Average Error: 1.9 → 1.9
Time: 49.8s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\sqrt[3]{\left(x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right) \cdot \frac{1}{y}} \cdot \left(\sqrt[3]{\left(x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right) \cdot \frac{1}{y}} \cdot \sqrt[3]{\left(x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right) \cdot \frac{1}{y}}\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\sqrt[3]{\left(x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right) \cdot \frac{1}{y}} \cdot \left(\sqrt[3]{\left(x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right) \cdot \frac{1}{y}} \cdot \sqrt[3]{\left(x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right) \cdot \frac{1}{y}}\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r2600287 = x;
        double r2600288 = y;
        double r2600289 = z;
        double r2600290 = log(r2600289);
        double r2600291 = r2600288 * r2600290;
        double r2600292 = t;
        double r2600293 = 1.0;
        double r2600294 = r2600292 - r2600293;
        double r2600295 = a;
        double r2600296 = log(r2600295);
        double r2600297 = r2600294 * r2600296;
        double r2600298 = r2600291 + r2600297;
        double r2600299 = b;
        double r2600300 = r2600298 - r2600299;
        double r2600301 = exp(r2600300);
        double r2600302 = r2600287 * r2600301;
        double r2600303 = r2600302 / r2600288;
        return r2600303;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r2600304 = x;
        double r2600305 = a;
        double r2600306 = log(r2600305);
        double r2600307 = t;
        double r2600308 = 1.0;
        double r2600309 = r2600307 - r2600308;
        double r2600310 = r2600306 * r2600309;
        double r2600311 = z;
        double r2600312 = log(r2600311);
        double r2600313 = y;
        double r2600314 = r2600312 * r2600313;
        double r2600315 = r2600310 + r2600314;
        double r2600316 = b;
        double r2600317 = r2600315 - r2600316;
        double r2600318 = exp(r2600317);
        double r2600319 = r2600304 * r2600318;
        double r2600320 = 1.0;
        double r2600321 = r2600320 / r2600313;
        double r2600322 = r2600319 * r2600321;
        double r2600323 = cbrt(r2600322);
        double r2600324 = r2600323 * r2600323;
        double r2600325 = r2600323 * r2600324;
        return r2600325;
}

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 div-inv1.9

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

  5. Applied add-cube-cbrt1.9

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

  6. Final simplification1.9

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

Reproduce

herbie shell --seed 2019132 +o rules:numerics
(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))