Average Error: 12.2 → 3.0
Time: 3.2s
Precision: binary64
\[\frac{x \cdot \left(y + z\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq 4.749321301586014 \cdot 10^{+140}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + z\right) \cdot \frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}{\sqrt[3]{z}}\\ \end{array}\]
\frac{x \cdot \left(y + z\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \leq 4.749321301586014 \cdot 10^{+140}:\\
\;\;\;\;\frac{x}{\frac{z}{y + z}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(y + z\right) \cdot \frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}{\sqrt[3]{z}}\\

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (+ y z)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= y 4.749321301586014e+140)
   (/ x (/ z (+ y z)))
   (/ (* (+ y z) (/ x (* (cbrt z) (cbrt z)))) (cbrt z))))
double code(double x, double y, double z) {
	return (x * (y + z)) / z;
}
↓
double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.749321301586014e+140) {
		tmp = x / (z / (y + z));
	} else {
		tmp = ((y + z) * (x / (cbrt(z) * cbrt(z)))) / cbrt(z);
	}
	return tmp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original12.2
Target2.9
Herbie3.0
\[\frac{x}{\frac{z}{y + z}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < 4.7493213015860137e140

    1. Initial program 12.1

      \[\frac{x \cdot \left(y + z\right)}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*_binary642.1

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y + z}}}\]

    if 4.7493213015860137e140 < y

    1. Initial program 13.4

      \[\frac{x \cdot \left(y + z\right)}{z}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt_binary6414.4

      \[\leadsto \frac{x \cdot \left(y + z\right)}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    4. Applied associate-/r*_binary6414.4

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(y + z\right)}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}{\sqrt[3]{z}}}\]

    5. Simplified11.1

      \[\leadsto \frac{\color{blue}{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \left(y + z\right)}}{\sqrt[3]{z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.749321301586014 \cdot 10^{+140}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + z\right) \cdot \frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}{\sqrt[3]{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020253 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (/ x (/ z (+ y z)))

  (/ (* x (+ y z)) z))