Average Error: 12.6 → 0.2
Time: 2.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.1371960954834437 \cdot 10^{-94}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.89027997349105774 \cdot 10^{27}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 5.7188809436523363 \cdot 10^{295}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\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 r816112 = x;
        double r816113 = y;
        double r816114 = z;
        double r816115 = r816113 - r816114;
        double r816116 = r816112 * r816115;
        double r816117 = r816116 / r816113;
        return r816117;
}
↓
double f(double x, double y, double z) {
        double r816118 = x;
        double r816119 = y;
        double r816120 = z;
        double r816121 = r816119 - r816120;
        double r816122 = r816118 * r816121;
        double r816123 = r816122 / r816119;
        double r816124 = -inf.0;
        bool r816125 = r816123 <= r816124;
        double r816126 = r816119 / r816121;
        double r816127 = r816118 / r816126;
        double r816128 = -1.1371960954834437e-94;
        bool r816129 = r816123 <= r816128;
        double r816130 = 1.8902799734910577e+27;
        bool r816131 = r816123 <= r816130;
        double r816132 = r816121 / r816119;
        double r816133 = r816118 * r816132;
        double r816134 = 5.718880943652336e+295;
        bool r816135 = r816123 <= r816134;
        double r816136 = r816135 ? r816123 : r816127;
        double r816137 = r816131 ? r816133 : r816136;
        double r816138 = r816129 ? r816123 : r816137;
        double r816139 = r816125 ? r816127 : r816138;
        return r816139;
}

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

    1. Initial program 61.9

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

    3. Applied associate-/l*0.3

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

    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 -1.1371960954834437e-94 < (/ (* x (- y z)) y) < 1.8902799734910577e+27

    1. Initial program 7.3

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

    3. Applied *-un-lft-identity7.3

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020056 
(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))