Average Error: 1.8 → 1.8
Time: 40.7s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}}\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}}\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r4280975 = x;
        double r4280976 = y;
        double r4280977 = z;
        double r4280978 = log(r4280977);
        double r4280979 = r4280976 * r4280978;
        double r4280980 = t;
        double r4280981 = 1.0;
        double r4280982 = r4280980 - r4280981;
        double r4280983 = a;
        double r4280984 = log(r4280983);
        double r4280985 = r4280982 * r4280984;
        double r4280986 = r4280979 + r4280985;
        double r4280987 = b;
        double r4280988 = r4280986 - r4280987;
        double r4280989 = exp(r4280988);
        double r4280990 = r4280975 * r4280989;
        double r4280991 = r4280990 / r4280976;
        return r4280991;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r4280992 = x;
        double r4280993 = exp(1.0);
        double r4280994 = a;
        double r4280995 = log(r4280994);
        double r4280996 = t;
        double r4280997 = 1.0;
        double r4280998 = r4280996 - r4280997;
        double r4280999 = r4280995 * r4280998;
        double r4281000 = z;
        double r4281001 = log(r4281000);
        double r4281002 = y;
        double r4281003 = r4281001 * r4281002;
        double r4281004 = r4280999 + r4281003;
        double r4281005 = b;
        double r4281006 = r4281004 - r4281005;
        double r4281007 = pow(r4280993, r4281006);
        double r4281008 = r4280992 * r4281007;
        double r4281009 = r4281008 / r4281002;
        double r4281010 = cbrt(r4281009);
        double r4281011 = exp(r4281006);
        double r4281012 = r4280992 * r4281011;
        double r4281013 = r4281012 / r4281002;
        double r4281014 = cbrt(r4281013);
        double r4281015 = r4281014 * r4281014;
        double r4281016 = r4281010 * r4281015;
        return r4281016;
}

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 1.8

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

  3. Applied add-cube-cbrt1.8

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

  5. Applied *-un-lft-identity1.8

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

  6. Applied exp-prod1.8

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

  7. Simplified1.8

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

  8. Final simplification1.8

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

Reproduce

herbie shell --seed 2019163 
(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))