Average Error: 2.0 → 1.0
Time: 40.4s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(\log z \cdot y + \left(t - 1\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{{e}^{\left(\left(\log z \cdot y + \left(t - 1\right) \cdot \log a\right) - b\right)}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \sqrt[3]{\sqrt[3]{y}}}{\sqrt[3]{e^{\left(\log z \cdot y + \left(t - 1\right) \cdot \log a\right) - b}}}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(\log z \cdot y + \left(t - 1\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{{e}^{\left(\left(\log z \cdot y + \left(t - 1\right) \cdot \log a\right) - b\right)}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \sqrt[3]{\sqrt[3]{y}}}{\sqrt[3]{e^{\left(\log z \cdot y + \left(t - 1\right) \cdot \log a\right) - b}}}}
double f(double x, double y, double z, double t, double a, double b) {
        double r3147270 = x;
        double r3147271 = y;
        double r3147272 = z;
        double r3147273 = log(r3147272);
        double r3147274 = r3147271 * r3147273;
        double r3147275 = t;
        double r3147276 = 1.0;
        double r3147277 = r3147275 - r3147276;
        double r3147278 = a;
        double r3147279 = log(r3147278);
        double r3147280 = r3147277 * r3147279;
        double r3147281 = r3147274 + r3147280;
        double r3147282 = b;
        double r3147283 = r3147281 - r3147282;
        double r3147284 = exp(r3147283);
        double r3147285 = r3147270 * r3147284;
        double r3147286 = r3147285 / r3147271;
        return r3147286;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3147287 = x;
        double r3147288 = cbrt(r3147287);
        double r3147289 = r3147288 * r3147288;
        double r3147290 = y;
        double r3147291 = cbrt(r3147290);
        double r3147292 = r3147291 * r3147291;
        double r3147293 = z;
        double r3147294 = log(r3147293);
        double r3147295 = r3147294 * r3147290;
        double r3147296 = t;
        double r3147297 = 1.0;
        double r3147298 = r3147296 - r3147297;
        double r3147299 = a;
        double r3147300 = log(r3147299);
        double r3147301 = r3147298 * r3147300;
        double r3147302 = r3147295 + r3147301;
        double r3147303 = b;
        double r3147304 = r3147302 - r3147303;
        double r3147305 = exp(r3147304);
        double r3147306 = cbrt(r3147305);
        double r3147307 = exp(1.0);
        double r3147308 = pow(r3147307, r3147304);
        double r3147309 = cbrt(r3147308);
        double r3147310 = r3147306 * r3147309;
        double r3147311 = r3147292 / r3147310;
        double r3147312 = r3147289 / r3147311;
        double r3147313 = cbrt(r3147291);
        double r3147314 = r3147313 * r3147313;
        double r3147315 = r3147314 * r3147313;
        double r3147316 = r3147315 / r3147306;
        double r3147317 = r3147288 / r3147316;
        double r3147318 = r3147312 * r3147317;
        return r3147318;
}

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. Using strategy rm

  3. Applied associate-/l*1.9

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

  5. Applied add-cube-cbrt2.0

    \[\leadsto \frac{x}{\frac{y}{\color{blue}{\left(\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}\right) \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}}}\]

  6. Applied add-cube-cbrt2.0

    \[\leadsto \frac{x}{\frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\left(\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}\right) \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}}\]

  7. Applied times-frac2.0

    \[\leadsto \frac{x}{\color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}}}\]

  8. Applied add-cube-cbrt2.0

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}}\]

  9. Applied times-frac1.0

    \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}}}\]
  10. Using strategy rm

  11. Applied add-cube-cbrt1.0

    \[\leadsto \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\color{blue}{\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \sqrt[3]{\sqrt[3]{y}}}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}}\]
  12. Using strategy rm

  13. Applied *-un-lft-identity1.0

    \[\leadsto \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\color{blue}{1 \cdot \left(\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b\right)}}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \sqrt[3]{\sqrt[3]{y}}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}}\]

  14. Applied exp-prod1.0

    \[\leadsto \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{\color{blue}{{\left(e^{1}\right)}^{\left(\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b\right)}}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \sqrt[3]{\sqrt[3]{y}}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}}\]

  15. Simplified1.0

    \[\leadsto \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{{\color{blue}{e}}^{\left(\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b\right)}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \sqrt[3]{\sqrt[3]{y}}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}}\]

  16. Final simplification1.0

    \[\leadsto \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(\log z \cdot y + \left(t - 1\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{{e}^{\left(\left(\log z \cdot y + \left(t - 1\right) \cdot \log a\right) - b\right)}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \sqrt[3]{\sqrt[3]{y}}}{\sqrt[3]{e^{\left(\log z \cdot y + \left(t - 1\right) \cdot \log a\right) - b}}}}\]

Reproduce

herbie shell --seed 2019179 
(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))