Average Error: 1.9 → 1.9
Time: 46.8s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}}
double f(double x, double y, double z, double t, double a, double b) {
        double r3192295 = x;
        double r3192296 = y;
        double r3192297 = z;
        double r3192298 = log(r3192297);
        double r3192299 = r3192296 * r3192298;
        double r3192300 = t;
        double r3192301 = 1.0;
        double r3192302 = r3192300 - r3192301;
        double r3192303 = a;
        double r3192304 = log(r3192303);
        double r3192305 = r3192302 * r3192304;
        double r3192306 = r3192299 + r3192305;
        double r3192307 = b;
        double r3192308 = r3192306 - r3192307;
        double r3192309 = exp(r3192308);
        double r3192310 = r3192295 * r3192309;
        double r3192311 = r3192310 / r3192296;
        return r3192311;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3192312 = x;
        double r3192313 = a;
        double r3192314 = log(r3192313);
        double r3192315 = t;
        double r3192316 = 1.0;
        double r3192317 = r3192315 - r3192316;
        double r3192318 = r3192314 * r3192317;
        double r3192319 = z;
        double r3192320 = log(r3192319);
        double r3192321 = y;
        double r3192322 = r3192320 * r3192321;
        double r3192323 = r3192318 + r3192322;
        double r3192324 = b;
        double r3192325 = r3192323 - r3192324;
        double r3192326 = exp(r3192325);
        double r3192327 = r3192312 * r3192326;
        double r3192328 = r3192327 / r3192321;
        double r3192329 = cbrt(r3192328);
        double r3192330 = r3192329 * r3192329;
        double r3192331 = r3192330 * r3192329;
        return r3192331;
}

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

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

  5. Applied add-log-exp1.9

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

  6. Applied rem-exp-log1.9

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

  7. Final simplification1.9

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

Reproduce

herbie shell --seed 2019132 
(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))