Average Error: 0.1 → 0.1
Time: 7.4s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + y \cdot \left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{\sqrt{z}}\right) + 1\right) - z\right) + \log \left(\sqrt[3]{\sqrt{z}}\right)\right) + \log \left(\sqrt{z}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + y \cdot \left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{\sqrt{z}}\right) + 1\right) - z\right) + \log \left(\sqrt[3]{\sqrt{z}}\right)\right) + \log \left(\sqrt{z}\right)\right)
double f(double x, double y, double z) {
        double r296572 = x;
        double r296573 = 0.5;
        double r296574 = r296572 * r296573;
        double r296575 = y;
        double r296576 = 1.0;
        double r296577 = z;
        double r296578 = r296576 - r296577;
        double r296579 = log(r296577);
        double r296580 = r296578 + r296579;
        double r296581 = r296575 * r296580;
        double r296582 = r296574 + r296581;
        return r296582;
}
↓
double f(double x, double y, double z) {
        double r296583 = x;
        double r296584 = 0.5;
        double r296585 = r296583 * r296584;
        double r296586 = y;
        double r296587 = 2.0;
        double r296588 = z;
        double r296589 = sqrt(r296588);
        double r296590 = cbrt(r296589);
        double r296591 = log(r296590);
        double r296592 = r296587 * r296591;
        double r296593 = 1.0;
        double r296594 = r296592 + r296593;
        double r296595 = r296594 - r296588;
        double r296596 = r296595 + r296591;
        double r296597 = log(r296589);
        double r296598 = r296596 + r296597;
        double r296599 = r296586 * r296598;
        double r296600 = r296585 + r296599;
        return r296600;
}

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. Using strategy rm

  7. Applied add-cube-cbrt0.1

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

  8. Applied log-prod0.1

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

  9. Applied associate-+r+0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020002 
(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)))))