Average Error: 1.9 → 0.1
Time: 30.2s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 6.144520496396345 \cdot 10^{+142}:\\ \;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\sqrt{e^{\log k \cdot m}}}{\sqrt{k}} \cdot \frac{a}{k}\right) \cdot \frac{\sqrt{e^{\log k \cdot m}}}{\sqrt{k}} + \left(\frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k}\right) \cdot \left(\frac{\frac{99}{k}}{k} - \frac{10}{k}\right)\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 6.144520496396345 \cdot 10^{+142}:\\
\;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\

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

\end{array}
double f(double a, double k, double m) {
        double r7368287 = a;
        double r7368288 = k;
        double r7368289 = m;
        double r7368290 = pow(r7368288, r7368289);
        double r7368291 = r7368287 * r7368290;
        double r7368292 = 1.0;
        double r7368293 = 10.0;
        double r7368294 = r7368293 * r7368288;
        double r7368295 = r7368292 + r7368294;
        double r7368296 = r7368288 * r7368288;
        double r7368297 = r7368295 + r7368296;
        double r7368298 = r7368291 / r7368297;
        return r7368298;
}
↓
double f(double a, double k, double m) {
        double r7368299 = k;
        double r7368300 = 6.144520496396345e+142;
        bool r7368301 = r7368299 <= r7368300;
        double r7368302 = m;
        double r7368303 = pow(r7368299, r7368302);
        double r7368304 = a;
        double r7368305 = r7368303 * r7368304;
        double r7368306 = 1.0;
        double r7368307 = 10.0;
        double r7368308 = r7368299 + r7368307;
        double r7368309 = r7368299 * r7368308;
        double r7368310 = r7368306 + r7368309;
        double r7368311 = r7368305 / r7368310;
        double r7368312 = log(r7368299);
        double r7368313 = r7368312 * r7368302;
        double r7368314 = exp(r7368313);
        double r7368315 = sqrt(r7368314);
        double r7368316 = sqrt(r7368299);
        double r7368317 = r7368315 / r7368316;
        double r7368318 = r7368304 / r7368299;
        double r7368319 = r7368317 * r7368318;
        double r7368320 = r7368319 * r7368317;
        double r7368321 = r7368314 / r7368299;
        double r7368322 = r7368318 * r7368321;
        double r7368323 = 99.0;
        double r7368324 = r7368323 / r7368299;
        double r7368325 = r7368324 / r7368299;
        double r7368326 = r7368307 / r7368299;
        double r7368327 = r7368325 - r7368326;
        double r7368328 = r7368322 * r7368327;
        double r7368329 = r7368320 + r7368328;
        double r7368330 = r7368301 ? r7368311 : r7368329;
        return r7368330;
}

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 < 6.144520496396345e+142

    1. Initial program 0.1

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

    2. Simplified0.1

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

    if 6.144520496396345e+142 < k

    1. Initial program 9.6

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

    2. Simplified9.6

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

    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

      \[\leadsto \color{blue}{\frac{e^{m \cdot \left(0 + \log k\right)}}{k} \cdot \frac{a}{k} + \left(\frac{e^{m \cdot \left(0 + \log k\right)}}{k} \cdot \frac{a}{k}\right) \cdot \left(\frac{\frac{99}{k}}{k} - \frac{10}{k}\right)}\]
    5. Using strategy rm

    6. Applied add-sqr-sqrt0.1

      \[\leadsto \frac{e^{m \cdot \left(0 + \log k\right)}}{\color{blue}{\sqrt{k} \cdot \sqrt{k}}} \cdot \frac{a}{k} + \left(\frac{e^{m \cdot \left(0 + \log k\right)}}{k} \cdot \frac{a}{k}\right) \cdot \left(\frac{\frac{99}{k}}{k} - \frac{10}{k}\right)\]

    7. Applied add-sqr-sqrt0.1

      \[\leadsto \frac{\color{blue}{\sqrt{e^{m \cdot \left(0 + \log k\right)}} \cdot \sqrt{e^{m \cdot \left(0 + \log k\right)}}}}{\sqrt{k} \cdot \sqrt{k}} \cdot \frac{a}{k} + \left(\frac{e^{m \cdot \left(0 + \log k\right)}}{k} \cdot \frac{a}{k}\right) \cdot \left(\frac{\frac{99}{k}}{k} - \frac{10}{k}\right)\]

    8. Applied times-frac0.1

      \[\leadsto \color{blue}{\left(\frac{\sqrt{e^{m \cdot \left(0 + \log k\right)}}}{\sqrt{k}} \cdot \frac{\sqrt{e^{m \cdot \left(0 + \log k\right)}}}{\sqrt{k}}\right)} \cdot \frac{a}{k} + \left(\frac{e^{m \cdot \left(0 + \log k\right)}}{k} \cdot \frac{a}{k}\right) \cdot \left(\frac{\frac{99}{k}}{k} - \frac{10}{k}\right)\]

    9. Applied associate-*l*0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 6.144520496396345 \cdot 10^{+142}:\\ \;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\sqrt{e^{\log k \cdot m}}}{\sqrt{k}} \cdot \frac{a}{k}\right) \cdot \frac{\sqrt{e^{\log k \cdot m}}}{\sqrt{k}} + \left(\frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k}\right) \cdot \left(\frac{\frac{99}{k}}{k} - \frac{10}{k}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019146 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))