Average Error: 0.1 → 0.1
Time: 5.0s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + \log \left(\sqrt[3]{z}\right) \cdot y\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + \left(\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)
double f(double x, double y, double z) {
        double r285931 = x;
        double r285932 = 0.5;
        double r285933 = r285931 * r285932;
        double r285934 = y;
        double r285935 = 1.0;
        double r285936 = z;
        double r285937 = r285935 - r285936;
        double r285938 = log(r285936);
        double r285939 = r285937 + r285938;
        double r285940 = r285934 * r285939;
        double r285941 = r285933 + r285940;
        return r285941;
}
↓
double f(double x, double y, double z) {
        double r285942 = x;
        double r285943 = 0.5;
        double r285944 = r285942 * r285943;
        double r285945 = 1.0;
        double r285946 = z;
        double r285947 = 2.0;
        double r285948 = cbrt(r285946);
        double r285949 = log(r285948);
        double r285950 = r285947 * r285949;
        double r285951 = r285946 - r285950;
        double r285952 = r285945 - r285951;
        double r285953 = y;
        double r285954 = r285952 * r285953;
        double r285955 = r285949 * r285953;
        double r285956 = r285954 + r285955;
        double r285957 = r285944 + r285956;
        return r285957;
}

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. 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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020024 
(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)))))