Average Error: 1.9 → 1.1
Time: 1.8m
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)} \cdot \left(x \cdot \frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)} \cdot \left(x \cdot \frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r15119323 = x;
        double r15119324 = y;
        double r15119325 = z;
        double r15119326 = log(r15119325);
        double r15119327 = r15119324 * r15119326;
        double r15119328 = t;
        double r15119329 = 1.0;
        double r15119330 = r15119328 - r15119329;
        double r15119331 = a;
        double r15119332 = log(r15119331);
        double r15119333 = r15119330 * r15119332;
        double r15119334 = r15119327 + r15119333;
        double r15119335 = b;
        double r15119336 = r15119334 - r15119335;
        double r15119337 = exp(r15119336);
        double r15119338 = r15119323 * r15119337;
        double r15119339 = r15119338 / r15119324;
        return r15119339;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r15119340 = a;
        double r15119341 = log(r15119340);
        double r15119342 = t;
        double r15119343 = 1.0;
        double r15119344 = r15119342 - r15119343;
        double r15119345 = r15119341 * r15119344;
        double r15119346 = z;
        double r15119347 = log(r15119346);
        double r15119348 = y;
        double r15119349 = r15119347 * r15119348;
        double r15119350 = r15119345 + r15119349;
        double r15119351 = b;
        double r15119352 = r15119350 - r15119351;
        double r15119353 = exp(r15119352);
        double r15119354 = cbrt(r15119353);
        double r15119355 = cbrt(r15119348);
        double r15119356 = cbrt(r15119355);
        double r15119357 = r15119356 * r15119356;
        double r15119358 = r15119356 * r15119357;
        double r15119359 = r15119354 / r15119358;
        double r15119360 = x;
        double r15119361 = r15119354 * r15119354;
        double r15119362 = r15119355 * r15119355;
        double r15119363 = r15119361 / r15119362;
        double r15119364 = r15119360 * r15119363;
        double r15119365 = r15119359 * r15119364;
        return r15119365;
}

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

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity1.9

    \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{\color{blue}{1 \cdot y}}\]

  4. Applied times-frac2.2

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\]

  5. Simplified2.2

    \[\leadsto \color{blue}{x} \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt2.2

    \[\leadsto x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}\]

  8. Applied add-cube-cbrt2.2

    \[\leadsto x \cdot \frac{\color{blue}{\left(\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right) \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}\]

  9. Applied times-frac2.2

    \[\leadsto x \cdot \color{blue}{\left(\frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}{\sqrt[3]{y}}\right)}\]

  10. Applied associate-*r*1.1

    \[\leadsto \color{blue}{\left(x \cdot \frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}{\sqrt[3]{y}}}\]
  11. Using strategy rm

  12. Applied add-cube-cbrt1.1

    \[\leadsto \left(x \cdot \frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}{\color{blue}{\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \sqrt[3]{\sqrt[3]{y}}}}\]

  13. Final simplification1.1

    \[\leadsto \frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)} \cdot \left(x \cdot \frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)\]

Reproduce

herbie shell --seed 2019125 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))