Average Error: 2.2 → 0.1
Time: 26.4s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 3.92173497976968962 \cdot 10^{149}:\\ \;\;\;\;\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{\frac{{k}^{4}}{a}} \cdot 99 + \left(\frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k} \cdot \frac{a}{k} - \frac{\left(10 \cdot a\right) \cdot {\left(\frac{1}{k}\right)}^{\left(-m\right)}}{{k}^{3}}\right)\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 3.92173497976968962 \cdot 10^{149}:\\
\;\;\;\;\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\\

\mathbf{else}:\\
\;\;\;\;\frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{\frac{{k}^{4}}{a}} \cdot 99 + \left(\frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k} \cdot \frac{a}{k} - \frac{\left(10 \cdot a\right) \cdot {\left(\frac{1}{k}\right)}^{\left(-m\right)}}{{k}^{3}}\right)\\

\end{array}
double f(double a, double k, double m) {
        double r159200 = a;
        double r159201 = k;
        double r159202 = m;
        double r159203 = pow(r159201, r159202);
        double r159204 = r159200 * r159203;
        double r159205 = 1.0;
        double r159206 = 10.0;
        double r159207 = r159206 * r159201;
        double r159208 = r159205 + r159207;
        double r159209 = r159201 * r159201;
        double r159210 = r159208 + r159209;
        double r159211 = r159204 / r159210;
        return r159211;
}
↓
double f(double a, double k, double m) {
        double r159212 = k;
        double r159213 = 3.9217349797696896e+149;
        bool r159214 = r159212 <= r159213;
        double r159215 = a;
        double r159216 = m;
        double r159217 = pow(r159212, r159216);
        double r159218 = r159215 * r159217;
        double r159219 = 1.0;
        double r159220 = 10.0;
        double r159221 = r159220 * r159212;
        double r159222 = r159219 + r159221;
        double r159223 = r159212 * r159212;
        double r159224 = r159222 + r159223;
        double r159225 = r159218 / r159224;
        double r159226 = 1.0;
        double r159227 = r159226 / r159212;
        double r159228 = -r159216;
        double r159229 = pow(r159227, r159228);
        double r159230 = 4.0;
        double r159231 = pow(r159212, r159230);
        double r159232 = r159231 / r159215;
        double r159233 = r159229 / r159232;
        double r159234 = 99.0;
        double r159235 = r159233 * r159234;
        double r159236 = r159229 / r159212;
        double r159237 = r159215 / r159212;
        double r159238 = r159236 * r159237;
        double r159239 = r159220 * r159215;
        double r159240 = r159239 * r159229;
        double r159241 = 3.0;
        double r159242 = pow(r159212, r159241);
        double r159243 = r159240 / r159242;
        double r159244 = r159238 - r159243;
        double r159245 = r159235 + r159244;
        double r159246 = r159214 ? r159225 : r159245;
        return r159246;
}

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 < 3.9217349797696896e+149

    1. Initial program 0.1

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

    if 3.9217349797696896e+149 < k

    1. Initial program 10.9

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

    3. Applied frac-2neg10.9

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

    4. Simplified10.9

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

    5. Taylor expanded around inf 10.9

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

    6. Simplified0.3

      \[\leadsto \color{blue}{\frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{\frac{{k}^{4}}{a}} \cdot 99 + \left(\frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k} \cdot \frac{a}{k} - \frac{\left(10 \cdot a\right) \cdot {\left(\frac{1}{k}\right)}^{\left(-m\right)}}{{k}^{3}}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 3.92173497976968962 \cdot 10^{149}:\\ \;\;\;\;\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{\frac{{k}^{4}}{a}} \cdot 99 + \left(\frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k} \cdot \frac{a}{k} - \frac{\left(10 \cdot a\right) \cdot {\left(\frac{1}{k}\right)}^{\left(-m\right)}}{{k}^{3}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))