Average Error: 0.1 → 0.1
Time: 19.9s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]
↓
\[\left(1.0 \cdot y + y \cdot \left(\log z - z\right)\right) + 0.5 \cdot x\]
x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)
↓
\left(1.0 \cdot y + y \cdot \left(\log z - z\right)\right) + 0.5 \cdot x
double f(double x, double y, double z) {
        double r14910676 = x;
        double r14910677 = 0.5;
        double r14910678 = r14910676 * r14910677;
        double r14910679 = y;
        double r14910680 = 1.0;
        double r14910681 = z;
        double r14910682 = r14910680 - r14910681;
        double r14910683 = log(r14910681);
        double r14910684 = r14910682 + r14910683;
        double r14910685 = r14910679 * r14910684;
        double r14910686 = r14910678 + r14910685;
        return r14910686;
}
↓
double f(double x, double y, double z) {
        double r14910687 = 1.0;
        double r14910688 = y;
        double r14910689 = r14910687 * r14910688;
        double r14910690 = z;
        double r14910691 = log(r14910690);
        double r14910692 = r14910691 - r14910690;
        double r14910693 = r14910688 * r14910692;
        double r14910694 = r14910689 + r14910693;
        double r14910695 = 0.5;
        double r14910696 = x;
        double r14910697 = r14910695 * r14910696;
        double r14910698 = r14910694 + r14910697;
        return r14910698;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Target

Original0.1
Target0.1
Herbie0.1
\[\left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right)\]

Derivation

  1. Initial program 0.1

    \[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\left(0.5 \cdot x + \left(1.0 \cdot y + y \cdot \log z\right)\right) - z \cdot y}\]

  3. Simplified0.1

    \[\leadsto \color{blue}{0.5 \cdot x + \left(y \cdot \left(\log z - z\right) + y \cdot 1.0\right)}\]

  4. Final simplification0.1

    \[\leadsto \left(1.0 \cdot y + y \cdot \left(\log z - z\right)\right) + 0.5 \cdot x\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"

  :herbie-target
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))