Average Error: 10.3 → 0.1
Time: 2.4s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.9866928941594857:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;z \le 3.7172346433831471 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.9866928941594857:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

\mathbf{elif}\;z \le 3.7172346433831471 \cdot 10^{-19}:\\
\;\;\;\;\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\\

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

\end{array}
double f(double x, double y, double z) {
        double r672750 = x;
        double r672751 = y;
        double r672752 = z;
        double r672753 = r672751 - r672752;
        double r672754 = 1.0;
        double r672755 = r672753 + r672754;
        double r672756 = r672750 * r672755;
        double r672757 = r672756 / r672752;
        return r672757;
}
↓
double f(double x, double y, double z) {
        double r672758 = z;
        double r672759 = -1.9866928941594857;
        bool r672760 = r672758 <= r672759;
        double r672761 = x;
        double r672762 = y;
        double r672763 = r672762 - r672758;
        double r672764 = 1.0;
        double r672765 = r672763 + r672764;
        double r672766 = r672758 / r672765;
        double r672767 = r672761 / r672766;
        double r672768 = 3.717234643383147e-19;
        bool r672769 = r672758 <= r672768;
        double r672770 = r672761 / r672758;
        double r672771 = r672770 * r672765;
        double r672772 = r672765 / r672758;
        double r672773 = r672761 * r672772;
        double r672774 = r672769 ? r672771 : r672773;
        double r672775 = r672760 ? r672767 : r672774;
        return r672775;
}

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

Original10.3
Target0.4
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -1.9866928941594857

    1. Initial program 17.5

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

    3. Applied associate-/l*0.1

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

    if -1.9866928941594857 < z < 3.717234643383147e-19

    1. Initial program 0.1

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

    3. Applied associate-/l*8.8

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1}}}\]
    4. Using strategy rm

    5. Applied associate-/r/0.1

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

    if 3.717234643383147e-19 < z

    1. Initial program 15.7

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

    3. Applied *-un-lft-identity15.7

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.9866928941594857:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;z \le 3.7172346433831471 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 +o rules:numerics
(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))