Average Error: 2.2 → 0.1
Time: 18.2s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 1.903140954813681112522300916794739229461 \cdot 10^{140}:\\ \;\;\;\;\frac{a}{\frac{1 + \left(k + 10\right) \cdot k}{{k}^{m}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{k} \cdot \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k} - \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)} \cdot \left(a \cdot 10\right)}{{k}^{3}}\right) + \frac{99 \cdot {\left(\frac{1}{k}\right)}^{\left(-m\right)}}{\frac{{k}^{4}}{a}}\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 1.903140954813681112522300916794739229461 \cdot 10^{140}:\\
\;\;\;\;\frac{a}{\frac{1 + \left(k + 10\right) \cdot k}{{k}^{m}}}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{a}{k} \cdot \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k} - \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)} \cdot \left(a \cdot 10\right)}{{k}^{3}}\right) + \frac{99 \cdot {\left(\frac{1}{k}\right)}^{\left(-m\right)}}{\frac{{k}^{4}}{a}}\\

\end{array}
double f(double a, double k, double m) {
        double r218347 = a;
        double r218348 = k;
        double r218349 = m;
        double r218350 = pow(r218348, r218349);
        double r218351 = r218347 * r218350;
        double r218352 = 1.0;
        double r218353 = 10.0;
        double r218354 = r218353 * r218348;
        double r218355 = r218352 + r218354;
        double r218356 = r218348 * r218348;
        double r218357 = r218355 + r218356;
        double r218358 = r218351 / r218357;
        return r218358;
}
↓
double f(double a, double k, double m) {
        double r218359 = k;
        double r218360 = 1.9031409548136811e+140;
        bool r218361 = r218359 <= r218360;
        double r218362 = a;
        double r218363 = 1.0;
        double r218364 = 10.0;
        double r218365 = r218359 + r218364;
        double r218366 = r218365 * r218359;
        double r218367 = r218363 + r218366;
        double r218368 = m;
        double r218369 = pow(r218359, r218368);
        double r218370 = r218367 / r218369;
        double r218371 = r218362 / r218370;
        double r218372 = r218362 / r218359;
        double r218373 = 1.0;
        double r218374 = r218373 / r218359;
        double r218375 = -r218368;
        double r218376 = pow(r218374, r218375);
        double r218377 = r218376 / r218359;
        double r218378 = r218372 * r218377;
        double r218379 = r218362 * r218364;
        double r218380 = r218376 * r218379;
        double r218381 = 3.0;
        double r218382 = pow(r218359, r218381);
        double r218383 = r218380 / r218382;
        double r218384 = r218378 - r218383;
        double r218385 = 99.0;
        double r218386 = r218385 * r218376;
        double r218387 = 4.0;
        double r218388 = pow(r218359, r218387);
        double r218389 = r218388 / r218362;
        double r218390 = r218386 / r218389;
        double r218391 = r218384 + r218390;
        double r218392 = r218361 ? r218371 : r218391;
        return r218392;
}

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 < 1.9031409548136811e+140

    1. Initial program 0.1

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

    2. Simplified0.1

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

    if 1.9031409548136811e+140 < k

    1. Initial program 10.1

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

    2. Simplified10.1

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

    4. Applied clear-num10.1

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

    5. Simplified10.1

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

    6. Taylor expanded around inf 10.1

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

    7. Simplified0.3

      \[\leadsto \color{blue}{\left(\frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k} \cdot \frac{a}{k} - \frac{\left(10 \cdot a\right) \cdot {\left(\frac{1}{k}\right)}^{\left(-m\right)}}{{k}^{3}}\right) + \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)} \cdot 99}{\frac{{k}^{4}}{a}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 1.903140954813681112522300916794739229461 \cdot 10^{140}:\\ \;\;\;\;\frac{a}{\frac{1 + \left(k + 10\right) \cdot k}{{k}^{m}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{k} \cdot \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k} - \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)} \cdot \left(a \cdot 10\right)}{{k}^{3}}\right) + \frac{99 \cdot {\left(\frac{1}{k}\right)}^{\left(-m\right)}}{\frac{{k}^{4}}{a}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))