Average Error: 0.1 → 0.1
Time: 20.4s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(\log \left({z}^{\frac{1}{3}}\right) + \left(\left(1 - z\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right)\right) \cdot y\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + \left(\log \left({z}^{\frac{1}{3}}\right) + \left(\left(1 - z\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right)\right) \cdot y
double f(double x, double y, double z) {
        double r18400598 = x;
        double r18400599 = 0.5;
        double r18400600 = r18400598 * r18400599;
        double r18400601 = y;
        double r18400602 = 1.0;
        double r18400603 = z;
        double r18400604 = r18400602 - r18400603;
        double r18400605 = log(r18400603);
        double r18400606 = r18400604 + r18400605;
        double r18400607 = r18400601 * r18400606;
        double r18400608 = r18400600 + r18400607;
        return r18400608;
}
↓
double f(double x, double y, double z) {
        double r18400609 = x;
        double r18400610 = 0.5;
        double r18400611 = r18400609 * r18400610;
        double r18400612 = z;
        double r18400613 = 0.3333333333333333;
        double r18400614 = pow(r18400612, r18400613);
        double r18400615 = log(r18400614);
        double r18400616 = 1.0;
        double r18400617 = r18400616 - r18400612;
        double r18400618 = cbrt(r18400612);
        double r18400619 = log(r18400618);
        double r18400620 = r18400619 + r18400619;
        double r18400621 = r18400617 + r18400620;
        double r18400622 = r18400615 + r18400621;
        double r18400623 = y;
        double r18400624 = r18400622 * r18400623;
        double r18400625 = r18400611 + r18400624;
        return r18400625;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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

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

  8. Applied pow1/30.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(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)))))