Average Error: 0.1 → 0.1
Time: 5.6s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + -1 \cdot \log \left(\frac{1}{z}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + -1 \cdot \log \left(\frac{1}{z}\right)\right)
double f(double x, double y, double z) {
        double r321467 = x;
        double r321468 = 0.5;
        double r321469 = r321467 * r321468;
        double r321470 = y;
        double r321471 = 1.0;
        double r321472 = z;
        double r321473 = r321471 - r321472;
        double r321474 = log(r321472);
        double r321475 = r321473 + r321474;
        double r321476 = r321470 * r321475;
        double r321477 = r321469 + r321476;
        return r321477;
}
↓
double f(double x, double y, double z) {
        double r321478 = x;
        double r321479 = 0.5;
        double r321480 = r321478 * r321479;
        double r321481 = y;
        double r321482 = 1.0;
        double r321483 = z;
        double r321484 = r321482 - r321483;
        double r321485 = -1.0;
        double r321486 = 1.0;
        double r321487 = r321486 / r321483;
        double r321488 = log(r321487);
        double r321489 = r321485 * r321488;
        double r321490 = r321484 + r321489;
        double r321491 = r321481 * r321490;
        double r321492 = r321480 + r321491;
        return r321492;
}

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-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

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

  7. Taylor expanded around inf 0.2

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020027 
(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)))))