Average Error: 2.0 → 0.1
Time: 16.5s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 3.2541396121661334 \cdot 10^{+153}:\\ \;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{m \cdot \log k}}{k} \cdot \frac{a}{k} + \left(\frac{e^{m \cdot \log k} \cdot \left(a \cdot 99\right)}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} - \left(\frac{e^{m \cdot \log k}}{k \cdot k} \cdot \frac{a}{k}\right) \cdot 10\right)\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 3.2541396121661334 \cdot 10^{+153}:\\
\;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\

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

\end{array}
double f(double a, double k, double m) {
        double r3302236 = a;
        double r3302237 = k;
        double r3302238 = m;
        double r3302239 = pow(r3302237, r3302238);
        double r3302240 = r3302236 * r3302239;
        double r3302241 = 1.0;
        double r3302242 = 10.0;
        double r3302243 = r3302242 * r3302237;
        double r3302244 = r3302241 + r3302243;
        double r3302245 = r3302237 * r3302237;
        double r3302246 = r3302244 + r3302245;
        double r3302247 = r3302240 / r3302246;
        return r3302247;
}
↓
double f(double a, double k, double m) {
        double r3302248 = k;
        double r3302249 = 3.2541396121661334e+153;
        bool r3302250 = r3302248 <= r3302249;
        double r3302251 = m;
        double r3302252 = pow(r3302248, r3302251);
        double r3302253 = a;
        double r3302254 = r3302252 * r3302253;
        double r3302255 = 1.0;
        double r3302256 = 10.0;
        double r3302257 = r3302248 + r3302256;
        double r3302258 = r3302248 * r3302257;
        double r3302259 = r3302255 + r3302258;
        double r3302260 = r3302254 / r3302259;
        double r3302261 = log(r3302248);
        double r3302262 = r3302251 * r3302261;
        double r3302263 = exp(r3302262);
        double r3302264 = r3302263 / r3302248;
        double r3302265 = r3302253 / r3302248;
        double r3302266 = r3302264 * r3302265;
        double r3302267 = 99.0;
        double r3302268 = r3302253 * r3302267;
        double r3302269 = r3302263 * r3302268;
        double r3302270 = r3302248 * r3302248;
        double r3302271 = r3302270 * r3302270;
        double r3302272 = r3302269 / r3302271;
        double r3302273 = r3302263 / r3302270;
        double r3302274 = r3302273 * r3302265;
        double r3302275 = r3302274 * r3302256;
        double r3302276 = r3302272 - r3302275;
        double r3302277 = r3302266 + r3302276;
        double r3302278 = r3302250 ? r3302260 : r3302277;
        return r3302278;
}

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 < 3.2541396121661334e+153

    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 3.2541396121661334e+153 < k

    1. Initial program 10.1

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

    2. Simplified10.1

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

    4. Applied add-sqr-sqrt10.1

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

    5. Applied times-frac10.0

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

    6. Taylor expanded around inf 10.1

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

    7. Simplified0.3

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 3.2541396121661334 \cdot 10^{+153}:\\ \;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{m \cdot \log k}}{k} \cdot \frac{a}{k} + \left(\frac{e^{m \cdot \log k} \cdot \left(a \cdot 99\right)}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} - \left(\frac{e^{m \cdot \log k}}{k \cdot k} \cdot \frac{a}{k}\right) \cdot 10\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019154 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))