Average Error: 0.1 → 0.1
Time: 4.9s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + y \cdot \left(\left(\left(1 - z\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{z}\right)\right)\]
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{z}\right)\right) + \log \left(\sqrt{z}\right)\right)
double f(double x, double y, double z) {
        double r239682 = x;
        double r239683 = 0.5;
        double r239684 = r239682 * r239683;
        double r239685 = y;
        double r239686 = 1.0;
        double r239687 = z;
        double r239688 = r239686 - r239687;
        double r239689 = log(r239687);
        double r239690 = r239688 + r239689;
        double r239691 = r239685 * r239690;
        double r239692 = r239684 + r239691;
        return r239692;
}
↓
double f(double x, double y, double z) {
        double r239693 = x;
        double r239694 = 0.5;
        double r239695 = r239693 * r239694;
        double r239696 = y;
        double r239697 = 1.0;
        double r239698 = z;
        double r239699 = r239697 - r239698;
        double r239700 = sqrt(r239698);
        double r239701 = log(r239700);
        double r239702 = r239699 + r239701;
        double r239703 = r239702 + r239701;
        double r239704 = r239696 * r239703;
        double r239705 = r239695 + r239704;
        return r239705;
}

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-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied associate-+r+0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(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)))))