Average Error: 12.3 → 1.0
Time: 6.8s
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 r658344 = x;
        double r658345 = y;
        double r658346 = z;
        double r658347 = r658345 - r658346;
        double r658348 = r658344 * r658347;
        double r658349 = r658348 / r658345;
        return r658349;
}
↓
double f(double x, double y, double z) {
        double r658350 = x;
        double r658351 = y;
        double r658352 = cbrt(r658351);
        double r658353 = r658352 * r658352;
        double r658354 = z;
        double r658355 = r658351 - r658354;
        double r658356 = cbrt(r658355);
        double r658357 = r658356 * r658356;
        double r658358 = r658353 / r658357;
        double r658359 = r658350 / r658358;
        double r658360 = r658352 / r658356;
        double r658361 = r658359 / r658360;
        return r658361;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

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Target

Original12.3
Target3.1
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Initial program 12.3

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

  3. Applied associate-/l*3.0

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

  5. Applied add-cube-cbrt4.2

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

  6. Applied add-cube-cbrt3.6

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

  7. Applied times-frac3.6

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

  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 2020045 
(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))