Average Error: 0.1 → 0.1
Time: 23.3s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(y \cdot \left(2 \cdot \log \left(\sqrt[3]{z}\right) + \left(1 - z\right)\right) + y \cdot \log \left({z}^{\frac{1}{3}}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + \left(y \cdot \left(2 \cdot \log \left(\sqrt[3]{z}\right) + \left(1 - z\right)\right) + y \cdot \log \left({z}^{\frac{1}{3}}\right)\right)
double f(double x, double y, double z) {
        double r280733 = x;
        double r280734 = 0.5;
        double r280735 = r280733 * r280734;
        double r280736 = y;
        double r280737 = 1.0;
        double r280738 = z;
        double r280739 = r280737 - r280738;
        double r280740 = log(r280738);
        double r280741 = r280739 + r280740;
        double r280742 = r280736 * r280741;
        double r280743 = r280735 + r280742;
        return r280743;
}
↓
double f(double x, double y, double z) {
        double r280744 = x;
        double r280745 = 0.5;
        double r280746 = r280744 * r280745;
        double r280747 = y;
        double r280748 = 2.0;
        double r280749 = z;
        double r280750 = cbrt(r280749);
        double r280751 = log(r280750);
        double r280752 = r280748 * r280751;
        double r280753 = 1.0;
        double r280754 = r280753 - r280749;
        double r280755 = r280752 + r280754;
        double r280756 = r280747 * r280755;
        double r280757 = 0.3333333333333333;
        double r280758 = pow(r280749, r280757);
        double r280759 = log(r280758);
        double r280760 = r280747 * r280759;
        double r280761 = r280756 + r280760;
        double r280762 = r280746 + r280761;
        return r280762;
}

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. Using strategy rm

  5. Applied add-cube-cbrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-lft-in0.1

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

  8. Applied associate-+r+0.1

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

  9. Simplified0.1

    \[\leadsto x \cdot 0.5 + \left(\color{blue}{y \cdot \left(2 \cdot \log \left(\sqrt[3]{z}\right) + \left(1 - z\right)\right)} + y \cdot \log \left(\sqrt[3]{z}\right)\right)\]
  10. Using strategy rm

  11. Applied pow1/30.1

    \[\leadsto x \cdot 0.5 + \left(y \cdot \left(2 \cdot \log \left(\sqrt[3]{z}\right) + \left(1 - z\right)\right) + y \cdot \log \color{blue}{\left({z}^{\frac{1}{3}}\right)}\right)\]

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019306 
(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)))))