Average Error: 0.1 → 0.1
Time: 27.4s
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 r17260581 = x;
        double r17260582 = 0.5;
        double r17260583 = r17260581 * r17260582;
        double r17260584 = y;
        double r17260585 = 1.0;
        double r17260586 = z;
        double r17260587 = r17260585 - r17260586;
        double r17260588 = log(r17260586);
        double r17260589 = r17260587 + r17260588;
        double r17260590 = r17260584 * r17260589;
        double r17260591 = r17260583 + r17260590;
        return r17260591;
}
↓
double f(double x, double y, double z) {
        double r17260592 = x;
        double r17260593 = 0.5;
        double r17260594 = r17260592 * r17260593;
        double r17260595 = z;
        double r17260596 = 0.3333333333333333;
        double r17260597 = pow(r17260595, r17260596);
        double r17260598 = log(r17260597);
        double r17260599 = 1.0;
        double r17260600 = r17260599 - r17260595;
        double r17260601 = cbrt(r17260595);
        double r17260602 = log(r17260601);
        double r17260603 = r17260602 + r17260602;
        double r17260604 = r17260600 + r17260603;
        double r17260605 = r17260598 + r17260604;
        double r17260606 = y;
        double r17260607 = r17260605 * r17260606;
        double r17260608 = r17260594 + r17260607;
        return r17260608;
}

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

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

  8. Applied pow1/30.1

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

  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)))))