Average Error: 12.2 → 1.0
Time: 3.4s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[x - \left(x \cdot \left(\sqrt[3]{z} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{y}}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
x - \left(x \cdot \left(\sqrt[3]{z} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{y}}
double code(double x, double y, double z) {
	return (((double) (x * ((double) (y - z)))) / y);
}
↓
double code(double x, double y, double z) {
	return ((double) (x - ((double) (((double) (x * ((double) (((double) cbrt(z)) * (((double) cbrt(z)) / ((double) (((double) cbrt(y)) * ((double) cbrt(y))))))))) * (((double) cbrt(z)) / ((double) cbrt(y)))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

Enter valid numbers for all inputs

Target

Original12.2
Target3.1
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Initial program 12.2

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

  2. Simplified3.2

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

  4. Applied add-cube-cbrt3.6

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

  5. Applied add-cube-cbrt3.7

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

  6. Applied times-frac3.7

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

  7. Applied associate-*r*1.0

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

  8. Simplified1.0

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

  9. Final simplification1.0

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

Reproduce

herbie shell --seed 2020199 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

  (/ (* x (- y z)) y))