Average Error: 2.0 → 0.1
Time: 18.2s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 1.3655055884626073 \cdot 10^{+132}:\\ \;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{e^{m \cdot \log k}}{\frac{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}{a}} \cdot 99 + -10 \cdot \left(\frac{e^{m \cdot \log k}}{k \cdot k} \cdot \frac{a}{k}\right)\right) + \frac{a}{k} \cdot \frac{e^{m \cdot \log k}}{k}\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 1.3655055884626073 \cdot 10^{+132}:\\
\;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\

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

\end{array}
double f(double a, double k, double m) {
        double r3500667 = a;
        double r3500668 = k;
        double r3500669 = m;
        double r3500670 = pow(r3500668, r3500669);
        double r3500671 = r3500667 * r3500670;
        double r3500672 = 1.0;
        double r3500673 = 10.0;
        double r3500674 = r3500673 * r3500668;
        double r3500675 = r3500672 + r3500674;
        double r3500676 = r3500668 * r3500668;
        double r3500677 = r3500675 + r3500676;
        double r3500678 = r3500671 / r3500677;
        return r3500678;
}
↓
double f(double a, double k, double m) {
        double r3500679 = k;
        double r3500680 = 1.3655055884626073e+132;
        bool r3500681 = r3500679 <= r3500680;
        double r3500682 = m;
        double r3500683 = pow(r3500679, r3500682);
        double r3500684 = a;
        double r3500685 = r3500683 * r3500684;
        double r3500686 = 1.0;
        double r3500687 = 10.0;
        double r3500688 = r3500679 + r3500687;
        double r3500689 = r3500679 * r3500688;
        double r3500690 = r3500686 + r3500689;
        double r3500691 = r3500685 / r3500690;
        double r3500692 = log(r3500679);
        double r3500693 = r3500682 * r3500692;
        double r3500694 = exp(r3500693);
        double r3500695 = r3500679 * r3500679;
        double r3500696 = r3500695 * r3500695;
        double r3500697 = r3500696 / r3500684;
        double r3500698 = r3500694 / r3500697;
        double r3500699 = 99.0;
        double r3500700 = r3500698 * r3500699;
        double r3500701 = -10.0;
        double r3500702 = r3500694 / r3500695;
        double r3500703 = r3500684 / r3500679;
        double r3500704 = r3500702 * r3500703;
        double r3500705 = r3500701 * r3500704;
        double r3500706 = r3500700 + r3500705;
        double r3500707 = r3500694 / r3500679;
        double r3500708 = r3500703 * r3500707;
        double r3500709 = r3500706 + r3500708;
        double r3500710 = r3500681 ? r3500691 : r3500709;
        return r3500710;
}

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 < 1.3655055884626073e+132

    1. Initial program 0.1

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

    2. Simplified0.1

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

    if 1.3655055884626073e+132 < k

    1. Initial program 8.7

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

    2. Simplified8.7

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

    3. Taylor expanded around inf 8.7

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

    4. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 1.3655055884626073 \cdot 10^{+132}:\\ \;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{e^{m \cdot \log k}}{\frac{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}{a}} \cdot 99 + -10 \cdot \left(\frac{e^{m \cdot \log k}}{k \cdot k} \cdot \frac{a}{k}\right)\right) + \frac{a}{k} \cdot \frac{e^{m \cdot \log k}}{k}\\ \end{array}\]

Reproduce

herbie shell --seed 2019155 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))