Average Error: 12.6 → 3.0
Time: 8.6s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4.428352457851485571386364768504698313663 \cdot 10^{148}:\\ \;\;\;\;x + \frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;z \le 4.465897606696847000231694834068591278595 \cdot 10^{-27}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -4.428352457851485571386364768504698313663 \cdot 10^{148}:\\
\;\;\;\;x + \frac{-z}{\frac{y}{x}}\\

\mathbf{elif}\;z \le 4.465897606696847000231694834068591278595 \cdot 10^{-27}:\\
\;\;\;\;x - \frac{x}{\frac{y}{z}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r612815 = x;
        double r612816 = y;
        double r612817 = z;
        double r612818 = r612816 - r612817;
        double r612819 = r612815 * r612818;
        double r612820 = r612819 / r612816;
        return r612820;
}
↓
double f(double x, double y, double z) {
        double r612821 = z;
        double r612822 = -4.4283524578514856e+148;
        bool r612823 = r612821 <= r612822;
        double r612824 = x;
        double r612825 = -r612821;
        double r612826 = y;
        double r612827 = r612826 / r612824;
        double r612828 = r612825 / r612827;
        double r612829 = r612824 + r612828;
        double r612830 = 4.465897606696847e-27;
        bool r612831 = r612821 <= r612830;
        double r612832 = r612826 / r612821;
        double r612833 = r612824 / r612832;
        double r612834 = r612824 - r612833;
        double r612835 = r612824 * r612821;
        double r612836 = r612835 / r612826;
        double r612837 = r612824 - r612836;
        double r612838 = r612831 ? r612834 : r612837;
        double r612839 = r612823 ? r612829 : r612838;
        return r612839;
}

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
Target2.8
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -4.4283524578514856e+148

    1. Initial program 11.3

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

    2. Taylor expanded around 0 10.1

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

    3. Simplified10.1

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

    5. Applied sub-neg10.1

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

    6. Simplified8.0

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

    if -4.4283524578514856e+148 < z < 4.465897606696847e-27

    1. Initial program 12.8

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

    3. Applied associate-/l*0.8

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

    4. Taylor expanded around 0 3.0

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

    5. Simplified0.8

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

    if 4.465897606696847e-27 < z

    1. Initial program 12.6

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

    2. Taylor expanded around 0 7.2

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

    3. Simplified7.2

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

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.428352457851485571386364768504698313663 \cdot 10^{148}:\\ \;\;\;\;x + \frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;z \le 4.465897606696847000231694834068591278595 \cdot 10^{-27}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(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))