Average Error: 12.9 → 2.3
Time: 2.3s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.14151570008284528 \cdot 10^{-287} \lor \neg \left(y \le 1.1999376738034261 \cdot 10^{-72}\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.14151570008284528 \cdot 10^{-287} \lor \neg \left(y \le 1.1999376738034261 \cdot 10^{-72}\right):\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r774444 = x;
        double r774445 = y;
        double r774446 = z;
        double r774447 = r774445 - r774446;
        double r774448 = r774444 * r774447;
        double r774449 = r774448 / r774445;
        return r774449;
}
↓
double f(double x, double y, double z) {
        double r774450 = y;
        double r774451 = -1.1415157000828453e-287;
        bool r774452 = r774450 <= r774451;
        double r774453 = 1.1999376738034261e-72;
        bool r774454 = r774450 <= r774453;
        double r774455 = !r774454;
        bool r774456 = r774452 || r774455;
        double r774457 = x;
        double r774458 = z;
        double r774459 = r774450 - r774458;
        double r774460 = r774459 / r774450;
        double r774461 = r774457 * r774460;
        double r774462 = r774457 * r774458;
        double r774463 = r774462 / r774450;
        double r774464 = r774457 - r774463;
        double r774465 = r774456 ? r774461 : r774464;
        return r774465;
}

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

Original12.9
Target3.2
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.1415157000828453e-287 or 1.1999376738034261e-72 < y

    1. Initial program 13.8

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

    3. Applied *-un-lft-identity13.8

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

    4. Applied times-frac1.7

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

    5. Simplified1.7

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

    if -1.1415157000828453e-287 < y < 1.1999376738034261e-72

    1. Initial program 8.8

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

    3. Applied associate-/l*10.4

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

    4. Taylor expanded around 0 5.3

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.14151570008284528 \cdot 10^{-287} \lor \neg \left(y \le 1.1999376738034261 \cdot 10^{-72}\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(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))