Average Error: 13.0 → 2.1
Time: 37.4s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -8.788234924117261 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;y \le 1.2762912970477182 \cdot 10^{-154}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -8.788234924117261 \cdot 10^{-91}:\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

\mathbf{elif}\;y \le 1.2762912970477182 \cdot 10^{-154}:\\
\;\;\;\;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 r37111117 = x;
        double r37111118 = y;
        double r37111119 = z;
        double r37111120 = r37111118 - r37111119;
        double r37111121 = r37111117 * r37111120;
        double r37111122 = r37111121 / r37111118;
        return r37111122;
}
↓
double f(double x, double y, double z) {
        double r37111123 = y;
        double r37111124 = -8.788234924117261e-91;
        bool r37111125 = r37111123 <= r37111124;
        double r37111126 = x;
        double r37111127 = z;
        double r37111128 = r37111123 - r37111127;
        double r37111129 = r37111128 / r37111123;
        double r37111130 = r37111126 * r37111129;
        double r37111131 = 1.2762912970477182e-154;
        bool r37111132 = r37111123 <= r37111131;
        double r37111133 = r37111126 * r37111127;
        double r37111134 = r37111133 / r37111123;
        double r37111135 = r37111126 - r37111134;
        double r37111136 = r37111132 ? r37111135 : r37111130;
        double r37111137 = r37111125 ? r37111130 : r37111136;
        return r37111137;
}

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
Target3.1
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -8.788234924117261e-91 or 1.2762912970477182e-154 < y

    1. Initial program 14.1

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

    3. Applied *-un-lft-identity14.1

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

    4. Applied times-frac0.8

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

    5. Simplified0.8

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

    if -8.788234924117261e-91 < y < 1.2762912970477182e-154

    1. Initial program 9.5

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

    2. Taylor expanded around 0 6.4

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

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -8.788234924117261 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;y \le 1.2762912970477182 \cdot 10^{-154}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(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))