Average Error: 11.9 → 2.9
Time: 18.1s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.398060602669454:\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.398060602669454:\\
\;\;\;\;x - x \cdot \frac{z}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r34353586 = x;
        double r34353587 = y;
        double r34353588 = z;
        double r34353589 = r34353587 - r34353588;
        double r34353590 = r34353586 * r34353589;
        double r34353591 = r34353590 / r34353587;
        return r34353591;
}
↓
double f(double x, double y, double z) {
        double r34353592 = y;
        double r34353593 = -3.398060602669454;
        bool r34353594 = r34353592 <= r34353593;
        double r34353595 = x;
        double r34353596 = z;
        double r34353597 = r34353596 / r34353592;
        double r34353598 = r34353595 * r34353597;
        double r34353599 = r34353595 - r34353598;
        double r34353600 = r34353595 * r34353596;
        double r34353601 = r34353600 / r34353592;
        double r34353602 = r34353595 - r34353601;
        double r34353603 = r34353594 ? r34353599 : r34353602;
        return r34353603;
}

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
Target2.7
Herbie2.9
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.398060602669454

    1. Initial program 15.9

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

    2. Taylor expanded around 0 5.1

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

    4. Applied *-un-lft-identity5.1

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

    5. Applied times-frac0.0

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

    6. Simplified0.0

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

    if -3.398060602669454 < y

    1. Initial program 10.3

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

    2. Taylor expanded around 0 4.1

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

  4. Final simplification2.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.398060602669454:\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(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))