ y z) (/ z (/ x z))))))))) 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) <= -1e+303) {
tmp = (y / z) / (z * (z / x));
} else if ((x * y) <= -1e-203) {
tmp = t_0;
} else if ((x * y) <= 5e-180) {
tmp = (y / z) / (fma(z, z, z) / x);
} else if ((x * y) <= 2e+132) {
tmp = t_0;
} else {
tmp = (y / z) / (z / (x / z));
}
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) <= -1e+303)
tmp = Float64(Float64(y / z) / Float64(z * Float64(z / x)));
elseif (Float64(x * y) <= -1e-203)
tmp = t_0;
elseif (Float64(x * y) <= 5e-180)
tmp = Float64(Float64(y / z) / Float64(fma(z, z, z) / x));
elseif (Float64(x * y) <= 2e+132)
tmp = t_0;
else
tmp = Float64(Float64(y / z) / Float64(z / Float64(x / z)));
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], -1e+303], N[(N[(y / z), $MachinePrecision] / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-203], t$95$0, If[LessEqual[N[(x * y), $MachinePrecision], 5e-180], N[(N[(y / z), $MachinePrecision] / N[(N[(z * z + z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+132], t$95$0, N[(N[(y / z), $MachinePrecision] / N[(z / N[(x / z), $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 -1 \cdot 10^{+303}:\\
\;\;\;\;\frac{\frac{y}{z}}{z \cdot \frac{z}{x}}\\
\mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-203}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-180}:\\
\;\;\;\;\frac{\frac{y}{z}}{\frac{\mathsf{fma}\left(z, z, z\right)}{x}}\\
\mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+132}:\\
\;\;\;\;t_0\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{y}{z}}{\frac{z}{\frac{x}{z}}}\\
\end{array}
Alternatives Alternative 1 Error 1.7 Cost 7496
\[\begin{array}{l}
\mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+303}:\\
\;\;\;\;\frac{\frac{y}{z}}{z \cdot \frac{z}{x}}\\
\mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-303}:\\
\;\;\;\;\frac{\frac{x \cdot y}{\mathsf{fma}\left(z, z, z\right)}}{z}\\
\mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-231}:\\
\;\;\;\;\frac{\frac{y}{z}}{\frac{z}{x}}\\
\mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+119}:\\
\;\;\;\;\frac{1}{z + 1} \cdot \frac{\frac{x \cdot y}{z}}{z}\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{y}{z}}{\frac{z}{\frac{x}{z}}}\\
\end{array}
\]
Alternative 2 Error 1.4 Cost 1872
\[\begin{array}{l}
t_0 := \frac{1}{z + 1} \cdot \frac{\frac{x \cdot y}{z}}{z}\\
\mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+303}:\\
\;\;\;\;\frac{\frac{y}{z}}{z \cdot \frac{z}{x}}\\
\mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-303}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-231}:\\
\;\;\;\;\frac{\frac{y}{z}}{\frac{z}{x}}\\
\mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+119}:\\
\;\;\;\;t_0\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{y}{z}}{\frac{z}{\frac{x}{z}}}\\
\end{array}
\]
Alternative 3 Error 3.3 Cost 1232
\[\begin{array}{l}
t_0 := \frac{y \cdot \frac{x}{z \cdot z}}{z + 1}\\
t_1 := \frac{\frac{y}{z}}{\frac{z}{\frac{x}{z}}}\\
\mathbf{if}\;z \leq -3.25 \cdot 10^{+47}:\\
\;\;\;\;t_1\\
\mathbf{elif}\;z \leq -1 \cdot 10^{-104}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;z \leq 10^{-90}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{z}{y}}\\
\mathbf{elif}\;z \leq 1.1369548196907596 \cdot 10^{+44}:\\
\;\;\;\;t_0\\
\mathbf{else}:\\
\;\;\;\;t_1\\
\end{array}
\]
Alternative 4 Error 3.3 Cost 1232
\[\begin{array}{l}
t_0 := \frac{y \cdot \frac{x}{z \cdot z}}{z + 1}\\
t_1 := \frac{z}{\frac{x}{z}}\\
\mathbf{if}\;z \leq -3.25 \cdot 10^{+47}:\\
\;\;\;\;\frac{\frac{y}{z}}{t_1}\\
\mathbf{elif}\;z \leq -1 \cdot 10^{-104}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;z \leq 10^{-90}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{z}{y}}\\
\mathbf{elif}\;z \leq 10^{+20}:\\
\;\;\;\;t_0\\
\mathbf{else}:\\
\;\;\;\;\frac{1}{z} \cdot \frac{y}{t_1}\\
\end{array}
\]
Alternative 5 Error 3.3 Cost 1232
\[\begin{array}{l}
t_0 := \frac{z}{\frac{x}{z}}\\
\mathbf{if}\;z \leq -1.3448661924577893 \cdot 10^{+55}:\\
\;\;\;\;\frac{\frac{y}{z}}{t_0}\\
\mathbf{elif}\;z \leq -1 \cdot 10^{-104}:\\
\;\;\;\;\frac{y}{\left(z + 1\right) \cdot \frac{z \cdot z}{x}}\\
\mathbf{elif}\;z \leq 10^{-90}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{z}{y}}\\
