Average Error: 2.1 → 0.2
Time: 29.5s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 2379.959343579875:\\ \;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{99 \cdot a}{\frac{k \cdot k}{\frac{e^{m \cdot \log k}}{k \cdot k}}} + \left(\frac{e^{m \cdot \log k} \cdot \frac{a}{k}}{k} - \frac{10}{k \cdot k} \cdot \frac{a \cdot e^{m \cdot \log k}}{k}\right)\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 2379.959343579875:\\
\;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\

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

\end{array}
double f(double a, double k, double m) {
        double r9290433 = a;
        double r9290434 = k;
        double r9290435 = m;
        double r9290436 = pow(r9290434, r9290435);
        double r9290437 = r9290433 * r9290436;
        double r9290438 = 1.0;
        double r9290439 = 10.0;
        double r9290440 = r9290439 * r9290434;
        double r9290441 = r9290438 + r9290440;
        double r9290442 = r9290434 * r9290434;
        double r9290443 = r9290441 + r9290442;
        double r9290444 = r9290437 / r9290443;
        return r9290444;
}
↓
double f(double a, double k, double m) {
        double r9290445 = k;
        double r9290446 = 2379.959343579875;
        bool r9290447 = r9290445 <= r9290446;
        double r9290448 = m;
        double r9290449 = pow(r9290445, r9290448);
        double r9290450 = a;
        double r9290451 = r9290449 * r9290450;
        double r9290452 = 1.0;
        double r9290453 = 10.0;
        double r9290454 = r9290445 + r9290453;
        double r9290455 = r9290445 * r9290454;
        double r9290456 = r9290452 + r9290455;
        double r9290457 = r9290451 / r9290456;
        double r9290458 = 99.0;
        double r9290459 = r9290458 * r9290450;
        double r9290460 = r9290445 * r9290445;
        double r9290461 = log(r9290445);
        double r9290462 = r9290448 * r9290461;
        double r9290463 = exp(r9290462);
        double r9290464 = r9290463 / r9290460;
        double r9290465 = r9290460 / r9290464;
        double r9290466 = r9290459 / r9290465;
        double r9290467 = r9290450 / r9290445;
        double r9290468 = r9290463 * r9290467;
        double r9290469 = r9290468 / r9290445;
        double r9290470 = r9290453 / r9290460;
        double r9290471 = r9290450 * r9290463;
        double r9290472 = r9290471 / r9290445;
        double r9290473 = r9290470 * r9290472;
        double r9290474 = r9290469 - r9290473;
        double r9290475 = r9290466 + r9290474;
        double r9290476 = r9290447 ? r9290457 : r9290475;
        return r9290476;
}

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 < 2379.959343579875

    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 *-un-lft-identity0.0

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

    5. Applied associate-*r*0.0

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

    6. Simplified0.0

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

    if 2379.959343579875 < k

    1. Initial program 5.5

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

    2. Simplified5.5

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

    4. Applied *-un-lft-identity5.5

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

    5. Applied associate-*r*5.5

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

    6. Simplified5.5

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

    7. Taylor expanded around -inf 62.9

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

    8. Simplified0.4

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 2379.959343579875:\\ \;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{99 \cdot a}{\frac{k \cdot k}{\frac{e^{m \cdot \log k}}{k \cdot k}}} + \left(\frac{e^{m \cdot \log k} \cdot \frac{a}{k}}{k} - \frac{10}{k \cdot k} \cdot \frac{a \cdot e^{m \cdot \log k}}{k}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019138 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))