Average Error: 1.9 → 23.2
Time: 38.3s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{{\left(\frac{1}{a}\right)}^{1}}{{\left(\frac{1}{z}\right)}^{y}} \cdot \frac{\frac{x}{y}}{\frac{e^{b}}{{a}^{t}}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{{\left(\frac{1}{a}\right)}^{1}}{{\left(\frac{1}{z}\right)}^{y}} \cdot \frac{\frac{x}{y}}{\frac{e^{b}}{{a}^{t}}}
double f(double x, double y, double z, double t, double a, double b) {
        double r58759 = x;
        double r58760 = y;
        double r58761 = z;
        double r58762 = log(r58761);
        double r58763 = r58760 * r58762;
        double r58764 = t;
        double r58765 = 1.0;
        double r58766 = r58764 - r58765;
        double r58767 = a;
        double r58768 = log(r58767);
        double r58769 = r58766 * r58768;
        double r58770 = r58763 + r58769;
        double r58771 = b;
        double r58772 = r58770 - r58771;
        double r58773 = exp(r58772);
        double r58774 = r58759 * r58773;
        double r58775 = r58774 / r58760;
        return r58775;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r58776 = 1.0;
        double r58777 = a;
        double r58778 = r58776 / r58777;
        double r58779 = 1.0;
        double r58780 = pow(r58778, r58779);
        double r58781 = z;
        double r58782 = r58776 / r58781;
        double r58783 = y;
        double r58784 = pow(r58782, r58783);
        double r58785 = r58780 / r58784;
        double r58786 = x;
        double r58787 = r58786 / r58783;
        double r58788 = b;
        double r58789 = exp(r58788);
        double r58790 = t;
        double r58791 = pow(r58777, r58790);
        double r58792 = r58789 / r58791;
        double r58793 = r58787 / r58792;
        double r58794 = r58785 * r58793;
        return r58794;
}

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-inv1.3

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

  6. Final simplification23.2

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

Reproduce

herbie shell --seed 2019297 
(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))