Average Error: 0.1 → 0.1
Time: 19.6s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[\left(y \cdot \left(2 \cdot \log \left(\sqrt[3]{z}\right) + \left(1 - z\right)\right) + \left(\log z \cdot y\right) \cdot \frac{1}{3}\right) + x \cdot 0.5\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
\left(y \cdot \left(2 \cdot \log \left(\sqrt[3]{z}\right) + \left(1 - z\right)\right) + \left(\log z \cdot y\right) \cdot \frac{1}{3}\right) + x \cdot 0.5
double f(double x, double y, double z) {
        double r223554 = x;
        double r223555 = 0.5;
        double r223556 = r223554 * r223555;
        double r223557 = y;
        double r223558 = 1.0;
        double r223559 = z;
        double r223560 = r223558 - r223559;
        double r223561 = log(r223559);
        double r223562 = r223560 + r223561;
        double r223563 = r223557 * r223562;
        double r223564 = r223556 + r223563;
        return r223564;
}
↓
double f(double x, double y, double z) {
        double r223565 = y;
        double r223566 = 2.0;
        double r223567 = z;
        double r223568 = cbrt(r223567);
        double r223569 = log(r223568);
        double r223570 = r223566 * r223569;
        double r223571 = 1.0;
        double r223572 = r223571 - r223567;
        double r223573 = r223570 + r223572;
        double r223574 = r223565 * r223573;
        double r223575 = log(r223567);
        double r223576 = r223575 * r223565;
        double r223577 = 0.3333333333333333;
        double r223578 = r223576 * r223577;
        double r223579 = r223574 + r223578;
        double r223580 = x;
        double r223581 = 0.5;
        double r223582 = r223580 * r223581;
        double r223583 = r223579 + r223582;
        return r223583;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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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-cube-cbrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-lft-in0.1

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

  8. Applied associate-+r+0.1

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

  9. Simplified0.1

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

  10. Taylor expanded around inf 0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 
(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)))))