Average Error: 2.0 → 0.1
Time: 16.9s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 3.636771010018003 \cdot 10^{+36}:\\ \;\;\;\;\left(\left({k}^{\left(\frac{\frac{m}{2}}{2}\right)} \cdot \frac{a}{1 + \left(k + 10\right) \cdot k}\right) \cdot {k}^{\left(\frac{\frac{m}{2}}{2}\right)}\right) \cdot {k}^{\left(\frac{m}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;{k}^{m} \cdot \left(\left(\frac{\frac{a}{k}}{k} - \frac{10}{\frac{k}{\frac{a}{k \cdot k}}}\right) + \frac{99}{k \cdot k} \cdot \frac{a}{k \cdot k}\right)\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 3.636771010018003 \cdot 10^{+36}:\\
\;\;\;\;\left(\left({k}^{\left(\frac{\frac{m}{2}}{2}\right)} \cdot \frac{a}{1 + \left(k + 10\right) \cdot k}\right) \cdot {k}^{\left(\frac{\frac{m}{2}}{2}\right)}\right) \cdot {k}^{\left(\frac{m}{2}\right)}\\

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

\end{array}
double f(double a, double k, double m) {
        double r6489621 = a;
        double r6489622 = k;
        double r6489623 = m;
        double r6489624 = pow(r6489622, r6489623);
        double r6489625 = r6489621 * r6489624;
        double r6489626 = 1.0;
        double r6489627 = 10.0;
        double r6489628 = r6489627 * r6489622;
        double r6489629 = r6489626 + r6489628;
        double r6489630 = r6489622 * r6489622;
        double r6489631 = r6489629 + r6489630;
        double r6489632 = r6489625 / r6489631;
        return r6489632;
}
↓
double f(double a, double k, double m) {
        double r6489633 = k;
        double r6489634 = 3.636771010018003e+36;
        bool r6489635 = r6489633 <= r6489634;
        double r6489636 = m;
        double r6489637 = 2.0;
        double r6489638 = r6489636 / r6489637;
        double r6489639 = r6489638 / r6489637;
        double r6489640 = pow(r6489633, r6489639);
        double r6489641 = a;
        double r6489642 = 1.0;
        double r6489643 = 10.0;
        double r6489644 = r6489633 + r6489643;
        double r6489645 = r6489644 * r6489633;
        double r6489646 = r6489642 + r6489645;
        double r6489647 = r6489641 / r6489646;
        double r6489648 = r6489640 * r6489647;
        double r6489649 = r6489648 * r6489640;
        double r6489650 = pow(r6489633, r6489638);
        double r6489651 = r6489649 * r6489650;
        double r6489652 = pow(r6489633, r6489636);
        double r6489653 = r6489641 / r6489633;
        double r6489654 = r6489653 / r6489633;
        double r6489655 = r6489633 * r6489633;
        double r6489656 = r6489641 / r6489655;
        double r6489657 = r6489633 / r6489656;
        double r6489658 = r6489643 / r6489657;
        double r6489659 = r6489654 - r6489658;
        double r6489660 = 99.0;
        double r6489661 = r6489660 / r6489655;
        double r6489662 = r6489661 * r6489656;
        double r6489663 = r6489659 + r6489662;
        double r6489664 = r6489652 * r6489663;
        double r6489665 = r6489635 ? r6489651 : r6489664;
        return r6489665;
}

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 < 3.636771010018003e+36

    1. Initial program 0.1

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

    2. Simplified0.0

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

    4. Applied sqr-pow0.1

      \[\leadsto \frac{a}{k \cdot \left(k + 10\right) + 1} \cdot \color{blue}{\left({k}^{\left(\frac{m}{2}\right)} \cdot {k}^{\left(\frac{m}{2}\right)}\right)}\]

    5. Applied associate-*r*0.1

      \[\leadsto \color{blue}{\left(\frac{a}{k \cdot \left(k + 10\right) + 1} \cdot {k}^{\left(\frac{m}{2}\right)}\right) \cdot {k}^{\left(\frac{m}{2}\right)}}\]
    6. Using strategy rm

    7. Applied sqr-pow0.1

      \[\leadsto \left(\frac{a}{k \cdot \left(k + 10\right) + 1} \cdot \color{blue}{\left({k}^{\left(\frac{\frac{m}{2}}{2}\right)} \cdot {k}^{\left(\frac{\frac{m}{2}}{2}\right)}\right)}\right) \cdot {k}^{\left(\frac{m}{2}\right)}\]

    8. Applied associate-*r*0.1

      \[\leadsto \color{blue}{\left(\left(\frac{a}{k \cdot \left(k + 10\right) + 1} \cdot {k}^{\left(\frac{\frac{m}{2}}{2}\right)}\right) \cdot {k}^{\left(\frac{\frac{m}{2}}{2}\right)}\right)} \cdot {k}^{\left(\frac{m}{2}\right)}\]

    if 3.636771010018003e+36 < k

    1. Initial program 5.7

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

    2. Simplified5.7

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

    3. Taylor expanded around -inf 5.7

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

    4. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 3.636771010018003 \cdot 10^{+36}:\\ \;\;\;\;\left(\left({k}^{\left(\frac{\frac{m}{2}}{2}\right)} \cdot \frac{a}{1 + \left(k + 10\right) \cdot k}\right) \cdot {k}^{\left(\frac{\frac{m}{2}}{2}\right)}\right) \cdot {k}^{\left(\frac{m}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;{k}^{m} \cdot \left(\left(\frac{\frac{a}{k}}{k} - \frac{10}{\frac{k}{\frac{a}{k \cdot k}}}\right) + \frac{99}{k \cdot k} \cdot \frac{a}{k \cdot k}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019130 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))