Average Error: 11.7 → 3.1
Time: 15.4s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.876455341869721 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;y \le 1.1367980230815625 \cdot 10^{-137}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.876455341869721 \cdot 10^{-13}:\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

\mathbf{elif}\;y \le 1.1367980230815625 \cdot 10^{-137}:\\
\;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r34242534 = x;
        double r34242535 = y;
        double r34242536 = z;
        double r34242537 = r34242535 - r34242536;
        double r34242538 = r34242534 * r34242537;
        double r34242539 = r34242538 / r34242535;
        return r34242539;
}
↓
double f(double x, double y, double z) {
        double r34242540 = y;
        double r34242541 = -1.876455341869721e-13;
        bool r34242542 = r34242540 <= r34242541;
        double r34242543 = x;
        double r34242544 = z;
        double r34242545 = r34242540 - r34242544;
        double r34242546 = r34242545 / r34242540;
        double r34242547 = r34242543 * r34242546;
        double r34242548 = 1.1367980230815625e-137;
        bool r34242549 = r34242540 <= r34242548;
        double r34242550 = r34242543 / r34242540;
        double r34242551 = r34242545 * r34242550;
        double r34242552 = r34242549 ? r34242551 : r34242547;
        double r34242553 = r34242542 ? r34242547 : r34242552;
        return r34242553;
}

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

Original11.7
Target2.9
Herbie3.1
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.876455341869721e-13 or 1.1367980230815625e-137 < y

    1. Initial program 13.3

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

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

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

    4. Applied times-frac0.6

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

    5. Simplified0.6

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

    if -1.876455341869721e-13 < y < 1.1367980230815625e-137

    1. Initial program 8.4

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

    3. Applied associate-/l*8.3

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

    5. Applied associate-/r/8.8

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

  4. Final simplification3.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.876455341869721 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;y \le 1.1367980230815625 \cdot 10^{-137}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 +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))