Average Error: 0.1 → 0.1
Time: 46.1s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]
↓
\[y \cdot \left(\left(1.0 - z\right) + \log z\right) + x \cdot 0.5\]
x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)
↓
y \cdot \left(\left(1.0 - z\right) + \log z\right) + x \cdot 0.5
double f(double x, double y, double z) {
        double r19204189 = x;
        double r19204190 = 0.5;
        double r19204191 = r19204189 * r19204190;
        double r19204192 = y;
        double r19204193 = 1.0;
        double r19204194 = z;
        double r19204195 = r19204193 - r19204194;
        double r19204196 = log(r19204194);
        double r19204197 = r19204195 + r19204196;
        double r19204198 = r19204192 * r19204197;
        double r19204199 = r19204191 + r19204198;
        return r19204199;
}
↓
double f(double x, double y, double z) {
        double r19204200 = y;
        double r19204201 = 1.0;
        double r19204202 = z;
        double r19204203 = r19204201 - r19204202;
        double r19204204 = log(r19204202);
        double r19204205 = r19204203 + r19204204;
        double r19204206 = r19204200 * r19204205;
        double r19204207 = x;
        double r19204208 = 0.5;
        double r19204209 = r19204207 * r19204208;
        double r19204210 = r19204206 + r19204209;
        return r19204210;
}

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

    \[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)}\right)\]

  4. Applied log-prod0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)}\right)\]

  5. Applied associate-+r+0.1

    \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(\left(1.0 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right)}\]
  6. Using strategy rm

  7. Applied pow1/30.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\left(\left(1.0 - z\right) + \log \left(\sqrt[3]{z} \cdot \color{blue}{{z}^{\frac{1}{3}}}\right)\right) + \log \left(\sqrt[3]{z}\right)\right)\]

  8. Applied pow1/30.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\left(\left(1.0 - z\right) + \log \left(\color{blue}{{z}^{\frac{1}{3}}} \cdot {z}^{\frac{1}{3}}\right)\right) + \log \left(\sqrt[3]{z}\right)\right)\]

  9. Applied pow-prod-up0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\left(\left(1.0 - z\right) + \log \color{blue}{\left({z}^{\left(\frac{1}{3} + \frac{1}{3}\right)}\right)}\right) + \log \left(\sqrt[3]{z}\right)\right)\]

  10. Simplified0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\left(\left(1.0 - z\right) + \log \left({z}^{\color{blue}{\frac{2}{3}}}\right)\right) + \log \left(\sqrt[3]{z}\right)\right)\]

  11. Taylor expanded around inf 0.2

    \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(\log \left({\left(\frac{1}{z}\right)}^{\frac{-1}{3}}\right) + \left(\log \left({\left(\frac{1}{z}\right)}^{\frac{-2}{3}}\right) + 1.0\right)\right) - z\right)}\]

  12. Simplified0.1

    \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(-\log z \cdot -1\right) + \left(1.0 - z\right)\right)}\]

  13. Final simplification0.1

    \[\leadsto y \cdot \left(\left(1.0 - z\right) + \log z\right) + x \cdot 0.5\]

Reproduce

herbie shell --seed 2019165 
(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)))))