Average Error: 1.8 → 0.2
Time: 41.6s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 7.594113741130119 \cdot 10^{+110}:\\ \;\;\;\;\frac{{k}^{m}}{\frac{k \cdot \left(10 + k\right) + 1}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(99 \cdot e^{m \cdot \log k}\right) \cdot a}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} + \frac{e^{m \cdot \log k} \cdot \frac{a}{k} - \left(e^{m \cdot \log k} \cdot \frac{a}{k}\right) \cdot \frac{10}{k}}{k}\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 7.594113741130119 \cdot 10^{+110}:\\
\;\;\;\;\frac{{k}^{m}}{\frac{k \cdot \left(10 + k\right) + 1}{a}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(99 \cdot e^{m \cdot \log k}\right) \cdot a}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} + \frac{e^{m \cdot \log k} \cdot \frac{a}{k} - \left(e^{m \cdot \log k} \cdot \frac{a}{k}\right) \cdot \frac{10}{k}}{k}\\

\end{array}
double f(double a, double k, double m) {
        double r9863600 = a;
        double r9863601 = k;
        double r9863602 = m;
        double r9863603 = pow(r9863601, r9863602);
        double r9863604 = r9863600 * r9863603;
        double r9863605 = 1.0;
        double r9863606 = 10.0;
        double r9863607 = r9863606 * r9863601;
        double r9863608 = r9863605 + r9863607;
        double r9863609 = r9863601 * r9863601;
        double r9863610 = r9863608 + r9863609;
        double r9863611 = r9863604 / r9863610;
        return r9863611;
}
↓
double f(double a, double k, double m) {
        double r9863612 = k;
        double r9863613 = 7.594113741130119e+110;
        bool r9863614 = r9863612 <= r9863613;
        double r9863615 = m;
        double r9863616 = pow(r9863612, r9863615);
        double r9863617 = 10.0;
        double r9863618 = r9863617 + r9863612;
        double r9863619 = r9863612 * r9863618;
        double r9863620 = 1.0;
        double r9863621 = r9863619 + r9863620;
        double r9863622 = a;
        double r9863623 = r9863621 / r9863622;
        double r9863624 = r9863616 / r9863623;
        double r9863625 = 99.0;
        double r9863626 = log(r9863612);
        double r9863627 = r9863615 * r9863626;
        double r9863628 = exp(r9863627);
        double r9863629 = r9863625 * r9863628;
        double r9863630 = r9863629 * r9863622;
        double r9863631 = r9863612 * r9863612;
        double r9863632 = r9863631 * r9863631;
        double r9863633 = r9863630 / r9863632;
        double r9863634 = r9863622 / r9863612;
        double r9863635 = r9863628 * r9863634;
        double r9863636 = r9863617 / r9863612;
        double r9863637 = r9863635 * r9863636;
        double r9863638 = r9863635 - r9863637;
        double r9863639 = r9863638 / r9863612;
        double r9863640 = r9863633 + r9863639;
        double r9863641 = r9863614 ? r9863624 : r9863640;
        return r9863641;
}

Error

Bits error versus a

Bits error versus k

Bits error versus m

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if k < 7.594113741130119e+110

    1. Initial program 0.1

      \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

    2. Simplified0.0

      \[\leadsto \color{blue}{\frac{{k}^{m} \cdot a}{k \cdot \left(k + 10\right) + 1}}\]
    3. Using strategy rm

    4. Applied associate-/l*0.2

      \[\leadsto \color{blue}{\frac{{k}^{m}}{\frac{k \cdot \left(k + 10\right) + 1}{a}}}\]

    if 7.594113741130119e+110 < k

    1. Initial program 7.3

      \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

    2. Simplified7.3

      \[\leadsto \color{blue}{\frac{{k}^{m} \cdot a}{k \cdot \left(k + 10\right) + 1}}\]
    3. Using strategy rm

    4. Applied flip3-+63.0

      \[\leadsto \frac{{k}^{m} \cdot a}{\color{blue}{\frac{{\left(k \cdot \left(k + 10\right)\right)}^{3} + {1}^{3}}{\left(k \cdot \left(k + 10\right)\right) \cdot \left(k \cdot \left(k + 10\right)\right) + \left(1 \cdot 1 - \left(k \cdot \left(k + 10\right)\right) \cdot 1\right)}}}\]

