Average Error: 12.5 → 1.0
Time: 13.6s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\frac{\frac{x}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}}{\frac{\sqrt[3]{y}}{\sqrt[3]{y - z}}}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\frac{\frac{x}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}}{\frac{\sqrt[3]{y}}{\sqrt[3]{y - z}}}
double f(double x, double y, double z) {
        double r475860 = x;
        double r475861 = y;
        double r475862 = z;
        double r475863 = r475861 - r475862;
        double r475864 = r475860 * r475863;
        double r475865 = r475864 / r475861;
        return r475865;
}
↓
double f(double x, double y, double z) {
        double r475866 = x;
        double r475867 = y;
        double r475868 = cbrt(r475867);
        double r475869 = r475868 * r475868;
        double r475870 = z;
        double r475871 = r475867 - r475870;
        double r475872 = cbrt(r475871);
        double r475873 = r475872 * r475872;
        double r475874 = r475869 / r475873;
        double r475875 = r475866 / r475874;
        double r475876 = r475868 / r475872;
        double r475877 = r475875 / r475876;
        return r475877;
}

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

Original12.5
Target2.9
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Initial program 12.5

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

  3. Applied associate-/l*2.7

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

  5. Applied add-cube-cbrt3.9

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

  6. Applied add-cube-cbrt3.2

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

  7. Applied times-frac3.2

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

  8. Applied associate-/r*1.0

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

  9. Final simplification1.0

    \[\leadsto \frac{\frac{x}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}}{\frac{\sqrt[3]{y}}{\sqrt[3]{y - z}}}\]

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e104) (- x (/ (* z x) y)) (if (< z 1.69397660138285259e213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

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