Average Error: 0.1 → 0.1
Time: 18.8s
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 r246383 = x;
        double r246384 = 0.5;
        double r246385 = r246383 * r246384;
        double r246386 = y;
        double r246387 = 1.0;
        double r246388 = z;
        double r246389 = r246387 - r246388;
        double r246390 = log(r246388);
        double r246391 = r246389 + r246390;
        double r246392 = r246386 * r246391;
        double r246393 = r246385 + r246392;
        return r246393;
}
↓
double f(double x, double y, double z) {
        double r246394 = x;
        double r246395 = 0.5;
        double r246396 = r246394 * r246395;
        double r246397 = z;
        double r246398 = 0.3333333333333333;
        double r246399 = pow(r246397, r246398);
        double r246400 = log(r246399);
        double r246401 = 1.0;
        double r246402 = r246401 - r246397;
        double r246403 = r246400 + r246402;
        double r246404 = cbrt(r246397);
        double r246405 = r246404 * r246404;
        double r246406 = log(r246405);
        double r246407 = r246403 + r246406;
        double r246408 = y;
        double r246409 = r246407 * r246408;
        double r246410 = r246396 + r246409;
        return r246410;
}

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)))))