Average Error: 1.9 → 1.2
Time: 12.6s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\left(x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}\right) \cdot \frac{1}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\left(x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}\right) \cdot \frac{1}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r77838 = x;
        double r77839 = y;
        double r77840 = z;
        double r77841 = log(r77840);
        double r77842 = r77839 * r77841;
        double r77843 = t;
        double r77844 = 1.0;
        double r77845 = r77843 - r77844;
        double r77846 = a;
        double r77847 = log(r77846);
        double r77848 = r77845 * r77847;
        double r77849 = r77842 + r77848;
        double r77850 = b;
        double r77851 = r77849 - r77850;
        double r77852 = exp(r77851);
        double r77853 = r77838 * r77852;
        double r77854 = r77853 / r77839;
        return r77854;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r77855 = x;
        double r77856 = 1.0;
        double r77857 = a;
        double r77858 = r77856 / r77857;
        double r77859 = 1.0;
        double r77860 = pow(r77858, r77859);
        double r77861 = y;
        double r77862 = z;
        double r77863 = r77856 / r77862;
        double r77864 = log(r77863);
        double r77865 = r77861 * r77864;
        double r77866 = log(r77858);
        double r77867 = t;
        double r77868 = r77866 * r77867;
        double r77869 = b;
        double r77870 = r77868 + r77869;
        double r77871 = r77865 + r77870;
        double r77872 = exp(r77871);
        double r77873 = r77860 / r77872;
        double r77874 = r77855 * r77873;
        double r77875 = r77856 / r77861;
        double r77876 = r77874 * r77875;
        return r77876;
}

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

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

  2. Taylor expanded around inf 1.9

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

  3. Simplified1.2

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

  5. Applied div-inv1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2020064 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))