Average Error: 1.7 → 0.1
Time: 24.4s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 6.005951583124144 \cdot 10^{+111}:\\ \;\;\;\;\frac{\frac{1}{\sqrt{1 + \left(k + 10\right) \cdot k}}}{\sqrt{1 + \left(k + 10\right) \cdot k}} \cdot \left({k}^{m} \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k}}{k} \cdot -10 + \left(\frac{e^{\log k \cdot m}}{\frac{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}{a}} \cdot 99 + \frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k}\right)\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 6.005951583124144 \cdot 10^{+111}:\\
\;\;\;\;\frac{\frac{1}{\sqrt{1 + \left(k + 10\right) \cdot k}}}{\sqrt{1 + \left(k + 10\right) \cdot k}} \cdot \left({k}^{m} \cdot a\right)\\

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

\end{array}
double f(double a, double k, double m) {
        double r3675269 = a;
        double r3675270 = k;
        double r3675271 = m;
        double r3675272 = pow(r3675270, r3675271);
        double r3675273 = r3675269 * r3675272;
        double r3675274 = 1.0;
        double r3675275 = 10.0;
        double r3675276 = r3675275 * r3675270;
        double r3675277 = r3675274 + r3675276;
        double r3675278 = r3675270 * r3675270;
        double r3675279 = r3675277 + r3675278;
        double r3675280 = r3675273 / r3675279;
        return r3675280;
}
↓
double f(double a, double k, double m) {
        double r3675281 = k;
        double r3675282 = 6.005951583124144e+111;
        bool r3675283 = r3675281 <= r3675282;
        double r3675284 = 1.0;
        double r3675285 = 10.0;
        double r3675286 = r3675281 + r3675285;
        double r3675287 = r3675286 * r3675281;
        double r3675288 = r3675284 + r3675287;
        double r3675289 = sqrt(r3675288);
        double r3675290 = r3675284 / r3675289;
        double r3675291 = r3675290 / r3675289;
        double r3675292 = m;
        double r3675293 = pow(r3675281, r3675292);
        double r3675294 = a;
        double r3675295 = r3675293 * r3675294;
        double r3675296 = r3675291 * r3675295;
        double r3675297 = r3675294 / r3675281;
        double r3675298 = log(r3675281);
        double r3675299 = r3675298 * r3675292;
        double r3675300 = exp(r3675299);
        double r3675301 = r3675300 / r3675281;
        double r3675302 = r3675297 * r3675301;
        double r3675303 = r3675302 / r3675281;
        double r3675304 = -10.0;
        double r3675305 = r3675303 * r3675304;
        double r3675306 = r3675281 * r3675281;
        double r3675307 = r3675306 * r3675306;
        double r3675308 = r3675307 / r3675294;
        double r3675309 = r3675300 / r3675308;
        double r3675310 = 99.0;
        double r3675311 = r3675309 * r3675310;
        double r3675312 = r3675311 + r3675302;
        double r3675313 = r3675305 + r3675312;
        double r3675314 = r3675283 ? r3675296 : r3675313;
        return r3675314;
}

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 < 6.005951583124144e+111

    1. Initial program 0.1

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

    2. Simplified0.0

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

    4. Applied div-inv0.1

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

    6. Applied add-sqr-sqrt0.1

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

    7. Applied associate-/r*0.1

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

    if 6.005951583124144e+111 < k

    1. Initial program 6.9

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

    2. Simplified6.9

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

    3. Taylor expanded around inf 6.9

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

    4. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 6.005951583124144 \cdot 10^{+111}:\\ \;\;\;\;\frac{\frac{1}{\sqrt{1 + \left(k + 10\right) \cdot k}}}{\sqrt{1 + \left(k + 10\right) \cdot k}} \cdot \left({k}^{m} \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k}}{k} \cdot -10 + \left(\frac{e^{\log k \cdot m}}{\frac{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}{a}} \cdot 99 + \frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019153 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))