Average Error: 2.0 → 0.1
Time: 37.9s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 1.0251482028952462 \cdot 10^{+139}:\\ \;\;\;\;\frac{\frac{{k}^{\left(\frac{m}{2}\right)} \cdot \left(a \cdot {k}^{\left(\frac{m}{2}\right)}\right)}{\sqrt{\left(k + 10\right) \cdot k + 1}}}{\sqrt{\left(k + 10\right) \cdot k + 1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k} - \left(\left(\frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k}\right) \cdot \frac{10}{k} - 99 \cdot \frac{a}{\frac{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}{e^{\log k \cdot m}}}\right)\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 1.0251482028952462 \cdot 10^{+139}:\\
\;\;\;\;\frac{\frac{{k}^{\left(\frac{m}{2}\right)} \cdot \left(a \cdot {k}^{\left(\frac{m}{2}\right)}\right)}{\sqrt{\left(k + 10\right) \cdot k + 1}}}{\sqrt{\left(k + 10\right) \cdot k + 1}}\\

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

\end{array}
double f(double a, double k, double m) {
        double r7176249 = a;
        double r7176250 = k;
        double r7176251 = m;
        double r7176252 = pow(r7176250, r7176251);
        double r7176253 = r7176249 * r7176252;
        double r7176254 = 1.0;
        double r7176255 = 10.0;
        double r7176256 = r7176255 * r7176250;
        double r7176257 = r7176254 + r7176256;
        double r7176258 = r7176250 * r7176250;
        double r7176259 = r7176257 + r7176258;
        double r7176260 = r7176253 / r7176259;
        return r7176260;
}
↓
double f(double a, double k, double m) {
        double r7176261 = k;
        double r7176262 = 1.0251482028952462e+139;
        bool r7176263 = r7176261 <= r7176262;
        double r7176264 = m;
        double r7176265 = 2.0;
        double r7176266 = r7176264 / r7176265;
        double r7176267 = pow(r7176261, r7176266);
        double r7176268 = a;
        double r7176269 = r7176268 * r7176267;
        double r7176270 = r7176267 * r7176269;
        double r7176271 = 10.0;
        double r7176272 = r7176261 + r7176271;
        double r7176273 = r7176272 * r7176261;
        double r7176274 = 1.0;
        double r7176275 = r7176273 + r7176274;
        double r7176276 = sqrt(r7176275);
        double r7176277 = r7176270 / r7176276;
        double r7176278 = r7176277 / r7176276;
        double r7176279 = r7176268 / r7176261;
        double r7176280 = log(r7176261);
        double r7176281 = r7176280 * r7176264;
        double r7176282 = exp(r7176281);
        double r7176283 = r7176282 / r7176261;
        double r7176284 = r7176279 * r7176283;
        double r7176285 = r7176271 / r7176261;
        double r7176286 = r7176284 * r7176285;
        double r7176287 = 99.0;
        double r7176288 = r7176261 * r7176261;
        double r7176289 = r7176288 * r7176288;
        double r7176290 = r7176289 / r7176282;
        double r7176291 = r7176268 / r7176290;
        double r7176292 = r7176287 * r7176291;
        double r7176293 = r7176286 - r7176292;
        double r7176294 = r7176284 - r7176293;
        double r7176295 = r7176263 ? r7176278 : r7176294;
        return r7176295;
}

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 < 1.0251482028952462e+139

    1. Initial program 0.1

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

    2. Simplified0.0

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

    4. Applied sqr-pow0.1

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

    5. Applied associate-*l*0.1

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

    7. Applied add-sqr-sqrt0.1

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

    8. Applied associate-/r*0.1

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

    if 1.0251482028952462e+139 < k

    1. Initial program 8.9

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

    2. Simplified8.9

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

    3. Taylor expanded around -inf 63.0

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

    4. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 1.0251482028952462 \cdot 10^{+139}:\\ \;\;\;\;\frac{\frac{{k}^{\left(\frac{m}{2}\right)} \cdot \left(a \cdot {k}^{\left(\frac{m}{2}\right)}\right)}{\sqrt{\left(k + 10\right) \cdot k + 1}}}{\sqrt{\left(k + 10\right) \cdot k + 1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k} - \left(\left(\frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k}\right) \cdot \frac{10}{k} - 99 \cdot \frac{a}{\frac{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}{e^{\log k \cdot m}}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019142 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))