Average Error: 0.1 → 0.1
Time: 6.5s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + y \cdot \left(\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + \log \left(\sqrt[3]{z}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + y \cdot \left(\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + \log \left(\sqrt[3]{z}\right)\right)
double f(double x, double y, double z) {
        double r329946 = x;
        double r329947 = 0.5;
        double r329948 = r329946 * r329947;
        double r329949 = y;
        double r329950 = 1.0;
        double r329951 = z;
        double r329952 = r329950 - r329951;
        double r329953 = log(r329951);
        double r329954 = r329952 + r329953;
        double r329955 = r329949 * r329954;
        double r329956 = r329948 + r329955;
        return r329956;
}
↓
double f(double x, double y, double z) {
        double r329957 = x;
        double r329958 = 0.5;
        double r329959 = r329957 * r329958;
        double r329960 = y;
        double r329961 = 2.0;
        double r329962 = z;
        double r329963 = cbrt(r329962);
        double r329964 = log(r329963);
        double r329965 = r329961 * r329964;
        double r329966 = 1.0;
        double r329967 = r329965 + r329966;
        double r329968 = r329967 - r329962;
        double r329969 = r329968 + r329964;
        double r329970 = r329960 * r329969;
        double r329971 = r329959 + r329970;
        return r329971;
}

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 add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied associate-+r+0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019354 
(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)))))