Average Error: 0.1 → 0.1
Time: 6.0s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[\left(y \cdot \left(\left(1 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + x \cdot 0.5\right) + \log \left(\sqrt[3]{z}\right) \cdot y\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
\left(y \cdot \left(\left(1 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + x \cdot 0.5\right) + \log \left(\sqrt[3]{z}\right) \cdot y
double f(double x, double y, double z) {
        double r331936 = x;
        double r331937 = 0.5;
        double r331938 = r331936 * r331937;
        double r331939 = y;
        double r331940 = 1.0;
        double r331941 = z;
        double r331942 = r331940 - r331941;
        double r331943 = log(r331941);
        double r331944 = r331942 + r331943;
        double r331945 = r331939 * r331944;
        double r331946 = r331938 + r331945;
        return r331946;
}
↓
double f(double x, double y, double z) {
        double r331947 = y;
        double r331948 = 1.0;
        double r331949 = z;
        double r331950 = r331948 - r331949;
        double r331951 = cbrt(r331949);
        double r331952 = r331951 * r331951;
        double r331953 = log(r331952);
        double r331954 = r331950 + r331953;
        double r331955 = r331947 * r331954;
        double r331956 = x;
        double r331957 = 0.5;
        double r331958 = r331956 * r331957;
        double r331959 = r331955 + r331958;
        double r331960 = log(r331951);
        double r331961 = r331960 * r331947;
        double r331962 = r331959 + r331961;
        return r331962;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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-prod0.2

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

  8. Applied distribute-rgt-in0.2

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

  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

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019353 
(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)))))