Average Error: 2.1 → 0.1
Time: 7.1m
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 1.0744642621858205 \cdot 10^{+133}:\\ \;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot e^{m \cdot \log k}}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} \cdot 99 + \left(\frac{\frac{a}{k}}{k} \cdot e^{m \cdot \log k} + \frac{-10}{\frac{\frac{k}{\frac{\frac{a}{k}}{k}}}{e^{m \cdot \log k}}}\right)\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 1.0744642621858205 \cdot 10^{+133}:\\
\;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\

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

\end{array}
double f(double a, double k, double m) {
        double r88798293 = a;
        double r88798294 = k;
        double r88798295 = m;
        double r88798296 = pow(r88798294, r88798295);
        double r88798297 = r88798293 * r88798296;
        double r88798298 = 1.0;
        double r88798299 = 10.0;
        double r88798300 = r88798299 * r88798294;
        double r88798301 = r88798298 + r88798300;
        double r88798302 = r88798294 * r88798294;
        double r88798303 = r88798301 + r88798302;
        double r88798304 = r88798297 / r88798303;
        return r88798304;
}
↓
double f(double a, double k, double m) {
        double r88798305 = k;
        double r88798306 = 1.0744642621858205e+133;
        bool r88798307 = r88798305 <= r88798306;
        double r88798308 = m;
        double r88798309 = pow(r88798305, r88798308);
        double r88798310 = a;
        double r88798311 = r88798309 * r88798310;
        double r88798312 = 1.0;
        double r88798313 = 10.0;
        double r88798314 = r88798305 + r88798313;
        double r88798315 = r88798305 * r88798314;
        double r88798316 = r88798312 + r88798315;
        double r88798317 = r88798311 / r88798316;
        double r88798318 = log(r88798305);
        double r88798319 = r88798308 * r88798318;
        double r88798320 = exp(r88798319);
        double r88798321 = r88798310 * r88798320;
        double r88798322 = r88798305 * r88798305;
        double r88798323 = r88798322 * r88798322;
        double r88798324 = r88798321 / r88798323;
        double r88798325 = 99.0;
        double r88798326 = r88798324 * r88798325;
        double r88798327 = r88798310 / r88798305;
        double r88798328 = r88798327 / r88798305;
        double r88798329 = r88798328 * r88798320;
        double r88798330 = -10.0;
        double r88798331 = r88798305 / r88798328;
        double r88798332 = r88798331 / r88798320;
        double r88798333 = r88798330 / r88798332;
        double r88798334 = r88798329 + r88798333;
        double r88798335 = r88798326 + r88798334;
        double r88798336 = r88798307 ? r88798317 : r88798335;
        return r88798336;
}

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 < 1.0744642621858205e+133

    1. Initial program 0.1

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

    2. Simplified0.1

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

    3. Taylor expanded around -inf 0.1

      \[\leadsto \frac{{k}^{m} \cdot a}{\color{blue}{\left({k}^{2} + 10 \cdot k\right)} + 1}\]

    4. Simplified0.1

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

    if 1.0744642621858205e+133 < k

    1. Initial program 9.3

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

    2. Simplified9.3

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

    3. Taylor expanded around -inf 9.3

      \[\leadsto \frac{{k}^{m} \cdot a}{\color{blue}{\left({k}^{2} + 10 \cdot k\right)} + 1}\]

    4. Simplified9.3

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

    6. Applied add-sqr-sqrt9.3

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

    7. Applied times-frac9.3

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

    8. Taylor expanded around -inf 63.0

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

    9. Simplified0.1

      \[\leadsto \color{blue}{99 \cdot \frac{e^{m \cdot \left(0 + \log k\right)} \cdot a}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} + \left(\frac{\frac{a}{k}}{k} \cdot e^{m \cdot \left(0 + \log k\right)} + \frac{-10}{\frac{\frac{k}{\frac{\frac{a}{k}}{k}}}{e^{m \cdot \left(0 + \log k\right)}}}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 1.0744642621858205 \cdot 10^{+133}:\\ \;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot e^{m \cdot \log k}}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} \cdot 99 + \left(\frac{\frac{a}{k}}{k} \cdot e^{m \cdot \log k} + \frac{-10}{\frac{\frac{k}{\frac{\frac{a}{k}}{k}}}{e^{m \cdot \log k}}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019124 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))