Average Error: 0.1 → 0.1
Time: 7.1s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log \left(\sqrt[3]{1} \cdot {y}^{\frac{2}{3}}\right) \cdot x + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right) + \log t\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log \left(\sqrt[3]{1} \cdot {y}^{\frac{2}{3}}\right) \cdot x + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right) + \log t\right)
double f(double x, double y, double z, double t) {
        double r112924 = x;
        double r112925 = y;
        double r112926 = log(r112925);
        double r112927 = r112924 * r112926;
        double r112928 = r112927 - r112925;
        double r112929 = z;
        double r112930 = r112928 - r112929;
        double r112931 = t;
        double r112932 = log(r112931);
        double r112933 = r112930 + r112932;
        return r112933;
}
↓
double f(double x, double y, double z, double t) {
        double r112934 = 1.0;
        double r112935 = cbrt(r112934);
        double r112936 = y;
        double r112937 = 0.6666666666666666;
        double r112938 = pow(r112936, r112937);
        double r112939 = r112935 * r112938;
        double r112940 = log(r112939);
        double r112941 = x;
        double r112942 = r112940 * r112941;
        double r112943 = cbrt(r112936);
        double r112944 = log(r112943);
        double r112945 = r112944 * r112941;
        double r112946 = r112945 - r112936;
        double r112947 = z;
        double r112948 = r112946 - r112947;
        double r112949 = t;
        double r112950 = log(r112949);
        double r112951 = r112948 + r112950;
        double r112952 = r112942 + r112951;
        return r112952;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-rgt-in0.1

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

  6. Applied associate--l+0.1

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

  7. Applied associate--l+0.1

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

  8. Applied associate-+l+0.1

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

  10. Applied *-un-lft-identity0.1

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

  11. Applied cbrt-prod0.1

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

  12. Applied associate-*l*0.1

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

  13. Simplified0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2020081 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))