Average Error: 0.1 → 0.1
Time: 18.7s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(\left(\log \left({z}^{\frac{1}{3}}\right) + \left(1 - z\right)\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot y\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + \left(\left(\log \left({z}^{\frac{1}{3}}\right) + \left(1 - z\right)\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot y
double f(double x, double y, double z) {
        double r248284 = x;
        double r248285 = 0.5;
        double r248286 = r248284 * r248285;
        double r248287 = y;
        double r248288 = 1.0;
        double r248289 = z;
        double r248290 = r248288 - r248289;
        double r248291 = log(r248289);
        double r248292 = r248290 + r248291;
        double r248293 = r248287 * r248292;
        double r248294 = r248286 + r248293;
        return r248294;
}
↓
double f(double x, double y, double z) {
        double r248295 = x;
        double r248296 = 0.5;
        double r248297 = r248295 * r248296;
        double r248298 = z;
        double r248299 = 0.3333333333333333;
        double r248300 = pow(r248298, r248299);
        double r248301 = log(r248300);
        double r248302 = 1.0;
        double r248303 = r248302 - r248298;
        double r248304 = r248301 + r248303;
        double r248305 = cbrt(r248298);
        double r248306 = r248305 * r248305;
        double r248307 = log(r248306);
        double r248308 = r248304 + r248307;
        double r248309 = y;
        double r248310 = r248308 * r248309;
        double r248311 = r248297 + r248310;
        return r248311;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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. Simplified0.1

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

  4. Applied add-cube-cbrt0.1

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

  5. Applied log-prod0.1

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

  6. Applied associate-+l+0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(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)))))