Average Error: 12.1 → 1.5
Time: 2.1s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -25525895.1273290403:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;x \le 7.8393557133259353 \cdot 10^{-22}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -25525895.1273290403:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;x \le 7.8393557133259353 \cdot 10^{-22}:\\
\;\;\;\;x - \frac{x \cdot z}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r854835 = x;
        double r854836 = y;
        double r854837 = z;
        double r854838 = r854836 - r854837;
        double r854839 = r854835 * r854838;
        double r854840 = r854839 / r854836;
        return r854840;
}
↓
double f(double x, double y, double z) {
        double r854841 = x;
        double r854842 = -25525895.12732904;
        bool r854843 = r854841 <= r854842;
        double r854844 = y;
        double r854845 = z;
        double r854846 = r854844 - r854845;
        double r854847 = r854844 / r854846;
        double r854848 = r854841 / r854847;
        double r854849 = 7.839355713325935e-22;
        bool r854850 = r854841 <= r854849;
        double r854851 = r854841 * r854845;
        double r854852 = r854851 / r854844;
        double r854853 = r854841 - r854852;
        double r854854 = r854846 / r854844;
        double r854855 = r854841 * r854854;
        double r854856 = r854850 ? r854853 : r854855;
        double r854857 = r854843 ? r854848 : r854856;
        return r854857;
}

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

Original12.1
Target3.1
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -25525895.12732904

    1. Initial program 23.3

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

    3. Applied associate-/l*0.1

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

    if -25525895.12732904 < x < 7.839355713325935e-22

    1. Initial program 4.7

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

    3. Applied associate-/l*5.0

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

    4. Taylor expanded around 0 2.5

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

    if 7.839355713325935e-22 < x

    1. Initial program 20.4

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

    3. Applied *-un-lft-identity20.4

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

    4. Applied times-frac0.2

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

    5. Simplified0.2

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -25525895.1273290403:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;x \le 7.8393557133259353 \cdot 10^{-22}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :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))