Average Error: 11.9 → 1.7
Time: 10.3s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.852536865846577753563856140775043031674 \cdot 10^{94} \lor \neg \left(x \le 3.306570835569777515664669260458863592173 \cdot 10^{-59}\right):\\ \;\;\;\;x \cdot \left(\left(y - z\right) \cdot \frac{1}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.852536865846577753563856140775043031674 \cdot 10^{94} \lor \neg \left(x \le 3.306570835569777515664669260458863592173 \cdot 10^{-59}\right):\\
\;\;\;\;x \cdot \left(\left(y - z\right) \cdot \frac{1}{y}\right)\\

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

\end{array}
double f(double x, double y, double z) {
        double r497484 = x;
        double r497485 = y;
        double r497486 = z;
        double r497487 = r497485 - r497486;
        double r497488 = r497484 * r497487;
        double r497489 = r497488 / r497485;
        return r497489;
}
↓
double f(double x, double y, double z) {
        double r497490 = x;
        double r497491 = -1.8525368658465778e+94;
        bool r497492 = r497490 <= r497491;
        double r497493 = 3.3065708355697775e-59;
        bool r497494 = r497490 <= r497493;
        double r497495 = !r497494;
        bool r497496 = r497492 || r497495;
        double r497497 = y;
        double r497498 = z;
        double r497499 = r497497 - r497498;
        double r497500 = 1.0;
        double r497501 = r497500 / r497497;
        double r497502 = r497499 * r497501;
        double r497503 = r497490 * r497502;
        double r497504 = r497490 * r497498;
        double r497505 = r497504 / r497497;
        double r497506 = r497490 - r497505;
        double r497507 = r497496 ? r497503 : r497506;
        return r497507;
}

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

Original11.9
Target3.1
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.8525368658465778e+94 or 3.3065708355697775e-59 < x

    1. Initial program 21.8

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

    2. Simplified7.9

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

    4. Applied clear-num8.1

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

    5. Simplified0.4

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{y}{y - z}}{x}}}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity0.4

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

    8. Applied *-un-lft-identity0.4

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

    9. Applied *-un-lft-identity0.4

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

    10. Applied times-frac0.4

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

    11. Applied times-frac0.4

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

    12. Applied add-cube-cbrt0.4

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{\frac{1}{1}}{1} \cdot \frac{\frac{y}{y - z}}{x}}\]

    13. Applied times-frac0.4

      \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\frac{1}{1}}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{\frac{y}{y - z}}{x}}}\]

    14. Simplified0.4

      \[\leadsto \color{blue}{1} \cdot \frac{\sqrt[3]{1}}{\frac{\frac{y}{y - z}}{x}}\]

    15. Simplified0.4

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

    if -1.8525368658465778e+94 < x < 3.3065708355697775e-59

    1. Initial program 5.2

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

    2. Simplified15.1

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

    4. Applied clear-num15.2

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

    5. Simplified4.6

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

    6. Taylor expanded around 0 2.6

      \[\leadsto \color{blue}{x - \frac{x \cdot z}{y}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.852536865846577753563856140775043031674 \cdot 10^{94} \lor \neg \left(x \le 3.306570835569777515664669260458863592173 \cdot 10^{-59}\right):\\ \;\;\;\;x \cdot \left(\left(y - z\right) \cdot \frac{1}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"

  :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))