Average Error: 0.1 → 0.1
Time: 15.9s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(\left(\left(1 - z\right) + \log \left({z}^{\frac{2}{3}}\right)\right) \cdot y + y \cdot \log \left(\sqrt[3]{z}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + \left(\left(\left(1 - z\right) + \log \left({z}^{\frac{2}{3}}\right)\right) \cdot y + y \cdot \log \left(\sqrt[3]{z}\right)\right)
double f(double x, double y, double z) {
        double r264556 = x;
        double r264557 = 0.5;
        double r264558 = r264556 * r264557;
        double r264559 = y;
        double r264560 = 1.0;
        double r264561 = z;
        double r264562 = r264560 - r264561;
        double r264563 = log(r264561);
        double r264564 = r264562 + r264563;
        double r264565 = r264559 * r264564;
        double r264566 = r264558 + r264565;
        return r264566;
}
↓
double f(double x, double y, double z) {
        double r264567 = x;
        double r264568 = 0.5;
        double r264569 = r264567 * r264568;
        double r264570 = 1.0;
        double r264571 = z;
        double r264572 = r264570 - r264571;
        double r264573 = 0.6666666666666666;
        double r264574 = pow(r264571, r264573);
        double r264575 = log(r264574);
        double r264576 = r264572 + r264575;
        double r264577 = y;
        double r264578 = r264576 * r264577;
        double r264579 = cbrt(r264571);
        double r264580 = log(r264579);
        double r264581 = r264577 * r264580;
        double r264582 = r264578 + r264581;
        double r264583 = r264569 + r264582;
        return r264583;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

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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

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

  8. Applied distribute-lft-in0.1

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

  9. Simplified0.1

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

  10. Simplified0.1

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

  12. Applied add-log-exp0.1

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

  13. Simplified0.1

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

  14. Final simplification0.1

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

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)))))