Average Error: 1.9 → 1.2
Time: 14.1s
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 r96144 = x;
        double r96145 = y;
        double r96146 = z;
        double r96147 = log(r96146);
        double r96148 = r96145 * r96147;
        double r96149 = t;
        double r96150 = 1.0;
        double r96151 = r96149 - r96150;
        double r96152 = a;
        double r96153 = log(r96152);
        double r96154 = r96151 * r96153;
        double r96155 = r96148 + r96154;
        double r96156 = b;
        double r96157 = r96155 - r96156;
        double r96158 = exp(r96157);
        double r96159 = r96144 * r96158;
        double r96160 = r96159 / r96145;
        return r96160;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r96161 = x;
        double r96162 = 1.0;
        double r96163 = a;
        double r96164 = r96162 / r96163;
        double r96165 = 1.0;
        double r96166 = pow(r96164, r96165);
        double r96167 = y;
        double r96168 = z;
        double r96169 = r96162 / r96168;
        double r96170 = log(r96169);
        double r96171 = r96167 * r96170;
        double r96172 = log(r96164);
        double r96173 = t;
        double r96174 = r96172 * r96173;
        double r96175 = b;
        double r96176 = r96174 + r96175;
        double r96177 = r96171 + r96176;
        double r96178 = exp(r96177);
        double r96179 = r96166 / r96178;
        double r96180 = r96161 * r96179;
        double r96181 = r96180 / r96167;
        return r96181;
}

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 2020049 
(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))