Average Error: 12.4 → 2.4
Time: 8.7s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.107279811299475 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;y \le 1.2762912970477182 \cdot 10^{-154}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.107279811299475 \cdot 10^{-178}:\\
\;\;\;\;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 r33815267 = x;
        double r33815268 = y;
        double r33815269 = z;
        double r33815270 = r33815268 - r33815269;
        double r33815271 = r33815267 * r33815270;
        double r33815272 = r33815271 / r33815268;
        return r33815272;
}
↓
double f(double x, double y, double z) {
        double r33815273 = y;
        double r33815274 = -2.107279811299475e-178;
        bool r33815275 = r33815273 <= r33815274;
        double r33815276 = x;
        double r33815277 = z;
        double r33815278 = r33815273 - r33815277;
        double r33815279 = r33815278 / r33815273;
        double r33815280 = r33815276 * r33815279;
        double r33815281 = 1.2762912970477182e-154;
        bool r33815282 = r33815273 <= r33815281;
        double r33815283 = r33815276 * r33815277;
        double r33815284 = r33815283 / r33815273;
        double r33815285 = r33815276 - r33815284;
        double r33815286 = r33815282 ? r33815285 : r33815280;
        double r33815287 = r33815275 ? r33815280 : r33815286;
        return r33815287;
}

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

Original12.4
Target3.0
Herbie2.4
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -2.107279811299475e-178 or 1.2762912970477182e-154 < y

    1. Initial program 12.6

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

    3. Applied *-un-lft-identity12.6

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

    4. Applied times-frac1.3

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

    5. Simplified1.3

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

    if -2.107279811299475e-178 < y < 1.2762912970477182e-154

    1. Initial program 10.9

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

    2. Taylor expanded around 0 8.0

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.107279811299475 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;y \le 1.2762912970477182 \cdot 10^{-154}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]

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))