Average Error: 12.8 → 1.9
Time: 1.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le 9.154941957803031 \cdot 10^{-62} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.74805499515868977 \cdot 10^{289}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le 9.154941957803031 \cdot 10^{-62} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.74805499515868977 \cdot 10^{289}\right):\\
\;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

\end{array}
double f(double x, double y, double z) {
        double r721186 = x;
        double r721187 = y;
        double r721188 = z;
        double r721189 = r721187 - r721188;
        double r721190 = r721186 * r721189;
        double r721191 = r721190 / r721187;
        return r721191;
}
↓
double f(double x, double y, double z) {
        double r721192 = x;
        double r721193 = y;
        double r721194 = z;
        double r721195 = r721193 - r721194;
        double r721196 = r721192 * r721195;
        double r721197 = r721196 / r721193;
        double r721198 = 9.154941957803031e-62;
        bool r721199 = r721197 <= r721198;
        double r721200 = 1.7480549951586898e+289;
        bool r721201 = r721197 <= r721200;
        double r721202 = !r721201;
        bool r721203 = r721199 || r721202;
        double r721204 = 1.0;
        double r721205 = r721194 / r721193;
        double r721206 = r721204 - r721205;
        double r721207 = r721192 * r721206;
        double r721208 = r721203 ? r721207 : r721197;
        return r721208;
}

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

Original12.8
Target3.0
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (- y z)) y) < 9.154941957803031e-62 or 1.7480549951586898e+289 < (/ (* x (- y z)) y)

    1. Initial program 17.0

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

    3. Applied *-un-lft-identity17.0

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

    4. Applied times-frac2.5

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

    5. Simplified2.5

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

    7. Applied div-sub2.5

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

    8. Simplified2.5

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

    if 9.154941957803031e-62 < (/ (* x (- y z)) y) < 1.7480549951586898e+289

    1. Initial program 0.3

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le 9.154941957803031 \cdot 10^{-62} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 1.74805499515868977 \cdot 10^{289}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020049 
(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))