Average Error: 10.3 → 0.6
Time: 2.4s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4.9681407171394229 \cdot 10^{89} \lor \neg \left(z \le 1.89365034514315576 \cdot 10^{32}\right):\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -4.9681407171394229 \cdot 10^{89} \lor \neg \left(z \le 1.89365034514315576 \cdot 10^{32}\right):\\
\;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r618446 = x;
        double r618447 = y;
        double r618448 = z;
        double r618449 = r618447 - r618448;
        double r618450 = 1.0;
        double r618451 = r618449 + r618450;
        double r618452 = r618446 * r618451;
        double r618453 = r618452 / r618448;
        return r618453;
}
↓
double f(double x, double y, double z) {
        double r618454 = z;
        double r618455 = -4.968140717139423e+89;
        bool r618456 = r618454 <= r618455;
        double r618457 = 1.8936503451431558e+32;
        bool r618458 = r618454 <= r618457;
        double r618459 = !r618458;
        bool r618460 = r618456 || r618459;
        double r618461 = x;
        double r618462 = y;
        double r618463 = r618462 - r618454;
        double r618464 = 1.0;
        double r618465 = r618463 + r618464;
        double r618466 = r618465 / r618454;
        double r618467 = r618461 * r618466;
        double r618468 = r618461 * r618465;
        double r618469 = r618468 / r618454;
        double r618470 = r618460 ? r618467 : r618469;
        return r618470;
}

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

Derivation

  1. Split input into 2 regimes

  2. if z < -4.968140717139423e+89 or 1.8936503451431558e+32 < z

    1. Initial program 19.6

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

    3. Applied *-un-lft-identity19.6

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    if -4.968140717139423e+89 < z < 1.8936503451431558e+32

    1. Initial program 1.1

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.9681407171394229 \cdot 10^{89} \lor \neg \left(z \le 1.89365034514315576 \cdot 10^{32}\right):\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020089 +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))