Average Error: 12.5 → 0.8
Time: 2.0s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -2.03190189492080534 \cdot 10^{98}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.6608708735287544 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 4.93193268925708101 \cdot 10^{238}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\
\;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -2.03190189492080534 \cdot 10^{98}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.6608708735287544 \cdot 10^{-84}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 4.93193268925708101 \cdot 10^{238}:\\
\;\;\;\;\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 r671957 = x;
        double r671958 = y;
        double r671959 = z;
        double r671960 = r671958 - r671959;
        double r671961 = r671957 * r671960;
        double r671962 = r671961 / r671958;
        return r671962;
}
↓
double f(double x, double y, double z) {
        double r671963 = x;
        double r671964 = y;
        double r671965 = z;
        double r671966 = r671964 - r671965;
        double r671967 = r671963 * r671966;
        double r671968 = r671967 / r671964;
        double r671969 = -inf.0;
        bool r671970 = r671968 <= r671969;
        double r671971 = r671963 / r671964;
        double r671972 = r671971 * r671966;
        double r671973 = -2.0319018949208053e+98;
        bool r671974 = r671968 <= r671973;
        double r671975 = 3.6608708735287544e-84;
        bool r671976 = r671968 <= r671975;
        double r671977 = r671964 / r671966;
        double r671978 = r671963 / r671977;
        double r671979 = 4.931932689257081e+238;
        bool r671980 = r671968 <= r671979;
        double r671981 = r671980 ? r671968 : r671978;
        double r671982 = r671976 ? r671978 : r671981;
        double r671983 = r671974 ? r671968 : r671982;
        double r671984 = r671970 ? r671972 : r671983;
        return r671984;
}

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

Original12.5
Target3.4
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) y) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-/l*0.1

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

    5. Applied associate-/r/0.1

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

    if -inf.0 < (/ (* x (- y z)) y) < -2.0319018949208053e+98 or 3.6608708735287544e-84 < (/ (* x (- y z)) y) < 4.931932689257081e+238

    1. Initial program 0.3

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

    if -2.0319018949208053e+98 < (/ (* x (- y z)) y) < 3.6608708735287544e-84 or 4.931932689257081e+238 < (/ (* x (- y z)) y)

    1. Initial program 13.5

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

    3. Applied associate-/l*1.3

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -2.03190189492080534 \cdot 10^{98}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.6608708735287544 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 4.93193268925708101 \cdot 10^{238}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 
(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))