Average Error: 1.9 → 1.9
Time: 52.9s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\left(\sqrt[3]{\frac{\left(\sqrt{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}}\right) \cdot x}{y}} \cdot \sqrt[3]{\frac{{e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot x}{y}}\right) \cdot \sqrt[3]{\frac{{e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot x}{y}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\left(\sqrt[3]{\frac{\left(\sqrt{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}}\right) \cdot x}{y}} \cdot \sqrt[3]{\frac{{e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot x}{y}}\right) \cdot \sqrt[3]{\frac{{e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot x}{y}}
double f(double x, double y, double z, double t, double a, double b) {
        double r3661129 = x;
        double r3661130 = y;
        double r3661131 = z;
        double r3661132 = log(r3661131);
        double r3661133 = r3661130 * r3661132;
        double r3661134 = t;
        double r3661135 = 1.0;
        double r3661136 = r3661134 - r3661135;
        double r3661137 = a;
        double r3661138 = log(r3661137);
        double r3661139 = r3661136 * r3661138;
        double r3661140 = r3661133 + r3661139;
        double r3661141 = b;
        double r3661142 = r3661140 - r3661141;
        double r3661143 = exp(r3661142);
        double r3661144 = r3661129 * r3661143;
        double r3661145 = r3661144 / r3661130;
        return r3661145;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3661146 = z;
        double r3661147 = log(r3661146);
        double r3661148 = y;
        double r3661149 = r3661147 * r3661148;
        double r3661150 = t;
        double r3661151 = 1.0;
        double r3661152 = r3661150 - r3661151;
        double r3661153 = a;
        double r3661154 = log(r3661153);
        double r3661155 = r3661152 * r3661154;
        double r3661156 = r3661149 + r3661155;
        double r3661157 = b;
        double r3661158 = r3661156 - r3661157;
        double r3661159 = exp(r3661158);
        double r3661160 = sqrt(r3661159);
        double r3661161 = r3661160 * r3661160;
        double r3661162 = x;
        double r3661163 = r3661161 * r3661162;
        double r3661164 = r3661163 / r3661148;
        double r3661165 = cbrt(r3661164);
        double r3661166 = exp(1.0);
        double r3661167 = pow(r3661166, r3661158);
        double r3661168 = r3661167 * r3661162;
        double r3661169 = r3661168 / r3661148;
        double r3661170 = cbrt(r3661169);
        double r3661171 = r3661165 * r3661170;
        double r3661172 = r3661171 * r3661170;
        return r3661172;
}

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 *-un-lft-identity1.9

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

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

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

  5. Applied distribute-lft-out--1.9

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

  6. Applied exp-prod1.9

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

  7. Simplified1.9

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

  9. Applied add-cube-cbrt1.9

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

  11. Applied e-exp-11.9

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

  12. Applied pow-exp1.9

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

  14. Applied add-sqr-sqrt1.9

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

  15. Final simplification1.9

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

Reproduce

herbie shell --seed 2019135 
(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))