Average Error: 9.9 → 0.2
Time: 10.8s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -13905844898214332094159488174298157285380 \lor \neg \left(x \le 9.371800790310021716388672147044997948808 \cdot 10^{-61}\right):\\ \;\;\;\;\left(\frac{1 \cdot x}{z} - x\right) + \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right) + \left(\frac{1 \cdot x}{z} - x\right)\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -13905844898214332094159488174298157285380 \lor \neg \left(x \le 9.371800790310021716388672147044997948808 \cdot 10^{-61}\right):\\
\;\;\;\;\left(\frac{1 \cdot x}{z} - x\right) + \frac{y}{\frac{z}{x}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r523456 = x;
        double r523457 = y;
        double r523458 = z;
        double r523459 = r523457 - r523458;
        double r523460 = 1.0;
        double r523461 = r523459 + r523460;
        double r523462 = r523456 * r523461;
        double r523463 = r523462 / r523458;
        return r523463;
}
↓
double f(double x, double y, double z) {
        double r523464 = x;
        double r523465 = -1.3905844898214332e+40;
        bool r523466 = r523464 <= r523465;
        double r523467 = 9.371800790310022e-61;
        bool r523468 = r523464 <= r523467;
        double r523469 = !r523468;
        bool r523470 = r523466 || r523469;
        double r523471 = 1.0;
        double r523472 = r523471 * r523464;
        double r523473 = z;
        double r523474 = r523472 / r523473;
        double r523475 = r523474 - r523464;
        double r523476 = y;
        double r523477 = r523473 / r523464;
        double r523478 = r523476 / r523477;
        double r523479 = r523475 + r523478;
        double r523480 = 1.0;
        double r523481 = r523480 / r523473;
        double r523482 = r523464 * r523476;
        double r523483 = r523481 * r523482;
        double r523484 = r523483 + r523475;
        double r523485 = r523470 ? r523479 : r523484;
        return r523485;
}

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

Original9.9
Target0.5
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.3905844898214332e+40 or 9.371800790310022e-61 < x

    1. Initial program 23.3

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

    2. Simplified0.4

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

    3. Taylor expanded around 0 7.9

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

    4. Simplified0.1

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

    if -1.3905844898214332e+40 < x < 9.371800790310022e-61

    1. Initial program 0.3

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

    2. Simplified14.8

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

    3. Taylor expanded around 0 0.2

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

    4. Simplified3.1

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

    6. Applied div-inv3.1

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

    7. Applied *-un-lft-identity3.1

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

    8. Applied times-frac0.3

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

    9. Simplified0.2

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -13905844898214332094159488174298157285380 \lor \neg \left(x \le 9.371800790310021716388672147044997948808 \cdot 10^{-61}\right):\\ \;\;\;\;\left(\frac{1 \cdot x}{z} - x\right) + \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right) + \left(\frac{1 \cdot x}{z} - x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))