Average Error: 2.1 → 1.5
Time: 20.3s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\left(\sqrt[3]{\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}} \cdot \sqrt[3]{\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\left(\sqrt[3]{\frac{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)}}}{y}} \cdot \sqrt[3]{\frac{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)}}}{y}}\right) \cdot \sqrt[3]{\frac{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)}}}{y}}
double f(double x, double y, double z, double t, double a, double b) {
        double r119296 = x;
        double r119297 = y;
        double r119298 = z;
        double r119299 = log(r119298);
        double r119300 = r119297 * r119299;
        double r119301 = t;
        double r119302 = 1.0;
        double r119303 = r119301 - r119302;
        double r119304 = a;
        double r119305 = log(r119304);
        double r119306 = r119303 * r119305;
        double r119307 = r119300 + r119306;
        double r119308 = b;
        double r119309 = r119307 - r119308;
        double r119310 = exp(r119309);
        double r119311 = r119296 * r119310;
        double r119312 = r119311 / r119297;
        return r119312;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r119313 = x;
        double r119314 = 1.0;
        double r119315 = a;
        double r119316 = r119314 / r119315;
        double r119317 = 1.0;
        double r119318 = pow(r119316, r119317);
        double r119319 = y;
        double r119320 = z;
        double r119321 = r119314 / r119320;
        double r119322 = log(r119321);
        double r119323 = r119319 * r119322;
        double r119324 = log(r119316);
        double r119325 = t;
        double r119326 = r119324 * r119325;
        double r119327 = b;
        double r119328 = r119326 + r119327;
        double r119329 = r119323 + r119328;
        double r119330 = exp(r119329);
        double r119331 = r119318 / r119330;
        double r119332 = r119313 * r119331;
        double r119333 = r119332 / r119319;
        double r119334 = cbrt(r119333);
        double r119335 = r119334 * r119334;
        double r119336 = r119335 * r119334;
        return r119336;
}

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 2.1

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

  2. Taylor expanded around inf 2.1

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

  3. Simplified1.4

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

  5. Applied add-cube-cbrt1.5

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

  6. Final simplification1.5

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

Reproduce

herbie shell --seed 2019318 
(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))