Average Error: 10.6 → 0.4
Time: 2.1s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.4723758122722615 \cdot 10^{110} \lor \neg \left(x \le 1.8053743254521745 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.4723758122722615 \cdot 10^{110} \lor \neg \left(x \le 1.8053743254521745 \cdot 10^{-20}\right):\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\

\end{array}
double f(double x, double y, double z) {
        double r736947 = x;
        double r736948 = y;
        double r736949 = z;
        double r736950 = r736948 - r736949;
        double r736951 = 1.0;
        double r736952 = r736950 + r736951;
        double r736953 = r736947 * r736952;
        double r736954 = r736953 / r736949;
        return r736954;
}
↓
double f(double x, double y, double z) {
        double r736955 = x;
        double r736956 = -1.4723758122722615e+110;
        bool r736957 = r736955 <= r736956;
        double r736958 = 1.8053743254521745e-20;
        bool r736959 = r736955 <= r736958;
        double r736960 = !r736959;
        bool r736961 = r736957 || r736960;
        double r736962 = z;
        double r736963 = y;
        double r736964 = r736963 - r736962;
        double r736965 = 1.0;
        double r736966 = r736964 + r736965;
        double r736967 = r736962 / r736966;
        double r736968 = r736955 / r736967;
        double r736969 = r736955 * r736963;
        double r736970 = r736969 / r736962;
        double r736971 = r736955 / r736962;
        double r736972 = r736965 * r736971;
        double r736973 = r736970 + r736972;
        double r736974 = r736973 - r736955;
        double r736975 = r736961 ? r736968 : r736974;
        return r736975;
}

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

Original10.6
Target0.4
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.4723758122722615e+110 or 1.8053743254521745e-20 < x

    1. Initial program 29.4

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*0.1

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

    if -1.4723758122722615e+110 < x < 1.8053743254521745e-20

    1. Initial program 1.5

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*4.4

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

    4. Taylor expanded around 0 0.5

      \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.4723758122722615 \cdot 10^{110} \lor \neg \left(x \le 1.8053743254521745 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1)) z))