Average Error: 12.9 → 1.1
Time: 2.6s
Precision: binary64
\[\frac{x \cdot \left(y + z\right)}{z}\]
↓
\[x + \left(x \cdot \left(\sqrt[3]{y} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]
\frac{x \cdot \left(y + z\right)}{z}
↓
x + \left(x \cdot \left(\sqrt[3]{y} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}
double code(double x, double y, double z) {
	return (((double) (x * ((double) (y + z)))) / z);
}
↓
double code(double x, double y, double z) {
	return ((double) (x + ((double) (((double) (x * ((double) (((double) cbrt(y)) * (((double) cbrt(y)) / ((double) (((double) cbrt(z)) * ((double) cbrt(z))))))))) * (((double) cbrt(y)) / ((double) cbrt(z)))))));
}

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

Original12.9
Target2.8
Herbie1.1
\[\frac{x}{\frac{z}{y + z}}\]

Derivation

  1. Initial program 12.9

    \[\frac{x \cdot \left(y + z\right)}{z}\]

  2. Simplified3.0

    \[\leadsto \color{blue}{x + x \cdot \frac{y}{z}}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt3.4

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

  5. Applied add-cube-cbrt3.5

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

  6. Applied times-frac3.5

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

  7. Applied associate-*r*1.1

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

  8. Simplified1.1

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

  9. Final simplification1.1

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

Reproduce

herbie shell --seed 2020196 
(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))