Average Error: 12.9 → 0.7
Time: 3.0s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -3.3281553970256071 \cdot 10^{-79}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{y}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -3.3281553970256071 \cdot 10^{-79}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r714723 = x;
        double r714724 = y;
        double r714725 = z;
        double r714726 = r714724 - r714725;
        double r714727 = r714723 * r714726;
        double r714728 = r714727 / r714724;
        return r714728;
}
↓
double f(double x, double y, double z) {
        double r714729 = x;
        double r714730 = y;
        double r714731 = z;
        double r714732 = r714730 - r714731;
        double r714733 = r714729 * r714732;
        double r714734 = r714733 / r714730;
        double r714735 = -inf.0;
        bool r714736 = r714734 <= r714735;
        double r714737 = r714732 / r714730;
        double r714738 = r714729 * r714737;
        double r714739 = -3.328155397025607e-79;
        bool r714740 = r714734 <= r714739;
        double r714741 = cbrt(r714732);
        double r714742 = r714741 * r714741;
        double r714743 = cbrt(r714730);
        double r714744 = r714743 * r714743;
        double r714745 = r714742 / r714744;
        double r714746 = r714729 * r714745;
        double r714747 = r714741 / r714743;
        double r714748 = r714746 * r714747;
        double r714749 = r714740 ? r714734 : r714748;
        double r714750 = r714736 ? r714738 : r714749;
        return r714750;
}

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
Target3.0
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) y) < -inf.0

    1. Initial program 64.0

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

    3. Applied *-un-lft-identity64.0

      \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{1 \cdot y}}\]

    4. Applied times-frac0.1

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y - z}{y}}\]

    5. Simplified0.1

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

    if -inf.0 < (/ (* x (- y z)) y) < -3.328155397025607e-79

    1. Initial program 0.2

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

    if -3.328155397025607e-79 < (/ (* x (- y z)) y)

    1. Initial program 12.3

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

    3. Applied *-un-lft-identity12.3

      \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{1 \cdot y}}\]

    4. Applied times-frac2.3

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y - z}{y}}\]

    5. Simplified2.3

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

    7. Applied add-cube-cbrt3.6

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

    8. Applied add-cube-cbrt2.8

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

    9. Applied times-frac2.8

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

    10. Applied associate-*r*0.9

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -3.3281553970256071 \cdot 10^{-79}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020039 +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 -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

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