Average Error: 13.0 → 3.5
Time: 2.0s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.666543304720725 \cdot 10^{104} \lor \neg \left(z \le 2.45560343256893582 \cdot 10^{-35}\right):\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.666543304720725 \cdot 10^{104} \lor \neg \left(z \le 2.45560343256893582 \cdot 10^{-35}\right):\\
\;\;\;\;x - \frac{x \cdot z}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r764374 = x;
        double r764375 = y;
        double r764376 = z;
        double r764377 = r764375 - r764376;
        double r764378 = r764374 * r764377;
        double r764379 = r764378 / r764375;
        return r764379;
}
↓
double f(double x, double y, double z) {
        double r764380 = z;
        double r764381 = -2.666543304720725e+104;
        bool r764382 = r764380 <= r764381;
        double r764383 = 2.455603432568936e-35;
        bool r764384 = r764380 <= r764383;
        double r764385 = !r764384;
        bool r764386 = r764382 || r764385;
        double r764387 = x;
        double r764388 = r764387 * r764380;
        double r764389 = y;
        double r764390 = r764388 / r764389;
        double r764391 = r764387 - r764390;
        double r764392 = r764380 / r764389;
        double r764393 = r764387 * r764392;
        double r764394 = r764387 - r764393;
        double r764395 = r764386 ? r764391 : r764394;
        return r764395;
}

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

Original13.0
Target3.5
Herbie3.5
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.666543304720725e+104 or 2.455603432568936e-35 < z

    1. Initial program 12.1

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

    3. Applied associate-/l*8.0

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

    4. Taylor expanded around 0 8.7

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

    if -2.666543304720725e+104 < z < 2.455603432568936e-35

    1. Initial program 13.5

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

    3. Applied associate-/l*0.4

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

    4. Taylor expanded around 0 2.9

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

    6. Applied *-un-lft-identity2.9

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

    7. Applied times-frac0.4

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

    8. Simplified0.4

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

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.666543304720725 \cdot 10^{104} \lor \neg \left(z \le 2.45560343256893582 \cdot 10^{-35}\right):\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(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))