Average Error: 2.1 → 0.0
Time: 32.2s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 1.367410316305712 \cdot 10^{+108}:\\ \;\;\;\;\frac{a}{\frac{1 + \left(k + 10\right) \cdot k}{{k}^{m}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{m \cdot \log k} \cdot 99}{\frac{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}{a}} + \left(-10 \cdot \frac{e^{m \cdot \log k}}{\frac{k \cdot \left(k \cdot k\right)}{a}} + \frac{\frac{a \cdot e^{m \cdot \log k}}{k}}{k}\right)\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 1.367410316305712 \cdot 10^{+108}:\\
\;\;\;\;\frac{a}{\frac{1 + \left(k + 10\right) \cdot k}{{k}^{m}}}\\

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

\end{array}
double f(double a, double k, double m) {
        double r7781352 = a;
        double r7781353 = k;
        double r7781354 = m;
        double r7781355 = pow(r7781353, r7781354);
        double r7781356 = r7781352 * r7781355;
        double r7781357 = 1.0;
        double r7781358 = 10.0;
        double r7781359 = r7781358 * r7781353;
        double r7781360 = r7781357 + r7781359;
        double r7781361 = r7781353 * r7781353;
        double r7781362 = r7781360 + r7781361;
        double r7781363 = r7781356 / r7781362;
        return r7781363;
}
↓
double f(double a, double k, double m) {
        double r7781364 = k;
        double r7781365 = 1.367410316305712e+108;
        bool r7781366 = r7781364 <= r7781365;
        double r7781367 = a;
        double r7781368 = 1.0;
        double r7781369 = 10.0;
        double r7781370 = r7781364 + r7781369;
        double r7781371 = r7781370 * r7781364;
        double r7781372 = r7781368 + r7781371;
        double r7781373 = m;
        double r7781374 = pow(r7781364, r7781373);
        double r7781375 = r7781372 / r7781374;
        double r7781376 = r7781367 / r7781375;
        double r7781377 = log(r7781364);
        double r7781378 = r7781373 * r7781377;
        double r7781379 = exp(r7781378);
        double r7781380 = 99.0;
        double r7781381 = r7781379 * r7781380;
        double r7781382 = r7781364 * r7781364;
        double r7781383 = r7781382 * r7781382;
        double r7781384 = r7781383 / r7781367;
        double r7781385 = r7781381 / r7781384;
        double r7781386 = -10.0;
        double r7781387 = r7781364 * r7781382;
        double r7781388 = r7781387 / r7781367;
        double r7781389 = r7781379 / r7781388;
        double r7781390 = r7781386 * r7781389;
        double r7781391 = r7781367 * r7781379;
        double r7781392 = r7781391 / r7781364;
        double r7781393 = r7781392 / r7781364;
        double r7781394 = r7781390 + r7781393;
        double r7781395 = r7781385 + r7781394;
        double r7781396 = r7781366 ? r7781376 : r7781395;
        return r7781396;
}

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 < 1.367410316305712e+108

    1. Initial program 0.1

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

    2. Simplified0.0

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

    if 1.367410316305712e+108 < k

    1. Initial program 8.2

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

    2. Simplified8.2

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

    3. Taylor expanded around inf 8.2

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

    4. Simplified0.1

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

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 1.367410316305712 \cdot 10^{+108}:\\ \;\;\;\;\frac{a}{\frac{1 + \left(k + 10\right) \cdot k}{{k}^{m}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{m \cdot \log k} \cdot 99}{\frac{\left(k \cdot k\right) \cdot \left(k \cdot k\right)}{a}} + \left(-10 \cdot \frac{e^{m \cdot \log k}}{\frac{k \cdot \left(k \cdot k\right)}{a}} + \frac{\frac{a \cdot e^{m \cdot \log k}}{k}}{k}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))