Average Error: 0.1 → 0.1
Time: 12.5s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[\left(\left(1 - z\right) \cdot y + x \cdot 0.5\right) + \log z \cdot y\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
\left(\left(1 - z\right) \cdot y + x \cdot 0.5\right) + \log z \cdot y
double f(double x, double y, double z) {
        double r269004 = x;
        double r269005 = 0.5;
        double r269006 = r269004 * r269005;
        double r269007 = y;
        double r269008 = 1.0;
        double r269009 = z;
        double r269010 = r269008 - r269009;
        double r269011 = log(r269009);
        double r269012 = r269010 + r269011;
        double r269013 = r269007 * r269012;
        double r269014 = r269006 + r269013;
        return r269014;
}
↓
double f(double x, double y, double z) {
        double r269015 = 1.0;
        double r269016 = z;
        double r269017 = r269015 - r269016;
        double r269018 = y;
        double r269019 = r269017 * r269018;
        double r269020 = x;
        double r269021 = 0.5;
        double r269022 = r269020 * r269021;
        double r269023 = r269019 + r269022;
        double r269024 = log(r269016);
        double r269025 = r269024 * r269018;
        double r269026 = r269023 + r269025;
        return r269026;
}

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. Using strategy rm

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied associate-+r+0.1

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

  6. Simplified0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\color{blue}{\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right)} + \log \left(\sqrt[3]{z}\right)\right)\]
  7. Using strategy rm

  8. Applied distribute-lft-in0.1

    \[\leadsto x \cdot 0.5 + \color{blue}{\left(y \cdot \left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)}\]

  9. Simplified0.1

    \[\leadsto x \cdot 0.5 + \left(y \cdot \left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + \color{blue}{\log \left({z}^{\frac{1}{3}}\right) \cdot y}\right)\]

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

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

  (+ (* x 0.5) (* y (+ (- 1 z) (log z)))))