\mathbf{elif}\;z \leq 10^{+20}:\\
\;\;\;\;\frac{y \cdot \frac{x}{z \cdot z}}{z + 1}\\
\mathbf{else}:\\
\;\;\;\;\frac{1}{z} \cdot \frac{y}{t_0}\\
\end{array}
\]
Alternative 6 Error 3.2 Cost 1232
\[\begin{array}{l}
t_0 := \frac{x \cdot y}{\left(z + 1\right) \cdot \left(z \cdot z\right)}\\
t_1 := \frac{z}{\frac{x}{z}}\\
\mathbf{if}\;z \leq -3.25 \cdot 10^{+47}:\\
\;\;\;\;\frac{\frac{y}{z}}{t_1}\\
\mathbf{elif}\;z \leq -1 \cdot 10^{-140}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;z \leq 10^{-70}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{z}{y}}\\
\mathbf{elif}\;z \leq 5.839418904491006 \cdot 10^{+54}:\\
\;\;\;\;t_0\\
\mathbf{else}:\\
\;\;\;\;\frac{1}{z} \cdot \frac{y}{t_1}\\
\end{array}
\]
Alternative 7 Error 4.6 Cost 968
\[\begin{array}{l}
\mathbf{if}\;z \leq -1 \cdot 10^{-60}:\\
\;\;\;\;\frac{y}{z \cdot z} \cdot \frac{x}{z + 1}\\
\mathbf{elif}\;z \leq 1:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{z}{y}}\\
\mathbf{else}:\\
\;\;\;\;\frac{1}{z} \cdot \frac{y}{\frac{z}{\frac{x}{z}}}\\
\end{array}
\]
Alternative 8 Error 4.4 Cost 840
\[\begin{array}{l}
t_0 := \frac{\frac{y}{z}}{z \cdot \frac{z}{x}}\\
\mathbf{if}\;z \leq -1:\\
\;\;\;\;t_0\\
\mathbf{elif}\;z \leq 1:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{z}{y}}\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\]
Alternative 9 Error 4.1 Cost 840
\[\begin{array}{l}
t_0 := \frac{\frac{y}{z}}{z \cdot \frac{z}{x}}\\
\mathbf{if}\;z \leq -1:\\
\;\;\;\;t_0\\
\mathbf{elif}\;z \leq 1:\\
\;\;\;\;\frac{x \cdot \left(\frac{y}{z} - y\right)}{z}\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\]
Alternative 10 Error 4.1 Cost 840
\[\begin{array}{l}
t_0 := \frac{\frac{y}{z}}{z \cdot \frac{z}{x}}\\
\mathbf{if}\;z \leq -1:\\
\;\;\;\;t_0\\
\mathbf{elif}\;z \leq 1:\\
\;\;\;\;\frac{\frac{y}{z} - y}{\frac{z}{x}}\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\]
Alternative 11 Error 4.1 Cost 840
\[\begin{array}{l}
\mathbf{if}\;z \leq -1:\\
\;\;\;\;\frac{\frac{y}{z}}{z \cdot \frac{z}{x}}\\
\mathbf{elif}\;z \leq 1:\\
\;\;\;\;\frac{\frac{y}{z} - y}{\frac{z}{x}}\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{y}{z}}{\frac{z}{\frac{x}{z}}}\\
\end{array}
\]
Alternative 12 Error 17.9 Cost 712
\[\begin{array}{l}
t_0 := \frac{y}{\frac{z \cdot z}{x}}\\
\mathbf{if}\;z \leq -1 \cdot 10^{-104}:\\
\;\;\;\;t_0\\
\mathbf{elif}\;z \leq 10^{-90}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{z}{y}}\\
\mathbf{else}:\\
\;\;\;\;t_0\\
\end{array}
\]
Alternative 13 Error 17.4 Cost 712
\[\begin{array}{l}
\mathbf{if}\;x \leq -1 \cdot 10^{+45}:\\
\;\;\;\;x \cdot \frac{y}{z \cdot z}\\
\mathbf{elif}\;x \leq -2.2043045098779213 \cdot 10^{-218}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{z}{y}}\\
\mathbf{else}:\\
\;\;\;\;\frac{y}{\frac{z}{\frac{x}{z}}}\\
\end{array}
\]
Alternative 14 Error 17.4 Cost 712
\[\begin{array}{l}
\mathbf{if}\;x \leq -1 \cdot 10^{+45}:\\
\;\;\;\;x \cdot \frac{y}{z \cdot z}\\
\mathbf{elif}\;x \leq -1.0271701134459973 \cdot 10^{-190}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{z}{y}}\\
\mathbf{else}:\\
\;\;\;\;\frac{y}{z \cdot \frac{z}{x}}\\
\end{array}
\]
Alternative 15 Error 18.7 Cost 580
\[\begin{array}{l}
\mathbf{if}\;y \leq 10^{+43}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{z}{y}}\\
\mathbf{else}:\\
\;\;\;\;\frac{y}{\frac{z}{\frac{x}{z}}}\\
\end{array}
\]
Alternative 16 Error 43.4 Cost 452
\[\begin{array}{l}
\mathbf{if}\;y \leq 1.8636723453605865 \cdot 10^{-91}:\\
\;\;\;\;x \cdot \frac{y}{z}\\
\mathbf{else}:\\
\;\;\;\;y \cdot \frac{x}{z}\\
\end{array}
\]
Alternative 17 Error 43.1 Cost 452
\[\begin{array}{l}
\mathbf{if}\;y \leq 1.8636723453605865 \cdot 10^{-91}:\\
\;\;\;\;x \cdot \frac{y}{z}\\
\mathbf{else}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\
\end{array}
\]
Alternative 18 Error 42.7 Cost 452
\[\begin{array}{l}
\mathbf{if}\;y \leq 1.8636723453605865 \cdot 10^{-91}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\
\mathbf{else}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\
\end{array}
\]
Alternative 19 Error 21.8 Cost 448
\[\frac{\frac{x}{z}}{\frac{z}{y}}
\]
Alternative 20 Error 48.8 Cost 320
\[\frac{x \cdot y}{z}
\]
Alternative 21 Error 46.1 Cost 320
\[y \cdot \frac{x}{z}
\]
