Average Error: 10.4 → 0.4
Time: 5.6s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.9720210046461049 \cdot 10^{69} \lor \neg \left(z \le 4.5427626806470244 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -6.9720210046461049 \cdot 10^{69} \lor \neg \left(z \le 4.5427626806470244 \cdot 10^{-57}\right):\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r946681 = x;
        double r946682 = y;
        double r946683 = z;
        double r946684 = r946682 - r946683;
        double r946685 = 1.0;
        double r946686 = r946684 + r946685;
        double r946687 = r946681 * r946686;
        double r946688 = r946687 / r946683;
        return r946688;
}
↓
double f(double x, double y, double z) {
        double r946689 = z;
        double r946690 = -6.972021004646105e+69;
        bool r946691 = r946689 <= r946690;
        double r946692 = 4.5427626806470244e-57;
        bool r946693 = r946689 <= r946692;
        double r946694 = !r946693;
        bool r946695 = r946691 || r946694;
        double r946696 = x;
        double r946697 = y;
        double r946698 = r946697 - r946689;
        double r946699 = 1.0;
        double r946700 = r946698 + r946699;
        double r946701 = r946689 / r946700;
        double r946702 = r946696 / r946701;
        double r946703 = r946696 * r946700;
        double r946704 = r946703 / r946689;
        double r946705 = r946695 ? r946702 : r946704;
        return r946705;
}

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

Original10.4
Target0.5
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 z < -6.972021004646105e+69 or 4.5427626806470244e-57 < z

    1. Initial program 17.0

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

    3. Applied associate-/l*0.1

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

    if -6.972021004646105e+69 < z < 4.5427626806470244e-57

    1. Initial program 0.7

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.9720210046461049 \cdot 10^{69} \lor \neg \left(z \le 4.5427626806470244 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020034 +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))