Average Error: 0.1 → 0.1
Time: 16.4s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[\left(0.5 \cdot x + \left(\left(1 - z\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y\right) + \log \left(\sqrt[3]{z}\right) \cdot y\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
\left(0.5 \cdot x + \left(\left(1 - z\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y\right) + \log \left(\sqrt[3]{z}\right) \cdot y
double f(double x, double y, double z) {
        double r14614967 = x;
        double r14614968 = 0.5;
        double r14614969 = r14614967 * r14614968;
        double r14614970 = y;
        double r14614971 = 1.0;
        double r14614972 = z;
        double r14614973 = r14614971 - r14614972;
        double r14614974 = log(r14614972);
        double r14614975 = r14614973 + r14614974;
        double r14614976 = r14614970 * r14614975;
        double r14614977 = r14614969 + r14614976;
        return r14614977;
}
↓
double f(double x, double y, double z) {
        double r14614978 = 0.5;
        double r14614979 = x;
        double r14614980 = r14614978 * r14614979;
        double r14614981 = 1.0;
        double r14614982 = z;
        double r14614983 = r14614981 - r14614982;
        double r14614984 = cbrt(r14614982);
        double r14614985 = log(r14614984);
        double r14614986 = r14614985 + r14614985;
        double r14614987 = r14614983 + r14614986;
        double r14614988 = y;
        double r14614989 = r14614987 * r14614988;
        double r14614990 = r14614980 + r14614989;
        double r14614991 = r14614985 * r14614988;
        double r14614992 = r14614990 + r14614991;
        return r14614992;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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. Applied associate-+r+0.1

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

  6. Applied add-cube-cbrt0.1

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

  7. Applied log-prod0.1

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

  8. Applied distribute-rgt-in0.1

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

  9. Applied associate-+r+0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(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)))))