Average Error: 2.0 → 1.1
Time: 40.4s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{1}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}}} \cdot \frac{x}{\frac{\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{{e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{1}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}}} \cdot \frac{x}{\frac{\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{{e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}}}
double f(double x, double y, double z, double t, double a, double b) {
        double r3168118 = x;
        double r3168119 = y;
        double r3168120 = z;
        double r3168121 = log(r3168120);
        double r3168122 = r3168119 * r3168121;
        double r3168123 = t;
        double r3168124 = 1.0;
        double r3168125 = r3168123 - r3168124;
        double r3168126 = a;
        double r3168127 = log(r3168126);
        double r3168128 = r3168125 * r3168127;
        double r3168129 = r3168122 + r3168128;
        double r3168130 = b;
        double r3168131 = r3168129 - r3168130;
        double r3168132 = exp(r3168131);
        double r3168133 = r3168118 * r3168132;
        double r3168134 = r3168133 / r3168119;
        return r3168134;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3168135 = 1.0;
        double r3168136 = y;
        double r3168137 = cbrt(r3168136);
        double r3168138 = r3168137 * r3168137;
        double r3168139 = a;
        double r3168140 = log(r3168139);
        double r3168141 = t;
        double r3168142 = 1.0;
        double r3168143 = r3168141 - r3168142;
        double r3168144 = r3168140 * r3168143;
        double r3168145 = z;
        double r3168146 = log(r3168145);
        double r3168147 = r3168146 * r3168136;
        double r3168148 = r3168144 + r3168147;
        double r3168149 = b;
        double r3168150 = r3168148 - r3168149;
        double r3168151 = exp(r3168150);
        double r3168152 = cbrt(r3168151);
        double r3168153 = r3168152 * r3168152;
        double r3168154 = r3168138 / r3168153;
        double r3168155 = r3168135 / r3168154;
        double r3168156 = x;
        double r3168157 = cbrt(r3168137);
        double r3168158 = cbrt(r3168138);
        double r3168159 = r3168157 * r3168158;
        double r3168160 = exp(1.0);
        double r3168161 = pow(r3168160, r3168150);
        double r3168162 = cbrt(r3168161);
        double r3168163 = r3168159 / r3168162;
        double r3168164 = r3168156 / r3168163;
        double r3168165 = r3168155 * r3168164;
        return r3168165;
}

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

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

  3. Applied associate-/l*1.9

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

  5. Applied add-cube-cbrt1.9

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

  6. Applied add-cube-cbrt1.9

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

  7. Applied times-frac1.9

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

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

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

  9. Applied times-frac1.1

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

  11. Applied *-un-lft-identity1.1

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

  12. Applied exp-prod1.1

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

  13. Simplified1.1

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

  15. Applied add-cube-cbrt1.1

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

  16. Applied cbrt-prod1.1

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

  17. Final simplification1.1

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

Reproduce

herbie shell --seed 2019171 
(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))