Average Error: 1.9 → 1.4
Time: 43.4s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{1}{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}} \cdot \frac{\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{x}}}\right) \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\frac{y}{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{1}{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}} \cdot \frac{\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{x}}}\right) \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\frac{y}{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}}
double f(double x, double y, double z, double t, double a, double b) {
        double r2921929 = x;
        double r2921930 = y;
        double r2921931 = z;
        double r2921932 = log(r2921931);
        double r2921933 = r2921930 * r2921932;
        double r2921934 = t;
        double r2921935 = 1.0;
        double r2921936 = r2921934 - r2921935;
        double r2921937 = a;
        double r2921938 = log(r2921937);
        double r2921939 = r2921936 * r2921938;
        double r2921940 = r2921933 + r2921939;
        double r2921941 = b;
        double r2921942 = r2921940 - r2921941;
        double r2921943 = exp(r2921942);
        double r2921944 = r2921929 * r2921943;
        double r2921945 = r2921944 / r2921930;
        return r2921945;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r2921946 = x;
        double r2921947 = cbrt(r2921946);
        double r2921948 = r2921947 * r2921947;
        double r2921949 = 1.0;
        double r2921950 = a;
        double r2921951 = log(r2921950);
        double r2921952 = t;
        double r2921953 = 1.0;
        double r2921954 = r2921952 - r2921953;
        double r2921955 = r2921951 * r2921954;
        double r2921956 = z;
        double r2921957 = log(r2921956);
        double r2921958 = y;
        double r2921959 = r2921957 * r2921958;
        double r2921960 = r2921955 + r2921959;
        double r2921961 = b;
        double r2921962 = r2921960 - r2921961;
        double r2921963 = exp(r2921962);
        double r2921964 = cbrt(r2921963);
        double r2921965 = r2921964 * r2921964;
        double r2921966 = r2921949 / r2921965;
        double r2921967 = r2921948 / r2921966;
        double r2921968 = cbrt(r2921947);
        double r2921969 = r2921968 * r2921968;
        double r2921970 = cbrt(r2921969);
        double r2921971 = cbrt(r2921968);
        double r2921972 = r2921970 * r2921971;
        double r2921973 = cbrt(r2921948);
        double r2921974 = r2921972 * r2921973;
        double r2921975 = r2921958 / r2921964;
        double r2921976 = r2921974 / r2921975;
        double r2921977 = r2921967 * r2921976;
        return r2921977;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.9

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  2. Using strategy rm

  3. Applied associate-/l*2.0

    \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt2.0

    \[\leadsto \frac{x}{\frac{y}{\color{blue}{\left(\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right) \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}}}\]

  6. Applied *-un-lft-identity2.0

    \[\leadsto \frac{x}{\frac{\color{blue}{1 \cdot y}}{\left(\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right) \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}}\]

  7. Applied times-frac2.0

    \[\leadsto \frac{x}{\color{blue}{\frac{1}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}} \cdot \frac{y}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}}}\]

  8. Applied add-cube-cbrt2.0

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\frac{1}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}} \cdot \frac{y}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}}\]

  9. Applied times-frac1.4

    \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{1}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}} \cdot \frac{\sqrt[3]{x}}{\frac{y}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}}}\]
  10. Using strategy rm

  11. Applied add-cube-cbrt1.4

    \[\leadsto \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{1}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}} \cdot \frac{\sqrt[3]{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}}{\frac{y}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}}\]

  12. Applied cbrt-prod1.4

    \[\leadsto \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{1}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}} \cdot \frac{\color{blue}{\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}}}{\frac{y}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}}\]
  13. Using strategy rm

  14. Applied add-cube-cbrt1.4

    \[\leadsto \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{1}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}} \cdot \frac{\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}\right) \cdot \sqrt[3]{\sqrt[3]{x}}}}}{\frac{y}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}}\]

  15. Applied cbrt-prod1.4

    \[\leadsto \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{1}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}} \cdot \frac{\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{x}}}\right)}}{\frac{y}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}}\]

  16. Final simplification1.4

    \[\leadsto \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{1}{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}} \cdot \frac{\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{x}}}\right) \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\frac{y}{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))