Average Error: 0.1 → 0.1
Time: 17.2s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + y \cdot \left(\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + \log \left(\sqrt[3]{z}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + y \cdot \left(\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + \log \left(\sqrt[3]{z}\right)\right)
double f(double x, double y, double z) {
        double r206697 = x;
        double r206698 = 0.5;
        double r206699 = r206697 * r206698;
        double r206700 = y;
        double r206701 = 1.0;
        double r206702 = z;
        double r206703 = r206701 - r206702;
        double r206704 = log(r206702);
        double r206705 = r206703 + r206704;
        double r206706 = r206700 * r206705;
        double r206707 = r206699 + r206706;
        return r206707;
}
↓
double f(double x, double y, double z) {
        double r206708 = x;
        double r206709 = 0.5;
        double r206710 = r206708 * r206709;
        double r206711 = y;
        double r206712 = 2.0;
        double r206713 = z;
        double r206714 = cbrt(r206713);
        double r206715 = log(r206714);
        double r206716 = r206712 * r206715;
        double r206717 = 1.0;
        double r206718 = r206716 + r206717;
        double r206719 = r206718 - r206713;
        double r206720 = r206719 + r206715;
        double r206721 = r206711 * r206720;
        double r206722 = r206710 + r206721;
        return r206722;
}

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

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(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)))))