Average Error: 13.0 → 1.4
Time: 3.5s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.446414607682033344844893055916604547379 \cdot 10^{-250}:\\ \;\;\;\;\left(x \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{y}}\\ \mathbf{elif}\;y \le 3572580006165377287364755677987733504:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.446414607682033344844893055916604547379 \cdot 10^{-250}:\\
\;\;\;\;\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}}\\

\mathbf{elif}\;y \le 3572580006165377287364755677987733504:\\
\;\;\;\;x - \frac{x \cdot z}{y}\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

\end{array}
double f(double x, double y, double z) {
        double r865511 = x;
        double r865512 = y;
        double r865513 = z;
        double r865514 = r865512 - r865513;
        double r865515 = r865511 * r865514;
        double r865516 = r865515 / r865512;
        return r865516;
}
↓
double f(double x, double y, double z) {
        double r865517 = y;
        double r865518 = -1.4464146076820333e-250;
        bool r865519 = r865517 <= r865518;
        double r865520 = x;
        double r865521 = z;
        double r865522 = r865517 - r865521;
        double r865523 = cbrt(r865522);
        double r865524 = r865523 * r865523;
        double r865525 = cbrt(r865517);
        double r865526 = r865525 * r865525;
        double r865527 = r865524 / r865526;
        double r865528 = r865520 * r865527;
        double r865529 = r865523 / r865525;
        double r865530 = r865528 * r865529;
        double r865531 = 3.572580006165377e+36;
        bool r865532 = r865517 <= r865531;
        double r865533 = r865520 * r865521;
        double r865534 = r865533 / r865517;
        double r865535 = r865520 - r865534;
        double r865536 = r865522 / r865517;
        double r865537 = r865520 * r865536;
        double r865538 = r865532 ? r865535 : r865537;
        double r865539 = r865519 ? r865530 : r865538;
        return r865539;
}

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

Original13.0
Target3.4
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.4464146076820333e-250

    1. Initial program 13.1

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

    3. Applied *-un-lft-identity13.1

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

    4. Applied times-frac2.5

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

    5. Simplified2.5

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

    7. Applied add-cube-cbrt3.7

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

    8. Applied add-cube-cbrt3.0

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

    9. Applied times-frac3.0

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

    10. Applied associate-*r*0.8

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

    if -1.4464146076820333e-250 < y < 3.572580006165377e+36

    1. Initial program 6.3

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

    3. Applied *-un-lft-identity6.3

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

    4. Applied times-frac8.1

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

    5. Simplified8.1

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

    7. Applied add-cube-cbrt9.2

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

    8. Applied associate-*l*9.2

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

    9. Taylor expanded around 0 3.7

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

    if 3.572580006165377e+36 < y

    1. Initial program 19.6

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

    3. Applied *-un-lft-identity19.6

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.446414607682033344844893055916604547379 \cdot 10^{-250}:\\ \;\;\;\;\left(x \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{y}}\\ \mathbf{elif}\;y \le 3572580006165377287364755677987733504:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(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))