Average Error: 2.0 → 1.3
Time: 18.3s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot \frac{e^{\log z \cdot y - \left(b - t \cdot \log a\right)}}{{a}^{1}}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{x \cdot \frac{e^{\log z \cdot y - \left(b - t \cdot \log a\right)}}{{a}^{1}}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r88222 = x;
        double r88223 = y;
        double r88224 = z;
        double r88225 = log(r88224);
        double r88226 = r88223 * r88225;
        double r88227 = t;
        double r88228 = 1.0;
        double r88229 = r88227 - r88228;
        double r88230 = a;
        double r88231 = log(r88230);
        double r88232 = r88229 * r88231;
        double r88233 = r88226 + r88232;
        double r88234 = b;
        double r88235 = r88233 - r88234;
        double r88236 = exp(r88235);
        double r88237 = r88222 * r88236;
        double r88238 = r88237 / r88223;
        return r88238;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r88239 = x;
        double r88240 = z;
        double r88241 = log(r88240);
        double r88242 = y;
        double r88243 = r88241 * r88242;
        double r88244 = b;
        double r88245 = t;
        double r88246 = a;
        double r88247 = log(r88246);
        double r88248 = r88245 * r88247;
        double r88249 = r88244 - r88248;
        double r88250 = r88243 - r88249;
        double r88251 = exp(r88250);
        double r88252 = 1.0;
        double r88253 = pow(r88246, r88252);
        double r88254 = r88251 / r88253;
        double r88255 = r88239 * r88254;
        double r88256 = r88255 / r88242;
        return r88256;
}

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

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020047 
(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))