Average Error: 2.0 → 0.1
Time: 40.8s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 3.765086051784335120389721235468612662668 \cdot 10^{91}:\\ \;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{m \cdot \log k}}{k \cdot k} \cdot \frac{a \cdot 99}{k \cdot k} + \left(\frac{a}{k} \cdot \frac{e^{m \cdot \log k}}{k} - \frac{e^{m \cdot \log k} \cdot 10}{k \cdot k} \cdot \frac{a}{k}\right)\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 3.765086051784335120389721235468612662668 \cdot 10^{91}:\\
\;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\

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

\end{array}
double f(double a, double k, double m) {
        double r7015604 = a;
        double r7015605 = k;
        double r7015606 = m;
        double r7015607 = pow(r7015605, r7015606);
        double r7015608 = r7015604 * r7015607;
        double r7015609 = 1.0;
        double r7015610 = 10.0;
        double r7015611 = r7015610 * r7015605;
        double r7015612 = r7015609 + r7015611;
        double r7015613 = r7015605 * r7015605;
        double r7015614 = r7015612 + r7015613;
        double r7015615 = r7015608 / r7015614;
        return r7015615;
}
↓
double f(double a, double k, double m) {
        double r7015616 = k;
        double r7015617 = 3.765086051784335e+91;
        bool r7015618 = r7015616 <= r7015617;
        double r7015619 = m;
        double r7015620 = pow(r7015616, r7015619);
        double r7015621 = a;
        double r7015622 = r7015620 * r7015621;
        double r7015623 = 1.0;
        double r7015624 = 10.0;
        double r7015625 = r7015616 + r7015624;
        double r7015626 = r7015616 * r7015625;
        double r7015627 = r7015623 + r7015626;
        double r7015628 = r7015622 / r7015627;
        double r7015629 = log(r7015616);
        double r7015630 = r7015619 * r7015629;
        double r7015631 = exp(r7015630);
        double r7015632 = r7015616 * r7015616;
        double r7015633 = r7015631 / r7015632;
        double r7015634 = 99.0;
        double r7015635 = r7015621 * r7015634;
        double r7015636 = r7015635 / r7015632;
        double r7015637 = r7015633 * r7015636;
        double r7015638 = r7015621 / r7015616;
        double r7015639 = r7015631 / r7015616;
        double r7015640 = r7015638 * r7015639;
        double r7015641 = r7015631 * r7015624;
        double r7015642 = r7015641 / r7015632;
        double r7015643 = r7015642 * r7015638;
        double r7015644 = r7015640 - r7015643;
        double r7015645 = r7015637 + r7015644;
        double r7015646 = r7015618 ? r7015628 : r7015645;
        return r7015646;
}

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 < 3.765086051784335e+91

    1. Initial program 0.1

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

    2. Simplified0.1

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

    4. Applied associate-*l/0.1

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

    if 3.765086051784335e+91 < k

    1. Initial program 6.9

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

    2. Simplified6.9

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

    3. Taylor expanded around -inf 64.0

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

    4. Simplified0.2

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 3.765086051784335120389721235468612662668 \cdot 10^{91}:\\ \;\;\;\;\frac{{k}^{m} \cdot a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{m \cdot \log k}}{k \cdot k} \cdot \frac{a \cdot 99}{k \cdot k} + \left(\frac{a}{k} \cdot \frac{e^{m \cdot \log k}}{k} - \frac{e^{m \cdot \log k} \cdot 10}{k \cdot k} \cdot \frac{a}{k}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))