Average Error: 1.8 → 1.8
Time: 44.7s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}}\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)}}{y}} \cdot \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)
double f(double x, double y, double z, double t, double a, double b) {
        double r4633114 = x;
        double r4633115 = y;
        double r4633116 = z;
        double r4633117 = log(r4633116);
        double r4633118 = r4633115 * r4633117;
        double r4633119 = t;
        double r4633120 = 1.0;
        double r4633121 = r4633119 - r4633120;
        double r4633122 = a;
        double r4633123 = log(r4633122);
        double r4633124 = r4633121 * r4633123;
        double r4633125 = r4633118 + r4633124;
        double r4633126 = b;
        double r4633127 = r4633125 - r4633126;
        double r4633128 = exp(r4633127);
        double r4633129 = r4633114 * r4633128;
        double r4633130 = r4633129 / r4633115;
        return r4633130;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r4633131 = x;
        double r4633132 = exp(1.0);
        double r4633133 = a;
        double r4633134 = log(r4633133);
        double r4633135 = t;
        double r4633136 = 1.0;
        double r4633137 = r4633135 - r4633136;
        double r4633138 = r4633134 * r4633137;
        double r4633139 = z;
        double r4633140 = log(r4633139);
        double r4633141 = y;
        double r4633142 = r4633140 * r4633141;
        double r4633143 = r4633138 + r4633142;
        double r4633144 = b;
        double r4633145 = r4633143 - r4633144;
        double r4633146 = pow(r4633132, r4633145);
        double r4633147 = r4633131 * r4633146;
        double r4633148 = r4633147 / r4633141;
        double r4633149 = cbrt(r4633148);
        double r4633150 = exp(r4633145);
        double r4633151 = r4633131 * r4633150;
        double r4633152 = r4633151 / r4633141;
        double r4633153 = cbrt(r4633152);
        double r4633154 = r4633153 * r4633153;
        double r4633155 = r4633149 * r4633154;
        return r4633155;
}

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 1.8

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

  3. Applied add-cube-cbrt1.8

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

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

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

  6. Applied exp-prod1.8

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

  7. Simplified1.8

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

  8. Final simplification1.8

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

Reproduce

herbie shell --seed 2019163 
(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))