Average Error: 2.0 → 23.3
Time: 31.7s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\frac{x}{y}}{\frac{{\left(\frac{1}{a}\right)}^{t}}{{z}^{y}}} \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{b}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{\frac{x}{y}}{\frac{{\left(\frac{1}{a}\right)}^{t}}{{z}^{y}}} \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{b}}
double f(double x, double y, double z, double t, double a, double b) {
        double r76720 = x;
        double r76721 = y;
        double r76722 = z;
        double r76723 = log(r76722);
        double r76724 = r76721 * r76723;
        double r76725 = t;
        double r76726 = 1.0;
        double r76727 = r76725 - r76726;
        double r76728 = a;
        double r76729 = log(r76728);
        double r76730 = r76727 * r76729;
        double r76731 = r76724 + r76730;
        double r76732 = b;
        double r76733 = r76731 - r76732;
        double r76734 = exp(r76733);
        double r76735 = r76720 * r76734;
        double r76736 = r76735 / r76721;
        return r76736;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r76737 = x;
        double r76738 = y;
        double r76739 = r76737 / r76738;
        double r76740 = 1.0;
        double r76741 = a;
        double r76742 = r76740 / r76741;
        double r76743 = t;
        double r76744 = pow(r76742, r76743);
        double r76745 = z;
        double r76746 = pow(r76745, r76738);
        double r76747 = r76744 / r76746;
        double r76748 = r76739 / r76747;
        double r76749 = 1.0;
        double r76750 = pow(r76742, r76749);
        double r76751 = b;
        double r76752 = exp(r76751);
        double r76753 = r76750 / r76752;
        double r76754 = r76748 * r76753;
        return r76754;
}

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 2.0

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

  2. Taylor expanded around inf 2.0

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

  3. Simplified1.3

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

  4. Final simplification23.3

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

Reproduce

herbie shell --seed 2019303 
(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))