Average Error: 0.1 → 0.1
Time: 18.0s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + y \cdot \left(\left(\left(1 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + y \cdot \left(\left(\left(1 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right)
double f(double x, double y, double z) {
        double r21422665 = x;
        double r21422666 = 0.5;
        double r21422667 = r21422665 * r21422666;
        double r21422668 = y;
        double r21422669 = 1.0;
        double r21422670 = z;
        double r21422671 = r21422669 - r21422670;
        double r21422672 = log(r21422670);
        double r21422673 = r21422671 + r21422672;
        double r21422674 = r21422668 * r21422673;
        double r21422675 = r21422667 + r21422674;
        return r21422675;
}
↓
double f(double x, double y, double z) {
        double r21422676 = x;
        double r21422677 = 0.5;
        double r21422678 = r21422676 * r21422677;
        double r21422679 = y;
        double r21422680 = 1.0;
        double r21422681 = z;
        double r21422682 = r21422680 - r21422681;
        double r21422683 = cbrt(r21422681);
        double r21422684 = r21422683 * r21422683;
        double r21422685 = log(r21422684);
        double r21422686 = r21422682 + r21422685;
        double r21422687 = log(r21422683);
        double r21422688 = r21422686 + r21422687;
        double r21422689 = r21422679 * r21422688;
        double r21422690 = r21422678 + r21422689;
        return r21422690;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(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)))))