Average Error: 0.1 → 0.1
Time: 40.1s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(x - \left(\left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(y + 0.5\right) \cdot \log \left({\left({y}^{\frac{2}{3}}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) - y\right)\right)\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(x - \left(\left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(y + 0.5\right) \cdot \log \left({\left({y}^{\frac{2}{3}}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) - y\right)\right)\right) - z
double f(double x, double y, double z) {
        double r293944 = x;
        double r293945 = y;
        double r293946 = 0.5;
        double r293947 = r293945 + r293946;
        double r293948 = log(r293945);
        double r293949 = r293947 * r293948;
        double r293950 = r293944 - r293949;
        double r293951 = r293950 + r293945;
        double r293952 = z;
        double r293953 = r293951 - r293952;
        return r293953;
}
↓
double f(double x, double y, double z) {
        double r293954 = x;
        double r293955 = y;
        double r293956 = 0.5;
        double r293957 = r293955 + r293956;
        double r293958 = cbrt(r293955);
        double r293959 = r293958 * r293958;
        double r293960 = log(r293959);
        double r293961 = r293957 * r293960;
        double r293962 = 0.6666666666666666;
        double r293963 = pow(r293955, r293962);
        double r293964 = 0.3333333333333333;
        double r293965 = pow(r293963, r293964);
        double r293966 = cbrt(r293958);
        double r293967 = r293965 * r293966;
        double r293968 = log(r293967);
        double r293969 = r293957 * r293968;
        double r293970 = r293969 - r293955;
        double r293971 = r293961 + r293970;
        double r293972 = r293954 - r293971;
        double r293973 = z;
        double r293974 = r293972 - r293973;
        return r293974;
}

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
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
  2. Using strategy rm

  3. Applied associate-+l-0.1

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

  5. Applied add-cube-cbrt0.1

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

  6. Applied log-prod0.2

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

  7. Applied distribute-lft-in0.2

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

  8. Applied associate--l+0.1

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

  10. Applied add-cube-cbrt0.1

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

  11. Applied cbrt-prod0.1

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

  12. Simplified0.1

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

  14. Applied pow1/30.1

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

  15. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))