Average Error: 10.4 → 1.8
Time: 40.9s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\left(1 + y\right) \cdot \frac{x}{z} - x\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\left(1 + y\right) \cdot \frac{x}{z} - x
double f(double x, double y, double z) {
        double r28847645 = x;
        double r28847646 = y;
        double r28847647 = z;
        double r28847648 = r28847646 - r28847647;
        double r28847649 = 1.0;
        double r28847650 = r28847648 + r28847649;
        double r28847651 = r28847645 * r28847650;
        double r28847652 = r28847651 / r28847647;
        return r28847652;
}
↓
double f(double x, double y, double z) {
        double r28847653 = 1.0;
        double r28847654 = y;
        double r28847655 = r28847653 + r28847654;
        double r28847656 = x;
        double r28847657 = z;
        double r28847658 = r28847656 / r28847657;
        double r28847659 = r28847655 * r28847658;
        double r28847660 = r28847659 - r28847656;
        return r28847660;
}

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
Target0.4
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Initial program 10.4

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

  3. Applied *-un-lft-identity10.4

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

  4. Applied times-frac3.3

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

  5. Simplified3.3

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

  6. Taylor expanded around 0 3.7

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

  7. Simplified1.8

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

  8. Final simplification1.8

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

Reproduce

herbie shell --seed 2019200 
(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))