Average Error: 12.6 → 3.3
Time: 14.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.997145875047444652240240655689849825805 \cdot 10^{-240} \lor \neg \left(y \le 5.997849739943499755512315945487169370901 \cdot 10^{-177}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x}{y} \cdot \left(-z\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.997145875047444652240240655689849825805 \cdot 10^{-240} \lor \neg \left(y \le 5.997849739943499755512315945487169370901 \cdot 10^{-177}\right):\\
\;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\

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

\end{array}
double f(double x, double y, double z) {
        double r568892 = x;
        double r568893 = y;
        double r568894 = z;
        double r568895 = r568893 - r568894;
        double r568896 = r568892 * r568895;
        double r568897 = r568896 / r568893;
        return r568897;
}
↓
double f(double x, double y, double z) {
        double r568898 = y;
        double r568899 = -2.9971458750474447e-240;
        bool r568900 = r568898 <= r568899;
        double r568901 = 5.9978497399435e-177;
        bool r568902 = r568898 <= r568901;
        double r568903 = !r568902;
        bool r568904 = r568900 || r568903;
        double r568905 = x;
        double r568906 = 1.0;
        double r568907 = z;
        double r568908 = r568907 / r568898;
        double r568909 = r568906 - r568908;
        double r568910 = r568905 * r568909;
        double r568911 = r568905 / r568898;
        double r568912 = -r568907;
        double r568913 = r568911 * r568912;
        double r568914 = r568905 + r568913;
        double r568915 = r568904 ? r568910 : r568914;
        return r568915;
}

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

Original12.6
Target3.4
Herbie3.3
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -2.9971458750474447e-240 or 5.9978497399435e-177 < y

    1. Initial program 12.8

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

    3. Applied associate-/l*1.8

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

    5. Applied div-inv2.1

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

    6. Simplified2.0

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

    if -2.9971458750474447e-240 < y < 5.9978497399435e-177

    1. Initial program 11.1

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

    3. Applied associate-/l*13.7

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

    5. Applied div-inv14.6

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

    6. Simplified14.6

      \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{y}\right)}\]
    7. Using strategy rm

    8. Applied sub-neg14.6

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

    9. Applied distribute-lft-in14.6

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

    10. Simplified14.6

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

    11. Simplified12.8

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

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.997145875047444652240240655689849825805 \cdot 10^{-240} \lor \neg \left(y \le 5.997849739943499755512315945487169370901 \cdot 10^{-177}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x}{y} \cdot \left(-z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019306 +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 -2.060202331921739e104) (- x (/ (* z x) y)) (if (< z 1.69397660138285259e213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

  (/ (* x (- y z)) y))