Average Error: 12.7 → 2.9
Time: 2.3s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.8688621848367084 \cdot 10^{248}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 \cdot \frac{y}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.8688621848367084 \cdot 10^{248}:\\
\;\;\;\;x - \frac{x \cdot z}{y}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{1 \cdot \frac{y}{y - z}}\\

\end{array}
double f(double x, double y, double z) {
        double r592393 = x;
        double r592394 = y;
        double r592395 = z;
        double r592396 = r592394 - r592395;
        double r592397 = r592393 * r592396;
        double r592398 = r592397 / r592394;
        return r592398;
}
↓
double f(double x, double y, double z) {
        double r592399 = z;
        double r592400 = -1.8688621848367084e+248;
        bool r592401 = r592399 <= r592400;
        double r592402 = x;
        double r592403 = r592402 * r592399;
        double r592404 = y;
        double r592405 = r592403 / r592404;
        double r592406 = r592402 - r592405;
        double r592407 = 1.0;
        double r592408 = r592404 - r592399;
        double r592409 = r592404 / r592408;
        double r592410 = r592407 * r592409;
        double r592411 = r592402 / r592410;
        double r592412 = r592401 ? r592406 : r592411;
        return r592412;
}

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

Original12.7
Target3.0
Herbie2.9
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.8688621848367084e+248

    1. Initial program 13.5

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

    3. Applied associate-/l*11.5

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

    4. Taylor expanded around 0 13.0

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

    if -1.8688621848367084e+248 < z

    1. Initial program 12.7

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

    3. Applied associate-/l*2.5

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

    5. Applied *-un-lft-identity2.5

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

    6. Applied *-un-lft-identity2.5

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

    7. Applied times-frac2.5

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

    8. Simplified2.5

      \[\leadsto \frac{x}{\color{blue}{1} \cdot \frac{y}{y - z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.8688621848367084 \cdot 10^{248}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 \cdot \frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020089 
(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))