Average Error: 1.9 → 0.1
Time: 20.2s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 5.127945408381113220037011205259685410545 \cdot 10^{118}:\\ \;\;\;\;\frac{1}{1 + \left(k + 10\right) \cdot k} \cdot \left({k}^{m} \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{k} \cdot \frac{e^{m \cdot \log k}}{k} - \frac{10 \cdot e^{m \cdot \log k}}{\frac{k \cdot \left(k \cdot k\right)}{a}}\right) + \frac{99}{k \cdot k} \cdot \frac{a \cdot e^{m \cdot \log k}}{k \cdot k}\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 5.127945408381113220037011205259685410545 \cdot 10^{118}:\\
\;\;\;\;\frac{1}{1 + \left(k + 10\right) \cdot k} \cdot \left({k}^{m} \cdot a\right)\\

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

\end{array}
double f(double a, double k, double m) {
        double r8668494 = a;
        double r8668495 = k;
        double r8668496 = m;
        double r8668497 = pow(r8668495, r8668496);
        double r8668498 = r8668494 * r8668497;
        double r8668499 = 1.0;
        double r8668500 = 10.0;
        double r8668501 = r8668500 * r8668495;
        double r8668502 = r8668499 + r8668501;
        double r8668503 = r8668495 * r8668495;
        double r8668504 = r8668502 + r8668503;
        double r8668505 = r8668498 / r8668504;
        return r8668505;
}
↓
double f(double a, double k, double m) {
        double r8668506 = k;
        double r8668507 = 5.127945408381113e+118;
        bool r8668508 = r8668506 <= r8668507;
        double r8668509 = 1.0;
        double r8668510 = 1.0;
        double r8668511 = 10.0;
        double r8668512 = r8668506 + r8668511;
        double r8668513 = r8668512 * r8668506;
        double r8668514 = r8668510 + r8668513;
        double r8668515 = r8668509 / r8668514;
        double r8668516 = m;
        double r8668517 = pow(r8668506, r8668516);
        double r8668518 = a;
        double r8668519 = r8668517 * r8668518;
        double r8668520 = r8668515 * r8668519;
        double r8668521 = r8668518 / r8668506;
        double r8668522 = log(r8668506);
        double r8668523 = r8668516 * r8668522;
        double r8668524 = exp(r8668523);
        double r8668525 = r8668524 / r8668506;
        double r8668526 = r8668521 * r8668525;
        double r8668527 = r8668511 * r8668524;
        double r8668528 = r8668506 * r8668506;
        double r8668529 = r8668506 * r8668528;
        double r8668530 = r8668529 / r8668518;
        double r8668531 = r8668527 / r8668530;
        double r8668532 = r8668526 - r8668531;
        double r8668533 = 99.0;
        double r8668534 = r8668533 / r8668528;
        double r8668535 = r8668518 * r8668524;
        double r8668536 = r8668535 / r8668528;
        double r8668537 = r8668534 * r8668536;
        double r8668538 = r8668532 + r8668537;
        double r8668539 = r8668508 ? r8668520 : r8668538;
        return r8668539;
}

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 < 5.127945408381113e+118

    1. Initial program 0.1

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

    2. Simplified0.1

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

    4. Applied div-inv0.1

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

    5. Applied *-un-lft-identity0.1

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

    6. Applied times-frac0.1

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

    7. Simplified0.1

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

    if 5.127945408381113e+118 < k

    1. Initial program 8.0

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

    2. Simplified8.0

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

    3. Taylor expanded around inf 8.0

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

    4. Simplified0.2

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 5.127945408381113220037011205259685410545 \cdot 10^{118}:\\ \;\;\;\;\frac{1}{1 + \left(k + 10\right) \cdot k} \cdot \left({k}^{m} \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{k} \cdot \frac{e^{m \cdot \log k}}{k} - \frac{10 \cdot e^{m \cdot \log k}}{\frac{k \cdot \left(k \cdot k\right)}{a}}\right) + \frac{99}{k \cdot k} \cdot \frac{a \cdot e^{m \cdot \log k}}{k \cdot k}\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))