    5. Applied associate-/r/63.0

      \[\leadsto \color{blue}{\frac{{k}^{m} \cdot a}{{\left(k \cdot \left(k + 10\right)\right)}^{3} + {1}^{3}} \cdot \left(\left(k \cdot \left(k + 10\right)\right) \cdot \left(k \cdot \left(k + 10\right)\right) + \left(1 \cdot 1 - \left(k \cdot \left(k + 10\right)\right) \cdot 1\right)\right)}\]

    6. Simplified63.0

      \[\leadsto \color{blue}{\frac{{k}^{m} \cdot a}{\left(\left(k \cdot \left(k + 10\right)\right) \cdot \left(k \cdot \left(k + 10\right)\right)\right) \cdot \left(k \cdot \left(k + 10\right)\right) + 1}} \cdot \left(\left(k \cdot \left(k + 10\right)\right) \cdot \left(k \cdot \left(k + 10\right)\right) + \left(1 \cdot 1 - \left(k \cdot \left(k + 10\right)\right) \cdot 1\right)\right)\]

    7. Taylor expanded around inf 7.3

      \[\leadsto \color{blue}{\left(99 \cdot \frac{e^{-1 \cdot \left(\log \left(\frac{1}{k}\right) \cdot m\right)} \cdot a}{{k}^{4}} + \frac{e^{-1 \cdot \left(\log \left(\frac{1}{k}\right) \cdot m\right)} \cdot a}{{k}^{2}}\right) - 10 \cdot \frac{e^{-1 \cdot \left(\log \left(\frac{1}{k}\right) \cdot m\right)} \cdot a}{{k}^{3}}}\]

    8. Simplified0.2

      \[\leadsto \color{blue}{\left(\frac{a}{k} \cdot \frac{e^{\left(-m\right) \cdot \left(-\log k\right)}}{k} - \frac{10}{k} \cdot \left(\frac{a}{k} \cdot \frac{e^{\left(-m\right) \cdot \left(-\log k\right)}}{k}\right)\right) + \frac{\left(99 \cdot e^{\left(-m\right) \cdot \left(-\log k\right)}\right) \cdot a}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}}\]
    9. Using strategy rm

    10. Applied associate-*r/0.2

      \[\leadsto \left(\frac{a}{k} \cdot \frac{e^{\left(-m\right) \cdot \left(-\log k\right)}}{k} - \frac{10}{k} \cdot \color{blue}{\frac{\frac{a}{k} \cdot e^{\left(-m\right) \cdot \left(-\log k\right)}}{k}}\right) + \frac{\left(99 \cdot e^{\left(-m\right) \cdot \left(-\log k\right)}\right) \cdot a}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}\]

    11. Applied associate-*r/0.2

      \[\leadsto \left(\frac{a}{k} \cdot \frac{e^{\left(-m\right) \cdot \left(-\log k\right)}}{k} - \color{blue}{\frac{\frac{10}{k} \cdot \left(\frac{a}{k} \cdot e^{\left(-m\right) \cdot \left(-\log k\right)}\right)}{k}}\right) + \frac{\left(99 \cdot e^{\left(-m\right) \cdot \left(-\log k\right)}\right) \cdot a}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}\]

    12. Applied associate-*r/0.2

      \[\leadsto \left(\color{blue}{\frac{\frac{a}{k} \cdot e^{\left(-m\right) \cdot \left(-\log k\right)}}{k}} - \frac{\frac{10}{k} \cdot \left(\frac{a}{k} \cdot e^{\left(-m\right) \cdot \left(-\log k\right)}\right)}{k}\right) + \frac{\left(99 \cdot e^{\left(-m\right) \cdot \left(-\log k\right)}\right) \cdot a}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}\]

    13. Applied sub-div0.2

      \[\leadsto \color{blue}{\frac{\frac{a}{k} \cdot e^{\left(-m\right) \cdot \left(-\log k\right)} - \frac{10}{k} \cdot \left(\frac{a}{k} \cdot e^{\left(-m\right) \cdot \left(-\log k\right)}\right)}{k}} + \frac{\left(99 \cdot e^{\left(-m\right) \cdot \left(-\log k\right)}\right) \cdot a}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 7.594113741130119 \cdot 10^{+110}:\\ \;\;\;\;\frac{{k}^{m}}{\frac{k \cdot \left(10 + k\right) + 1}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(99 \cdot e^{m \cdot \log k}\right) \cdot a}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} + \frac{e^{m \cdot \log k} \cdot \frac{a}{k} - \left(e^{m \cdot \log k} \cdot \frac{a}{k}\right) \cdot \frac{10}{k}}{k}\\ \end{array}\]

Reproduce

herbie shell --seed 2019151 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))