Average Error: 0.1 → 0.1
Time: 20.5s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]
↓
\[\left(\left(\left(1.0 - z\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + \log \left({z}^{\frac{1}{3}}\right) \cdot y\right) + x \cdot 0.5\]
x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)
↓
\left(\left(\left(1.0 - z\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + \log \left({z}^{\frac{1}{3}}\right) \cdot y\right) + x \cdot 0.5
double f(double x, double y, double z) {
        double r14348766 = x;
        double r14348767 = 0.5;
        double r14348768 = r14348766 * r14348767;
        double r14348769 = y;
        double r14348770 = 1.0;
        double r14348771 = z;
        double r14348772 = r14348770 - r14348771;
        double r14348773 = log(r14348771);
        double r14348774 = r14348772 + r14348773;
        double r14348775 = r14348769 * r14348774;
        double r14348776 = r14348768 + r14348775;
        return r14348776;
}
↓
double f(double x, double y, double z) {
        double r14348777 = 1.0;
        double r14348778 = z;
        double r14348779 = r14348777 - r14348778;
        double r14348780 = cbrt(r14348778);
        double r14348781 = log(r14348780);
        double r14348782 = r14348781 + r14348781;
        double r14348783 = r14348779 + r14348782;
        double r14348784 = y;
        double r14348785 = r14348783 * r14348784;
        double r14348786 = 0.3333333333333333;
        double r14348787 = pow(r14348778, r14348786);
        double r14348788 = log(r14348787);
        double r14348789 = r14348788 * r14348784;
        double r14348790 = r14348785 + r14348789;
        double r14348791 = x;
        double r14348792 = 0.5;
        double r14348793 = r14348791 * r14348792;
        double r14348794 = r14348790 + r14348793;
        return r14348794;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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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. Using strategy rm

  3. Applied add-cube-cbrt0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)}\right)\]

  4. Applied log-prod0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)}\right)\]

  5. Applied associate-+r+0.1

    \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(\left(1.0 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right)}\]

  6. Simplified0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\color{blue}{\left(\left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right) + \left(1.0 - z\right)\right)} + \log \left(\sqrt[3]{z}\right)\right)\]
  7. Using strategy rm

  8. Applied distribute-rgt-in0.1

    \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(\left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right) + \left(1.0 - z\right)\right) \cdot y + \log \left(\sqrt[3]{z}\right) \cdot y\right)}\]
  9. Using strategy rm

  10. Applied pow1/30.1

    \[\leadsto x \cdot 0.5 + \left(\left(\left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right) + \left(1.0 - z\right)\right) \cdot y + \log \color{blue}{\left({z}^{\frac{1}{3}}\right)} \cdot y\right)\]

  11. Final simplification0.1

    \[\leadsto \left(\left(\left(1.0 - z\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + \log \left({z}^{\frac{1}{3}}\right) \cdot y\right) + x \cdot 0.5\]

Reproduce

herbie shell --seed 2019165 
(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)))))