Average Error: 10.3 → 0.5
Time: 21.7s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -8953946801625355128083054592 \lor \neg \left(x \le 2.590538009135805678082833971438481635892 \cdot 10^{145}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + 1\right) \cdot x}{z} - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -8953946801625355128083054592 \lor \neg \left(x \le 2.590538009135805678082833971438481635892 \cdot 10^{145}\right):\\
\;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\

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

\end{array}
double f(double x, double y, double z) {
        double r409612 = x;
        double r409613 = y;
        double r409614 = z;
        double r409615 = r409613 - r409614;
        double r409616 = 1.0;
        double r409617 = r409615 + r409616;
        double r409618 = r409612 * r409617;
        double r409619 = r409618 / r409614;
        return r409619;
}
↓
double f(double x, double y, double z) {
        double r409620 = x;
        double r409621 = -8.953946801625355e+27;
        bool r409622 = r409620 <= r409621;
        double r409623 = 2.5905380091358057e+145;
        bool r409624 = r409620 <= r409623;
        double r409625 = !r409624;
        bool r409626 = r409622 || r409625;
        double r409627 = z;
        double r409628 = r409620 / r409627;
        double r409629 = 1.0;
        double r409630 = y;
        double r409631 = r409629 + r409630;
        double r409632 = r409628 * r409631;
        double r409633 = r409632 - r409620;
        double r409634 = r409630 + r409629;
        double r409635 = r409634 * r409620;
        double r409636 = r409635 / r409627;
        double r409637 = r409636 - r409620;
        double r409638 = r409626 ? r409633 : r409637;
        return r409638;
}

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
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -8.953946801625355e+27 or 2.5905380091358057e+145 < x

    1. Initial program 33.9

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

    2. Taylor expanded around 0 10.9

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

    3. Simplified0.1

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

    if -8.953946801625355e+27 < x < 2.5905380091358057e+145

    1. Initial program 2.2

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

    2. Taylor expanded around 0 0.7

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

    3. Simplified2.3

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

    5. Applied associate-*l/0.7

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

    6. Simplified0.7

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8953946801625355128083054592 \lor \neg \left(x \le 2.590538009135805678082833971438481635892 \cdot 10^{145}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + 1\right) \cdot x}{z} - x\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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))