Average Error: 0.1 → 0.1
Time: 4.2s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[\left(\log \left({z}^{\frac{1}{3}}\right) \cdot y + \left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y\right) + x \cdot 0.5\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
\left(\log \left({z}^{\frac{1}{3}}\right) \cdot y + \left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y\right) + x \cdot 0.5
double f(double x, double y, double z) {
        double r319173 = x;
        double r319174 = 0.5;
        double r319175 = r319173 * r319174;
        double r319176 = y;
        double r319177 = 1.0;
        double r319178 = z;
        double r319179 = r319177 - r319178;
        double r319180 = log(r319178);
        double r319181 = r319179 + r319180;
        double r319182 = r319176 * r319181;
        double r319183 = r319175 + r319182;
        return r319183;
}
↓
double f(double x, double y, double z) {
        double r319184 = z;
        double r319185 = 0.3333333333333333;
        double r319186 = pow(r319184, r319185);
        double r319187 = log(r319186);
        double r319188 = y;
        double r319189 = r319187 * r319188;
        double r319190 = 1.0;
        double r319191 = 2.0;
        double r319192 = cbrt(r319184);
        double r319193 = log(r319192);
        double r319194 = r319191 * r319193;
        double r319195 = r319184 - r319194;
        double r319196 = r319190 - r319195;
        double r319197 = r319196 * r319188;
        double r319198 = r319189 + r319197;
        double r319199 = x;
        double r319200 = 0.5;
        double r319201 = r319199 * r319200;
        double r319202 = r319198 + r319201;
        return r319202;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

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. Using strategy rm

  3. Applied distribute-lft-in0.1

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

  5. Applied add-cube-cbrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-rgt-in0.1

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

  8. Applied associate-+r+0.1

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

  9. Simplified0.1

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

  11. Applied pow10.1

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

  12. Applied log-pow0.1

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

  13. Applied associate-*l*0.1

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

  14. Simplified0.1

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

  15. Final simplification0.1

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

Reproduce

herbie shell --seed 2020064 
(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)))))