Average Error: 1.9 → 1.2
Time: 15.5s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{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)}}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r86980 = x;
        double r86981 = y;
        double r86982 = z;
        double r86983 = log(r86982);
        double r86984 = r86981 * r86983;
        double r86985 = t;
        double r86986 = 1.0;
        double r86987 = r86985 - r86986;
        double r86988 = a;
        double r86989 = log(r86988);
        double r86990 = r86987 * r86989;
        double r86991 = r86984 + r86990;
        double r86992 = b;
        double r86993 = r86991 - r86992;
        double r86994 = exp(r86993);
        double r86995 = r86980 * r86994;
        double r86996 = r86995 / r86981;
        return r86996;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r86997 = x;
        double r86998 = 1.0;
        double r86999 = a;
        double r87000 = r86998 / r86999;
        double r87001 = 1.0;
        double r87002 = pow(r87000, r87001);
        double r87003 = y;
        double r87004 = z;
        double r87005 = r86998 / r87004;
        double r87006 = log(r87005);
        double r87007 = r87003 * r87006;
        double r87008 = log(r87000);
        double r87009 = t;
        double r87010 = r87008 * r87009;
        double r87011 = b;
        double r87012 = r87010 + r87011;
        double r87013 = r87007 + r87012;
        double r87014 = exp(r87013);
        double r87015 = r87002 / r87014;
        double r87016 = r86997 * r87015;
        double r87017 = r87016 / r87003;
        return r87017;
}

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. Final simplification1.2

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

Reproduce

herbie shell --seed 2020002 
(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))