Average Error: 0.1 → 0.1
Time: 4.6s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(y \cdot \left(\left(1 - z\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{z}\right) \cdot y\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + \left(y \cdot \left(\left(1 - z\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{z}\right) \cdot y\right)
double f(double x, double y, double z) {
        double r274606 = x;
        double r274607 = 0.5;
        double r274608 = r274606 * r274607;
        double r274609 = y;
        double r274610 = 1.0;
        double r274611 = z;
        double r274612 = r274610 - r274611;
        double r274613 = log(r274611);
        double r274614 = r274612 + r274613;
        double r274615 = r274609 * r274614;
        double r274616 = r274608 + r274615;
        return r274616;
}
↓
double f(double x, double y, double z) {
        double r274617 = x;
        double r274618 = 0.5;
        double r274619 = r274617 * r274618;
        double r274620 = y;
        double r274621 = 1.0;
        double r274622 = z;
        double r274623 = r274621 - r274622;
        double r274624 = sqrt(r274622);
        double r274625 = log(r274624);
        double r274626 = r274623 + r274625;
        double r274627 = r274620 * r274626;
        double r274628 = r274625 * r274620;
        double r274629 = r274627 + r274628;
        double r274630 = r274619 + r274629;
        return r274630;
}

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-sqr-sqrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-rgt-in0.1

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

  8. Applied associate-+r+0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020081 
(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)))))