Average Error: 1.7 → 1.7
Time: 49.0s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}\right)} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}} \cdot \sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}}\right)\right)\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}\right)} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}} \cdot \sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}}\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r3272954 = x;
        double r3272955 = y;
        double r3272956 = z;
        double r3272957 = log(r3272956);
        double r3272958 = r3272955 * r3272957;
        double r3272959 = t;
        double r3272960 = 1.0;
        double r3272961 = r3272959 - r3272960;
        double r3272962 = a;
        double r3272963 = log(r3272962);
        double r3272964 = r3272961 * r3272963;
        double r3272965 = r3272958 + r3272964;
        double r3272966 = b;
        double r3272967 = r3272965 - r3272966;
        double r3272968 = exp(r3272967);
        double r3272969 = r3272954 * r3272968;
        double r3272970 = r3272969 / r3272955;
        return r3272970;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3272971 = x;
        double r3272972 = exp(1.0);
        double r3272973 = a;
        double r3272974 = log(r3272973);
        double r3272975 = t;
        double r3272976 = 1.0;
        double r3272977 = r3272975 - r3272976;
        double r3272978 = r3272974 * r3272977;
        double r3272979 = z;
        double r3272980 = log(r3272979);
        double r3272981 = y;
        double r3272982 = r3272980 * r3272981;
        double r3272983 = r3272978 + r3272982;
        double r3272984 = b;
        double r3272985 = r3272983 - r3272984;
        double r3272986 = pow(r3272972, r3272985);
        double r3272987 = r3272971 * r3272986;
        double r3272988 = r3272987 / r3272981;
        double r3272989 = cbrt(r3272988);
        double r3272990 = exp(r3272985);
        double r3272991 = r3272971 * r3272990;
        double r3272992 = r3272991 / r3272981;
        double r3272993 = cbrt(r3272992);
        double r3272994 = r3272993 * r3272993;
        double r3272995 = r3272993 * r3272994;
        double r3272996 = cbrt(r3272995);
        double r3272997 = cbrt(r3272993);
        double r3272998 = r3272997 * r3272997;
        double r3272999 = r3272997 * r3272998;
        double r3273000 = r3272996 * r3272999;
        double r3273001 = r3272989 * r3273000;
        return r3273001;
}

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 1.7

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.7

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

  5. Applied *-un-lft-identity1.7

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

  6. Applied exp-prod1.7

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

  7. Simplified1.7

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

  9. Applied add-cube-cbrt1.7

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

  11. Applied add-cbrt-cube1.7

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

  12. Final simplification1.7

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(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))