Average Error: 2.2 → 0.1
Time: 9.3s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 8.14236707063809 \cdot 10^{+129}:\\ \;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{e^{m \cdot \log k}}{\frac{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}{a}} \cdot 99 + -10 \cdot \left(\frac{e^{m \cdot \log k}}{k \cdot k} \cdot \frac{a}{k}\right)\right) + \frac{a}{k} \cdot \frac{e^{m \cdot \log k}}{k}\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 8.14236707063809 \cdot 10^{+129}:\\
\;\;\;\;\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 r2875209 = a;
        double r2875210 = k;
        double r2875211 = m;
        double r2875212 = pow(r2875210, r2875211);
        double r2875213 = r2875209 * r2875212;
        double r2875214 = 1.0;
        double r2875215 = 10.0;
        double r2875216 = r2875215 * r2875210;
        double r2875217 = r2875214 + r2875216;
        double r2875218 = r2875210 * r2875210;
        double r2875219 = r2875217 + r2875218;
        double r2875220 = r2875213 / r2875219;
        return r2875220;
}
↓
double f(double a, double k, double m) {
        double r2875221 = k;
        double r2875222 = 8.14236707063809e+129;
        bool r2875223 = r2875221 <= r2875222;
        double r2875224 = m;
        double r2875225 = pow(r2875221, r2875224);
        double r2875226 = a;
        double r2875227 = r2875225 * r2875226;
        double r2875228 = 1.0;
        double r2875229 = 10.0;
        double r2875230 = r2875221 + r2875229;
        double r2875231 = r2875221 * r2875230;
        double r2875232 = r2875228 + r2875231;
        double r2875233 = r2875227 / r2875232;
        double r2875234 = log(r2875221);
        double r2875235 = r2875224 * r2875234;
        double r2875236 = exp(r2875235);
        double r2875237 = r2875221 * r2875221;
        double r2875238 = r2875237 * r2875237;
        double r2875239 = r2875238 / r2875226;
        double r2875240 = r2875236 / r2875239;
        double r2875241 = 99.0;
        double r2875242 = r2875240 * r2875241;
        double r2875243 = -10.0;
        double r2875244 = r2875236 / r2875237;
        double r2875245 = r2875226 / r2875221;
        double r2875246 = r2875244 * r2875245;
        double r2875247 = r2875243 * r2875246;
        double r2875248 = r2875242 + r2875247;
        double r2875249 = r2875236 / r2875221;
        double r2875250 = r2875245 * r2875249;
        double r2875251 = r2875248 + r2875250;
        double r2875252 = r2875223 ? r2875233 : r2875251;
        return r2875252;
}

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 < 8.14236707063809e+129

    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 8.14236707063809e+129 < k

    1. Initial program 9.7

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

    2. Simplified9.7

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

    3. Taylor expanded around inf 9.7

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

    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

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 8.14236707063809 \cdot 10^{+129}:\\ \;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{e^{m \cdot \log k}}{\frac{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}{a}} \cdot 99 + -10 \cdot \left(\frac{e^{m \cdot \log k}}{k \cdot k} \cdot \frac{a}{k}\right)\right) + \frac{a}{k} \cdot \frac{e^{m \cdot \log k}}{k}\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))