Average Error: 2.0 → 1.0
Time: 37.2s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x}{\frac{\sqrt[3]{y}}{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}} \cdot \frac{1}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{x}{\frac{\sqrt[3]{y}}{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}} \cdot \frac{1}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\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}}}}
double f(double x, double y, double z, double t, double a, double b) {
        double r1219288 = x;
        double r1219289 = y;
        double r1219290 = z;
        double r1219291 = log(r1219290);
        double r1219292 = r1219289 * r1219291;
        double r1219293 = t;
        double r1219294 = 1.0;
        double r1219295 = r1219293 - r1219294;
        double r1219296 = a;
        double r1219297 = log(r1219296);
        double r1219298 = r1219295 * r1219297;
        double r1219299 = r1219292 + r1219298;
        double r1219300 = b;
        double r1219301 = r1219299 - r1219300;
        double r1219302 = exp(r1219301);
        double r1219303 = r1219288 * r1219302;
        double r1219304 = r1219303 / r1219289;
        return r1219304;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1219305 = x;
        double r1219306 = y;
        double r1219307 = cbrt(r1219306);
        double r1219308 = a;
        double r1219309 = log(r1219308);
        double r1219310 = t;
        double r1219311 = 1.0;
        double r1219312 = r1219310 - r1219311;
        double r1219313 = r1219309 * r1219312;
        double r1219314 = z;
        double r1219315 = log(r1219314);
        double r1219316 = r1219315 * r1219306;
        double r1219317 = r1219313 + r1219316;
        double r1219318 = b;
        double r1219319 = r1219317 - r1219318;
        double r1219320 = exp(r1219319);
        double r1219321 = cbrt(r1219320);
        double r1219322 = r1219307 / r1219321;
        double r1219323 = r1219305 / r1219322;
        double r1219324 = 1.0;
        double r1219325 = r1219307 * r1219307;
        double r1219326 = r1219321 * r1219321;
        double r1219327 = r1219325 / r1219326;
        double r1219328 = r1219324 / r1219327;
        double r1219329 = r1219323 * r1219328;
        return r1219329;
}

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

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

  3. Applied associate-/l*1.9

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

  5. Applied add-cube-cbrt1.9

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

  6. Applied add-cube-cbrt1.9

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

  7. Applied times-frac1.9

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

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

    \[\leadsto \frac{\color{blue}{1 \cdot x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}}\]

  9. Applied times-frac1.0

    \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}} \cdot \frac{x}{\frac{\sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}}}}\]

  10. Final simplification1.0

    \[\leadsto \frac{x}{\frac{\sqrt[3]{y}}{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}} \cdot \frac{1}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}}}\]

Reproduce

herbie shell --seed 2019153 
(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))