Average Error: 12.6 → 0.2
Time: 3.4s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.1371960954834437 \cdot 10^{-94}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.89027997349105774 \cdot 10^{27}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 5.7188809436523363 \cdot 10^{295}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.1371960954834437 \cdot 10^{-94}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.89027997349105774 \cdot 10^{27}:\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 5.7188809436523363 \cdot 10^{295}:\\
\;\;\;\;\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 r908493 = x;
        double r908494 = y;
        double r908495 = z;
        double r908496 = r908494 - r908495;
        double r908497 = r908493 * r908496;
        double r908498 = r908497 / r908494;
        return r908498;
}
↓
double f(double x, double y, double z) {
        double r908499 = x;
        double r908500 = y;
        double r908501 = z;
        double r908502 = r908500 - r908501;
        double r908503 = r908499 * r908502;
        double r908504 = r908503 / r908500;
        double r908505 = -inf.0;
        bool r908506 = r908504 <= r908505;
        double r908507 = r908502 / r908500;
        double r908508 = r908499 * r908507;
        double r908509 = -1.1371960954834437e-94;
        bool r908510 = r908504 <= r908509;
        double r908511 = 1.8902799734910577e+27;
        bool r908512 = r908504 <= r908511;
        double r908513 = 5.718880943652336e+295;
        bool r908514 = r908504 <= r908513;
        double r908515 = r908500 / r908502;
        double r908516 = r908499 / r908515;
        double r908517 = r908514 ? r908504 : r908516;
        double r908518 = r908512 ? r908508 : r908517;
        double r908519 = r908510 ? r908504 : r908518;
        double r908520 = r908506 ? r908508 : r908519;
        return r908520;
}

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
Target3.0
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) y) < -inf.0 or -1.1371960954834437e-94 < (/ (* x (- y z)) y) < 1.8902799734910577e+27

    1. Initial program 16.6

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

    3. Applied *-un-lft-identity16.6

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    if -inf.0 < (/ (* x (- y z)) y) < -1.1371960954834437e-94 or 1.8902799734910577e+27 < (/ (* x (- y z)) y) < 5.718880943652336e+295

    1. Initial program 0.2

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

    if 5.718880943652336e+295 < (/ (* x (- y z)) y)

    1. Initial program 60.0

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

    3. Applied associate-/l*0.6

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.1371960954834437 \cdot 10^{-94}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.89027997349105774 \cdot 10^{27}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 5.7188809436523363 \cdot 10^{295}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 +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))