Average Error: 1.9 → 1.2
Time: 14.9s
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 r76035 = x;
        double r76036 = y;
        double r76037 = z;
        double r76038 = log(r76037);
        double r76039 = r76036 * r76038;
        double r76040 = t;
        double r76041 = 1.0;
        double r76042 = r76040 - r76041;
        double r76043 = a;
        double r76044 = log(r76043);
        double r76045 = r76042 * r76044;
        double r76046 = r76039 + r76045;
        double r76047 = b;
        double r76048 = r76046 - r76047;
        double r76049 = exp(r76048);
        double r76050 = r76035 * r76049;
        double r76051 = r76050 / r76036;
        return r76051;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r76052 = x;
        double r76053 = 1.0;
        double r76054 = a;
        double r76055 = r76053 / r76054;
        double r76056 = 1.0;
        double r76057 = pow(r76055, r76056);
        double r76058 = y;
        double r76059 = z;
        double r76060 = r76053 / r76059;
        double r76061 = log(r76060);
        double r76062 = r76058 * r76061;
        double r76063 = log(r76055);
        double r76064 = t;
        double r76065 = r76063 * r76064;
        double r76066 = b;
        double r76067 = r76065 + r76066;
        double r76068 = r76062 + r76067;
        double r76069 = exp(r76068);
        double r76070 = r76057 / r76069;
        double r76071 = r76052 * r76070;
        double r76072 = r76071 / r76058;
        return r76072;
}

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 2020083 
(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))