Average Error: 2.1 → 0.1
Time: 25.5s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 73317554942727741440:\\ \;\;\;\;\frac{a}{\frac{1 + \left(k + 10\right) \cdot k}{{k}^{m}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k} + \frac{e^{\log k \cdot m}}{\frac{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}{a}} \cdot 99\right) - \frac{10 \cdot e^{\log k \cdot m}}{\frac{k \cdot \left(k \cdot k\right)}{a}}\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 73317554942727741440:\\
\;\;\;\;\frac{a}{\frac{1 + \left(k + 10\right) \cdot k}{{k}^{m}}}\\

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

\end{array}
double f(double a, double k, double m) {
        double r10684690 = a;
        double r10684691 = k;
        double r10684692 = m;
        double r10684693 = pow(r10684691, r10684692);
        double r10684694 = r10684690 * r10684693;
        double r10684695 = 1.0;
        double r10684696 = 10.0;
        double r10684697 = r10684696 * r10684691;
        double r10684698 = r10684695 + r10684697;
        double r10684699 = r10684691 * r10684691;
        double r10684700 = r10684698 + r10684699;
        double r10684701 = r10684694 / r10684700;
        return r10684701;
}
↓
double f(double a, double k, double m) {
        double r10684702 = k;
        double r10684703 = 7.331755494272774e+19;
        bool r10684704 = r10684702 <= r10684703;
        double r10684705 = a;
        double r10684706 = 1.0;
        double r10684707 = 10.0;
        double r10684708 = r10684702 + r10684707;
        double r10684709 = r10684708 * r10684702;
        double r10684710 = r10684706 + r10684709;
        double r10684711 = m;
        double r10684712 = pow(r10684702, r10684711);
        double r10684713 = r10684710 / r10684712;
        double r10684714 = r10684705 / r10684713;
        double r10684715 = r10684705 / r10684702;
        double r10684716 = log(r10684702);
        double r10684717 = r10684716 * r10684711;
        double r10684718 = exp(r10684717);
        double r10684719 = r10684718 / r10684702;
        double r10684720 = r10684715 * r10684719;
        double r10684721 = r10684702 * r10684702;
        double r10684722 = r10684721 * r10684721;
        double r10684723 = r10684722 / r10684705;
        double r10684724 = r10684718 / r10684723;
        double r10684725 = 99.0;
        double r10684726 = r10684724 * r10684725;
        double r10684727 = r10684720 + r10684726;
        double r10684728 = r10684707 * r10684718;
        double r10684729 = r10684702 * r10684721;
        double r10684730 = r10684729 / r10684705;
        double r10684731 = r10684728 / r10684730;
        double r10684732 = r10684727 - r10684731;
        double r10684733 = r10684704 ? r10684714 : r10684732;
        return r10684733;
}

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 < 7.331755494272774e+19

    1. Initial program 0.1

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

    2. Simplified0.0

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

    if 7.331755494272774e+19 < k

    1. Initial program 5.7

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

    2. Simplified5.7

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

    3. Taylor expanded around inf 5.7

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

    4. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 73317554942727741440:\\ \;\;\;\;\frac{a}{\frac{1 + \left(k + 10\right) \cdot k}{{k}^{m}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k} + \frac{e^{\log k \cdot m}}{\frac{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}{a}} \cdot 99\right) - \frac{10 \cdot e^{\log k \cdot m}}{\frac{k \cdot \left(k \cdot k\right)}{a}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))