Average Error: 1.8 → 1.2
Time: 26.2s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\left(\left(x \cdot \frac{\sqrt{{\left(\frac{1}{a}\right)}^{1}}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \frac{\sqrt{{\left(\frac{1}{a}\right)}^{1}}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \frac{1}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\left(\left(x \cdot \frac{\sqrt{{\left(\frac{1}{a}\right)}^{1}}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \frac{\sqrt{{\left(\frac{1}{a}\right)}^{1}}}{\sqrt{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \frac{1}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r248 = x;
        double r249 = y;
        double r250 = z;
        double r251 = log(r250);
        double r252 = r249 * r251;
        double r253 = t;
        double r254 = 1.0;
        double r255 = r253 - r254;
        double r256 = a;
        double r257 = log(r256);
        double r258 = r255 * r257;
        double r259 = r252 + r258;
        double r260 = b;
        double r261 = r259 - r260;
        double r262 = exp(r261);
        double r263 = r248 * r262;
        double r264 = r263 / r249;
        return r264;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r265 = x;
        double r266 = 1.0;
        double r267 = a;
        double r268 = r266 / r267;
        double r269 = 1.0;
        double r270 = pow(r268, r269);
        double r271 = sqrt(r270);
        double r272 = y;
        double r273 = z;
        double r274 = r266 / r273;
        double r275 = log(r274);
        double r276 = r272 * r275;
        double r277 = log(r268);
        double r278 = t;
        double r279 = r277 * r278;
        double r280 = b;
        double r281 = r279 + r280;
        double r282 = r276 + r281;
        double r283 = exp(r282);
        double r284 = sqrt(r283);
        double r285 = r271 / r284;
        double r286 = r265 * r285;
        double r287 = r286 * r285;
        double r288 = r266 / r272;
        double r289 = r287 * r288;
        return r289;
}

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 1.8

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

  2. Taylor expanded around inf 1.8

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

  3. Simplified1.1

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

  5. Applied div-inv1.1

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

  7. Applied add-sqr-sqrt1.1

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

  8. Applied add-sqr-sqrt1.2

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

  9. Applied times-frac1.2

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

  10. Applied associate-*r*1.2

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

  11. Final simplification1.2

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

Reproduce

herbie shell --seed 2020025 
(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))