Average Error: 12.3 → 2.3
Time: 7.4s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -8.641964883760676028697634483308586359187 \cdot 10^{195}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;z \le -2.135421934910598903580057538097509586825 \cdot 10^{97}:\\ \;\;\;\;x - \frac{\frac{x}{y}}{\frac{1}{z}}\\ \mathbf{elif}\;z \le 3.023089069211749401356410852189364064413 \cdot 10^{56}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;z \le 1.146116329563046779001996723315272963304 \cdot 10^{178}:\\ \;\;\;\;x - \frac{\frac{x}{y}}{\frac{1}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -8.641964883760676028697634483308586359187 \cdot 10^{195}:\\
\;\;\;\;x - \frac{x}{\frac{y}{z}}\\

\mathbf{elif}\;z \le -2.135421934910598903580057538097509586825 \cdot 10^{97}:\\
\;\;\;\;x - \frac{\frac{x}{y}}{\frac{1}{z}}\\

\mathbf{elif}\;z \le 3.023089069211749401356410852189364064413 \cdot 10^{56}:\\
\;\;\;\;x - \frac{x}{\frac{y}{z}}\\

\mathbf{elif}\;z \le 1.146116329563046779001996723315272963304 \cdot 10^{178}:\\
\;\;\;\;x - \frac{\frac{x}{y}}{\frac{1}{z}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r505660 = x;
        double r505661 = y;
        double r505662 = z;
        double r505663 = r505661 - r505662;
        double r505664 = r505660 * r505663;
        double r505665 = r505664 / r505661;
        return r505665;
}
↓
double f(double x, double y, double z) {
        double r505666 = z;
        double r505667 = -8.641964883760676e+195;
        bool r505668 = r505666 <= r505667;
        double r505669 = x;
        double r505670 = y;
        double r505671 = r505670 / r505666;
        double r505672 = r505669 / r505671;
        double r505673 = r505669 - r505672;
        double r505674 = -2.135421934910599e+97;
        bool r505675 = r505666 <= r505674;
        double r505676 = r505669 / r505670;
        double r505677 = 1.0;
        double r505678 = r505677 / r505666;
        double r505679 = r505676 / r505678;
        double r505680 = r505669 - r505679;
        double r505681 = 3.0230890692117494e+56;
        bool r505682 = r505666 <= r505681;
        double r505683 = 1.1461163295630468e+178;
        bool r505684 = r505666 <= r505683;
        double r505685 = r505669 * r505666;
        double r505686 = r505685 / r505670;
        double r505687 = r505669 - r505686;
        double r505688 = r505684 ? r505680 : r505687;
        double r505689 = r505682 ? r505673 : r505688;
        double r505690 = r505675 ? r505680 : r505689;
        double r505691 = r505668 ? r505673 : r505690;
        return r505691;
}

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

Original12.3
Target3.4
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -8.641964883760676e+195 or -2.135421934910599e+97 < z < 3.0230890692117494e+56

    1. Initial program 12.5

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

    2. Taylor expanded around 0 3.5

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

    4. Applied associate-/l*1.4

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

    if -8.641964883760676e+195 < z < -2.135421934910599e+97 or 3.0230890692117494e+56 < z < 1.1461163295630468e+178

    1. Initial program 11.1

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

    2. Taylor expanded around 0 7.4

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

    4. Applied associate-/l*7.3

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

    6. Applied div-inv7.4

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

    7. Applied associate-/r*1.9

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

    if 1.1461163295630468e+178 < z

    1. Initial program 13.3

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

    2. Taylor expanded around 0 12.7

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -8.641964883760676028697634483308586359187 \cdot 10^{195}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;z \le -2.135421934910598903580057538097509586825 \cdot 10^{97}:\\ \;\;\;\;x - \frac{\frac{x}{y}}{\frac{1}{z}}\\ \mathbf{elif}\;z \le 3.023089069211749401356410852189364064413 \cdot 10^{56}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;z \le 1.146116329563046779001996723315272963304 \cdot 10^{178}:\\ \;\;\;\;x - \frac{\frac{x}{y}}{\frac{1}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 
(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))