Average Error: 12.4 → 1.6
Time: 11.6s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} = -\infty:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le -3.693303907308183443165362004771863513953 \cdot 10^{91}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{1}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} = -\infty:\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le -3.693303907308183443165362004771863513953 \cdot 10^{91}:\\
\;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{y \cdot \frac{1}{y - z}}\\

\end{array}
double f(double x, double y, double z) {
        double r23030032 = x;
        double r23030033 = y;
        double r23030034 = z;
        double r23030035 = r23030033 - r23030034;
        double r23030036 = r23030032 * r23030035;
        double r23030037 = r23030036 / r23030033;
        return r23030037;
}
↓
double f(double x, double y, double z) {
        double r23030038 = y;
        double r23030039 = z;
        double r23030040 = r23030038 - r23030039;
        double r23030041 = x;
        double r23030042 = r23030040 * r23030041;
        double r23030043 = r23030042 / r23030038;
        double r23030044 = -inf.0;
        bool r23030045 = r23030043 <= r23030044;
        double r23030046 = r23030040 / r23030038;
        double r23030047 = r23030041 * r23030046;
        double r23030048 = -3.6933039073081834e+91;
        bool r23030049 = r23030043 <= r23030048;
        double r23030050 = 1.0;
        double r23030051 = r23030050 / r23030040;
        double r23030052 = r23030038 * r23030051;
        double r23030053 = r23030041 / r23030052;
        double r23030054 = r23030049 ? r23030043 : r23030053;
        double r23030055 = r23030045 ? r23030047 : r23030054;
        return r23030055;
}

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

Original12.4
Target3.2
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) y) < -inf.0

    1. Initial program 64.0

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

    3. Applied *-un-lft-identity64.0

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    if -inf.0 < (/ (* x (- y z)) y) < -3.6933039073081834e+91

    1. Initial program 0.2

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

    if -3.6933039073081834e+91 < (/ (* x (- y z)) y)

    1. Initial program 9.6

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

    3. Applied associate-/l*1.9

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

    5. Applied div-inv2.0

      \[\leadsto \frac{x}{\color{blue}{y \cdot \frac{1}{y - z}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} = -\infty:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le -3.693303907308183443165362004771863513953 \cdot 10^{91}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{1}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"

  :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))