Average Error: 0.1 → 0.1
Time: 4.9s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[\left(y \cdot \left(\left(1 - z\right) + \log \left({z}^{\frac{1}{3}} \cdot \sqrt[3]{z}\right)\right) + x \cdot 0.5\right) + \log \left(\sqrt[3]{z}\right) \cdot y\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
\left(y \cdot \left(\left(1 - z\right) + \log \left({z}^{\frac{1}{3}} \cdot \sqrt[3]{z}\right)\right) + x \cdot 0.5\right) + \log \left(\sqrt[3]{z}\right) \cdot y
double f(double x, double y, double z) {
        double r298595 = x;
        double r298596 = 0.5;
        double r298597 = r298595 * r298596;
        double r298598 = y;
        double r298599 = 1.0;
        double r298600 = z;
        double r298601 = r298599 - r298600;
        double r298602 = log(r298600);
        double r298603 = r298601 + r298602;
        double r298604 = r298598 * r298603;
        double r298605 = r298597 + r298604;
        return r298605;
}
↓
double f(double x, double y, double z) {
        double r298606 = y;
        double r298607 = 1.0;
        double r298608 = z;
        double r298609 = r298607 - r298608;
        double r298610 = 0.3333333333333333;
        double r298611 = pow(r298608, r298610);
        double r298612 = cbrt(r298608);
        double r298613 = r298611 * r298612;
        double r298614 = log(r298613);
        double r298615 = r298609 + r298614;
        double r298616 = r298606 * r298615;
        double r298617 = x;
        double r298618 = 0.5;
        double r298619 = r298617 * r298618;
        double r298620 = r298616 + r298619;
        double r298621 = log(r298612);
        double r298622 = r298621 * r298606;
        double r298623 = r298620 + r298622;
        return r298623;
}

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 distribute-lft-in0.1

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

  4. Applied associate-+r+0.1

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

  6. Applied add-cube-cbrt0.1

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

  7. Applied log-prod0.1

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

  8. Applied distribute-rgt-in0.1

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

  9. Applied associate-+r+0.1

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

  10. Simplified0.1

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

  12. Applied pow1/30.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019356 
(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)))))