Average Error: 1.9 → 1.3
Time: 2.3m
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}} \cdot \sqrt[3]{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}}{\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}} \cdot \frac{x \cdot \left(\sqrt[3]{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}} \cdot \sqrt[3]{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}\right)}{\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)}\right)\]
\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]{y}} \cdot \left(\frac{\sqrt[3]{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}} \cdot \sqrt[3]{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}}{\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}} \cdot \frac{x \cdot \left(\sqrt[3]{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}} \cdot \sqrt[3]{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}\right)}{\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)}\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r5021263 = x;
        double r5021264 = y;
        double r5021265 = z;
        double r5021266 = log(r5021265);
        double r5021267 = r5021264 * r5021266;
        double r5021268 = t;
        double r5021269 = 1.0;
        double r5021270 = r5021268 - r5021269;
        double r5021271 = a;
        double r5021272 = log(r5021271);
        double r5021273 = r5021270 * r5021272;
        double r5021274 = r5021267 + r5021273;
        double r5021275 = b;
        double r5021276 = r5021274 - r5021275;
        double r5021277 = exp(r5021276);
        double r5021278 = r5021263 * r5021277;
        double r5021279 = r5021278 / r5021264;
        return r5021279;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r5021280 = a;
        double r5021281 = log(r5021280);
        double r5021282 = t;
        double r5021283 = 1.0;
        double r5021284 = r5021282 - r5021283;
        double r5021285 = r5021281 * r5021284;
        double r5021286 = z;
        double r5021287 = log(r5021286);
        double r5021288 = y;
        double r5021289 = r5021287 * r5021288;
        double r5021290 = r5021285 + r5021289;
        double r5021291 = b;
        double r5021292 = r5021290 - r5021291;
        double r5021293 = exp(r5021292);
        double r5021294 = cbrt(r5021293);
        double r5021295 = cbrt(r5021288);
        double r5021296 = r5021294 / r5021295;
        double r5021297 = sqrt(r5021293);
        double r5021298 = cbrt(r5021297);
        double r5021299 = r5021298 * r5021298;
        double r5021300 = cbrt(r5021295);
        double r5021301 = r5021300 * r5021300;
        double r5021302 = r5021299 / r5021301;
        double r5021303 = x;
        double r5021304 = r5021303 * r5021299;
        double r5021305 = r5021301 * r5021301;
        double r5021306 = r5021304 / r5021305;
        double r5021307 = r5021302 * r5021306;
        double r5021308 = r5021296 * r5021307;
        return r5021308;
}

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 add-cube-cbrt1.9

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

  4. Applied add-cube-cbrt1.9

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

  5. Applied associate-*r*1.9

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

  6. Applied times-frac1.5

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

  8. Applied add-cube-cbrt1.5

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

  9. Applied add-cube-cbrt1.5

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

  10. Applied swap-sqr1.5

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

  11. Applied add-sqr-sqrt1.5

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

  12. Applied cbrt-prod1.5

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

  13. Applied add-sqr-sqrt1.5

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

  14. Applied cbrt-prod1.5

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

  15. Applied swap-sqr1.5

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

  16. Applied associate-*r*1.5

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

  17. Applied times-frac1.3

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

  18. Final simplification1.3

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

Reproduce

herbie shell --seed 2019158 
(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))