Average Error: 0.1 → 0.1
Time: 5.8s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + 1 \cdot \log z\right)\]
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 z\right)
double f(double x, double y, double z) {
        double r268389 = x;
        double r268390 = 0.5;
        double r268391 = r268389 * r268390;
        double r268392 = y;
        double r268393 = 1.0;
        double r268394 = z;
        double r268395 = r268393 - r268394;
        double r268396 = log(r268394);
        double r268397 = r268395 + r268396;
        double r268398 = r268392 * r268397;
        double r268399 = r268391 + r268398;
        return r268399;
}
↓
double f(double x, double y, double z) {
        double r268400 = x;
        double r268401 = 0.5;
        double r268402 = r268400 * r268401;
        double r268403 = y;
        double r268404 = 1.0;
        double r268405 = z;
        double r268406 = r268404 - r268405;
        double r268407 = 1.0;
        double r268408 = log(r268405);
        double r268409 = r268407 * r268408;
        double r268410 = r268406 + r268409;
        double r268411 = r268403 * r268410;
        double r268412 = r268402 + r268411;
        return r268412;
}

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 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 0.1

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

  8. Taylor expanded around 0 0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020056 
(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)))))