Average Error: 0.1 → 0.1
Time: 12.3s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[\left(y \cdot \log z + \left(1 - z\right) \cdot y\right) + x \cdot 0.5\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
\left(y \cdot \log z + \left(1 - z\right) \cdot y\right) + x \cdot 0.5
double f(double x, double y, double z) {
        double r173768 = x;
        double r173769 = 0.5;
        double r173770 = r173768 * r173769;
        double r173771 = y;
        double r173772 = 1.0;
        double r173773 = z;
        double r173774 = r173772 - r173773;
        double r173775 = log(r173773);
        double r173776 = r173774 + r173775;
        double r173777 = r173771 * r173776;
        double r173778 = r173770 + r173777;
        return r173778;
}
↓
double f(double x, double y, double z) {
        double r173779 = y;
        double r173780 = z;
        double r173781 = log(r173780);
        double r173782 = r173779 * r173781;
        double r173783 = 1.0;
        double r173784 = r173783 - r173780;
        double r173785 = r173784 * r173779;
        double r173786 = r173782 + r173785;
        double r173787 = x;
        double r173788 = 0.5;
        double r173789 = r173787 * r173788;
        double r173790 = r173786 + r173789;
        return r173790;
}

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

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

  2. Simplified0.1

    \[\leadsto \color{blue}{x \cdot 0.5 + y \cdot \left(\log z + \left(1 - z\right)\right)}\]
  3. Using strategy rm

  4. Applied distribute-rgt-in0.1

    \[\leadsto x \cdot 0.5 + \color{blue}{\left(\log z \cdot y + \left(1 - z\right) \cdot y\right)}\]

  5. Simplified0.1

    \[\leadsto x \cdot 0.5 + \left(\color{blue}{y \cdot \log z} + \left(1 - z\right) \cdot y\right)\]

  6. Final simplification0.1

    \[\leadsto \left(y \cdot \log z + \left(1 - z\right) \cdot y\right) + x \cdot 0.5\]

Reproduce

herbie shell --seed 2019179 
(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)))))