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

↓

\[x \cdot 0.5 + \left(y \cdot \mathsf{fma}\left(2, \log \left(\sqrt[3]{z}\right), 1 - z\right) + \log \left({z}^{\frac{1}{3}}\right) \cdot y\right)\]

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

↓

x \cdot 0.5 + \left(y \cdot \mathsf{fma}\left(2, \log \left(\sqrt[3]{z}\right), 1 - z\right) + \log \left({z}^{\frac{1}{3}}\right) \cdot y\right)

double f(double x, double y, double z) {
        double r229734 = x;
        double r229735 = 0.5;
        double r229736 = r229734 * r229735;
        double r229737 = y;
        double r229738 = 1.0;
        double r229739 = z;
        double r229740 = r229738 - r229739;
        double r229741 = log(r229739);
        double r229742 = r229740 + r229741;
        double r229743 = r229737 * r229742;
        double r229744 = r229736 + r229743;
        return r229744;
}

↓

double f(double x, double y, double z) {
        double r229745 = x;
        double r229746 = 0.5;
        double r229747 = r229745 * r229746;
        double r229748 = y;
        double r229749 = 2.0;
        double r229750 = z;
        double r229751 = cbrt(r229750);
        double r229752 = log(r229751);
        double r229753 = 1.0;
        double r229754 = r229753 - r229750;
        double r229755 = fma(r229749, r229752, r229754);
        double r229756 = r229748 * r229755;
        double r229757 = 0.3333333333333333;
        double r229758 = pow(r229750, r229757);
        double r229759 = log(r229758);
        double r229760 = r229759 * r229748;
        double r229761 = r229756 + r229760;
        double r229762 = r229747 + r229761;
        return r229762;
}

Original	0.1
Target	0.1
Herbie	0.1

Derivation

Initial program 0.1
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
Using strategy rm
Applied add-cube-cbrt0.1
\[\leadsto x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)}\right)\]
Applied log-prod0.1
\[\leadsto x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)}\right)\]
Applied associate-+r+0.1
\[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(\left(1 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right)}\]
Simplified0.1
\[\leadsto x \cdot 0.5 + y \cdot \left(\color{blue}{\mathsf{fma}\left(2, \log \left(\sqrt[3]{z}\right), 1 - z\right)} + \log \left(\sqrt[3]{z}\right)\right)\]
Using strategy rm
Applied distribute-lft-in0.1
\[\leadsto x \cdot 0.5 + \color{blue}{\left(y \cdot \mathsf{fma}\left(2, \log \left(\sqrt[3]{z}\right), 1 - z\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)}\]
Simplified0.1
\[\leadsto x \cdot 0.5 + \left(y \cdot \mathsf{fma}\left(2, \log \left(\sqrt[3]{z}\right), 1 - z\right) + \color{blue}{\log \left({z}^{\frac{1}{3}}\right) \cdot y}\right)\]
Final simplification0.1
\[\leadsto x \cdot 0.5 + \left(y \cdot \mathsf{fma}\left(2, \log \left(\sqrt[3]{z}\right), 1 - z\right) + \log \left({z}^{\frac{1}{3}}\right) \cdot y\right)\]

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(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)))))

Error

Target

Derivation

Reproduce