Average Error: 10.3 → 0.1
Time: 2.3s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -159.566156241908544:\\ \;\;\;\;\frac{x}{{\left(\frac{z}{\left(y - z\right) + 1}\right)}^{1}}\\ \mathbf{elif}\;z \le 8.26470253112780802 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -159.566156241908544:\\
\;\;\;\;\frac{x}{{\left(\frac{z}{\left(y - z\right) + 1}\right)}^{1}}\\

\mathbf{elif}\;z \le 8.26470253112780802 \cdot 10^{-8}:\\
\;\;\;\;\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 r705718 = x;
        double r705719 = y;
        double r705720 = z;
        double r705721 = r705719 - r705720;
        double r705722 = 1.0;
        double r705723 = r705721 + r705722;
        double r705724 = r705718 * r705723;
        double r705725 = r705724 / r705720;
        return r705725;
}
↓
double f(double x, double y, double z) {
        double r705726 = z;
        double r705727 = -159.56615624190854;
        bool r705728 = r705726 <= r705727;
        double r705729 = x;
        double r705730 = y;
        double r705731 = r705730 - r705726;
        double r705732 = 1.0;
        double r705733 = r705731 + r705732;
        double r705734 = r705726 / r705733;
        double r705735 = 1.0;
        double r705736 = pow(r705734, r705735);
        double r705737 = r705729 / r705736;
        double r705738 = 8.264702531127808e-08;
        bool r705739 = r705726 <= r705738;
        double r705740 = r705729 / r705726;
        double r705741 = r705740 * r705733;
        double r705742 = r705733 / r705726;
        double r705743 = r705729 * r705742;
        double r705744 = r705739 ? r705741 : r705743;
        double r705745 = r705728 ? r705737 : r705744;
        return r705745;
}

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 < -159.56615624190854

    1. Initial program 17.1

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

    3. Applied associate-/l*0.1

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

    5. Applied pow10.1

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

    if -159.56615624190854 < z < 8.264702531127808e-08

    1. Initial program 0.1

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

    3. Applied associate-/l*8.5

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1}}}\]
    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 8.264702531127808e-08 < z

    1. Initial program 16.3

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

    3. Applied *-un-lft-identity16.3

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

    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

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -159.566156241908544:\\ \;\;\;\;\frac{x}{{\left(\frac{z}{\left(y - z\right) + 1}\right)}^{1}}\\ \mathbf{elif}\;z \le 8.26470253112780802 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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))