Average Error: 12.6 → 1.5
Time: 27.5s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -6.083035639847637607654497125773830646304 \cdot 10^{292}:\\ \;\;\;\;\frac{\frac{x}{\sqrt{\frac{y}{y - z}}}}{\sqrt{\frac{y}{y - z}}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -8.175248265444713739055182742884957439272 \cdot 10^{123}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 4597572249704838144:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.095545649072277509917652984108949902858 \cdot 10^{260}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -6.083035639847637607654497125773830646304 \cdot 10^{292}:\\
\;\;\;\;\frac{\frac{x}{\sqrt{\frac{y}{y - z}}}}{\sqrt{\frac{y}{y - z}}}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -8.175248265444713739055182742884957439272 \cdot 10^{123}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 4597572249704838144:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.095545649072277509917652984108949902858 \cdot 10^{260}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r51390553 = x;
        double r51390554 = y;
        double r51390555 = z;
        double r51390556 = r51390554 - r51390555;
        double r51390557 = r51390553 * r51390556;
        double r51390558 = r51390557 / r51390554;
        return r51390558;
}
↓
double f(double x, double y, double z) {
        double r51390559 = x;
        double r51390560 = y;
        double r51390561 = z;
        double r51390562 = r51390560 - r51390561;
        double r51390563 = r51390559 * r51390562;
        double r51390564 = r51390563 / r51390560;
        double r51390565 = -6.083035639847638e+292;
        bool r51390566 = r51390564 <= r51390565;
        double r51390567 = r51390560 / r51390562;
        double r51390568 = sqrt(r51390567);
        double r51390569 = r51390559 / r51390568;
        double r51390570 = r51390569 / r51390568;
        double r51390571 = -8.175248265444714e+123;
        bool r51390572 = r51390564 <= r51390571;
        double r51390573 = 4.597572249704838e+18;
        bool r51390574 = r51390564 <= r51390573;
        double r51390575 = r51390559 / r51390567;
        double r51390576 = 1.0955456490722775e+260;
        bool r51390577 = r51390564 <= r51390576;
        double r51390578 = r51390577 ? r51390564 : r51390575;
        double r51390579 = r51390574 ? r51390575 : r51390578;
        double r51390580 = r51390572 ? r51390564 : r51390579;
        double r51390581 = r51390566 ? r51390570 : r51390580;
        return r51390581;
}

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
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) y) < -6.083035639847638e+292

    1. Initial program 57.7

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

    3. Applied associate-/l*1.0

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

    5. Applied add-sqr-sqrt8.5

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

    6. Applied associate-/r*8.5

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

    if -6.083035639847638e+292 < (/ (* x (- y z)) y) < -8.175248265444714e+123 or 4.597572249704838e+18 < (/ (* x (- y z)) y) < 1.0955456490722775e+260

    1. Initial program 0.2

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

    if -8.175248265444714e+123 < (/ (* x (- y z)) y) < 4.597572249704838e+18 or 1.0955456490722775e+260 < (/ (* x (- y z)) y)

    1. Initial program 11.7

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

    3. Applied associate-/l*1.1

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -6.083035639847637607654497125773830646304 \cdot 10^{292}:\\ \;\;\;\;\frac{\frac{x}{\sqrt{\frac{y}{y - z}}}}{\sqrt{\frac{y}{y - z}}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -8.175248265444713739055182742884957439272 \cdot 10^{123}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 4597572249704838144:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.095545649072277509917652984108949902858 \cdot 10^{260}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 +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))