Average Error: 12.7 → 2.9
Time: 2.6s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.8688621848367084 \cdot 10^{248}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{{\left(\frac{y}{y - z}\right)}^{1}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.8688621848367084 \cdot 10^{248}:\\
\;\;\;\;x - \frac{x \cdot z}{y}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{{\left(\frac{y}{y - z}\right)}^{1}}\\

\end{array}
double f(double x, double y, double z) {
        double r755768 = x;
        double r755769 = y;
        double r755770 = z;
        double r755771 = r755769 - r755770;
        double r755772 = r755768 * r755771;
        double r755773 = r755772 / r755769;
        return r755773;
}
↓
double f(double x, double y, double z) {
        double r755774 = z;
        double r755775 = -1.8688621848367084e+248;
        bool r755776 = r755774 <= r755775;
        double r755777 = x;
        double r755778 = r755777 * r755774;
        double r755779 = y;
        double r755780 = r755778 / r755779;
        double r755781 = r755777 - r755780;
        double r755782 = r755779 - r755774;
        double r755783 = r755779 / r755782;
        double r755784 = 1.0;
        double r755785 = pow(r755783, r755784);
        double r755786 = r755777 / r755785;
        double r755787 = r755776 ? r755781 : r755786;
        return r755787;
}

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

Original12.7
Target3.0
Herbie2.9
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.8688621848367084e+248

    1. Initial program 13.5

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

    3. Applied associate-/l*11.5

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

    4. Taylor expanded around 0 13.0

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

    if -1.8688621848367084e+248 < z

    1. Initial program 12.7

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

    3. Applied associate-/l*2.5

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

    5. Applied pow12.5

      \[\leadsto \frac{x}{\color{blue}{{\left(\frac{y}{y - z}\right)}^{1}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.8688621848367084 \cdot 10^{248}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{{\left(\frac{y}{y - z}\right)}^{1}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020089 +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))