Average Error: 12.7 → 0.4
Time: 2.7s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -5.74240735694960229 \cdot 10^{-106}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.0101904628573289 \cdot 10^{139}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.14880917404541375 \cdot 10^{307}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]
\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 -5.74240735694960229 \cdot 10^{-106}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.0101904628573289 \cdot 10^{139}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.14880917404541375 \cdot 10^{307}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r823919 = x;
        double r823920 = y;
        double r823921 = z;
        double r823922 = r823920 - r823921;
        double r823923 = r823919 * r823922;
        double r823924 = r823923 / r823920;
        return r823924;
}
↓
double f(double x, double y, double z) {
        double r823925 = x;
        double r823926 = y;
        double r823927 = z;
        double r823928 = r823926 - r823927;
        double r823929 = r823925 * r823928;
        double r823930 = r823929 / r823926;
        double r823931 = -inf.0;
        bool r823932 = r823930 <= r823931;
        double r823933 = r823926 / r823928;
        double r823934 = r823925 / r823933;
        double r823935 = -5.742407356949602e-106;
        bool r823936 = r823930 <= r823935;
        double r823937 = 1.0101904628573289e+139;
        bool r823938 = r823930 <= r823937;
        double r823939 = 3.1488091740454137e+307;
        bool r823940 = r823930 <= r823939;
        double r823941 = r823925 / r823926;
        double r823942 = r823941 * r823928;
        double r823943 = r823940 ? r823930 : r823942;
        double r823944 = r823938 ? r823934 : r823943;
        double r823945 = r823936 ? r823930 : r823944;
        double r823946 = r823932 ? r823934 : r823945;
        return r823946;
}

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

Original12.7
Target3.4
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) y) < -inf.0 or -5.742407356949602e-106 < (/ (* x (- y z)) y) < 1.0101904628573289e+139

    1. Initial program 14.1

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

    3. Applied associate-/l*0.6

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

    if -inf.0 < (/ (* x (- y z)) y) < -5.742407356949602e-106 or 1.0101904628573289e+139 < (/ (* x (- y z)) y) < 3.1488091740454137e+307

    1. Initial program 0.3

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

    if 3.1488091740454137e+307 < (/ (* x (- y z)) y)

    1. Initial program 63.7

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

    3. Applied associate-/l*0.3

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

    5. Applied associate-/r/0.2

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -5.74240735694960229 \cdot 10^{-106}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.0101904628573289 \cdot 10^{139}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.14880917404541375 \cdot 10^{307}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +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))