Average Error: 12.7 → 0.4
Time: 1.2m
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \le -2.523673116498965249180632340744567270682 \cdot 10^{284}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le -3.256094014734885958876760293725805613458 \cdot 10^{-72}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le 1.040091529858863440688059953611168253115 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le 2.546060910949810566653930570467710796416 \cdot 10^{306}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \le -2.523673116498965249180632340744567270682 \cdot 10^{284}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le -3.256094014734885958876760293725805613458 \cdot 10^{-72}:\\
\;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le 1.040091529858863440688059953611168253115 \cdot 10^{-197}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le 2.546060910949810566653930570467710796416 \cdot 10^{306}:\\
\;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r41310907 = x;
        double r41310908 = y;
        double r41310909 = z;
        double r41310910 = r41310908 - r41310909;
        double r41310911 = r41310907 * r41310910;
        double r41310912 = r41310911 / r41310908;
        return r41310912;
}
↓
double f(double x, double y, double z) {
        double r41310913 = y;
        double r41310914 = z;
        double r41310915 = r41310913 - r41310914;
        double r41310916 = x;
        double r41310917 = r41310915 * r41310916;
        double r41310918 = r41310917 / r41310913;
        double r41310919 = -2.5236731164989652e+284;
        bool r41310920 = r41310918 <= r41310919;
        double r41310921 = r41310913 / r41310915;
        double r41310922 = r41310916 / r41310921;
        double r41310923 = -3.256094014734886e-72;
        bool r41310924 = r41310918 <= r41310923;
        double r41310925 = 1.0400915298588634e-197;
        bool r41310926 = r41310918 <= r41310925;
        double r41310927 = 2.5460609109498106e+306;
        bool r41310928 = r41310918 <= r41310927;
        double r41310929 = r41310928 ? r41310918 : r41310922;
        double r41310930 = r41310926 ? r41310922 : r41310929;
        double r41310931 = r41310924 ? r41310918 : r41310930;
        double r41310932 = r41310920 ? r41310922 : r41310931;
        return r41310932;
}

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
Target3.2
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (- y z)) y) < -2.5236731164989652e+284 or -3.256094014734886e-72 < (/ (* x (- y z)) y) < 1.0400915298588634e-197 or 2.5460609109498106e+306 < (/ (* x (- y z)) y)

    1. Initial program 32.6

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

    3. Applied associate-/l*0.6

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

    if -2.5236731164989652e+284 < (/ (* x (- y z)) y) < -3.256094014734886e-72 or 1.0400915298588634e-197 < (/ (* x (- y z)) y) < 2.5460609109498106e+306

    1. Initial program 0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{y} \le -2.523673116498965249180632340744567270682 \cdot 10^{284}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le -3.256094014734885958876760293725805613458 \cdot 10^{-72}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le 1.040091529858863440688059953611168253115 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot x}{y} \le 2.546060910949810566653930570467710796416 \cdot 10^{306}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(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))