Average Error: 2.2 → 1.4
Time: 35.5s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot \frac{{a}^{\left(-1\right)}}{e^{b + \left(-\left(\log a \cdot t + \log z \cdot y\right)\right)}}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{x \cdot \frac{{a}^{\left(-1\right)}}{e^{b + \left(-\left(\log a \cdot t + \log z \cdot y\right)\right)}}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r67190 = x;
        double r67191 = y;
        double r67192 = z;
        double r67193 = log(r67192);
        double r67194 = r67191 * r67193;
        double r67195 = t;
        double r67196 = 1.0;
        double r67197 = r67195 - r67196;
        double r67198 = a;
        double r67199 = log(r67198);
        double r67200 = r67197 * r67199;
        double r67201 = r67194 + r67200;
        double r67202 = b;
        double r67203 = r67201 - r67202;
        double r67204 = exp(r67203);
        double r67205 = r67190 * r67204;
        double r67206 = r67205 / r67191;
        return r67206;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r67207 = x;
        double r67208 = a;
        double r67209 = 1.0;
        double r67210 = -r67209;
        double r67211 = pow(r67208, r67210);
        double r67212 = b;
        double r67213 = log(r67208);
        double r67214 = t;
        double r67215 = r67213 * r67214;
        double r67216 = z;
        double r67217 = log(r67216);
        double r67218 = y;
        double r67219 = r67217 * r67218;
        double r67220 = r67215 + r67219;
        double r67221 = -r67220;
        double r67222 = r67212 + r67221;
        double r67223 = exp(r67222);
        double r67224 = r67211 / r67223;
        double r67225 = r67207 * r67224;
        double r67226 = r67225 / r67218;
        return r67226;
}

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 2.2

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

  2. Taylor expanded around inf 2.2

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

  3. Simplified1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019208 
(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))