Average Error: 2.1 → 0.1
Time: 31.4s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 76238299450607616000:\\ \;\;\;\;\frac{{k}^{m}}{k \cdot \left(10 + k\right) + 1} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k} + \left(\frac{e^{\log k \cdot m}}{k \cdot k} \cdot \frac{a}{k \cdot k}\right) \cdot 99\right) - \frac{10 \cdot e^{\log k \cdot m}}{k \cdot k} \cdot \frac{a}{k}\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 76238299450607616000:\\
\;\;\;\;\frac{{k}^{m}}{k \cdot \left(10 + k\right) + 1} \cdot a\\

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

\end{array}
double f(double a, double k, double m) {
        double r8914658 = a;
        double r8914659 = k;
        double r8914660 = m;
        double r8914661 = pow(r8914659, r8914660);
        double r8914662 = r8914658 * r8914661;
        double r8914663 = 1.0;
        double r8914664 = 10.0;
        double r8914665 = r8914664 * r8914659;
        double r8914666 = r8914663 + r8914665;
        double r8914667 = r8914659 * r8914659;
        double r8914668 = r8914666 + r8914667;
        double r8914669 = r8914662 / r8914668;
        return r8914669;
}
↓
double f(double a, double k, double m) {
        double r8914670 = k;
        double r8914671 = 7.623829945060762e+19;
        bool r8914672 = r8914670 <= r8914671;
        double r8914673 = m;
        double r8914674 = pow(r8914670, r8914673);
        double r8914675 = 10.0;
        double r8914676 = r8914675 + r8914670;
        double r8914677 = r8914670 * r8914676;
        double r8914678 = 1.0;
        double r8914679 = r8914677 + r8914678;
        double r8914680 = r8914674 / r8914679;
        double r8914681 = a;
        double r8914682 = r8914680 * r8914681;
        double r8914683 = r8914681 / r8914670;
        double r8914684 = log(r8914670);
        double r8914685 = r8914684 * r8914673;
        double r8914686 = exp(r8914685);
        double r8914687 = r8914686 / r8914670;
        double r8914688 = r8914683 * r8914687;
        double r8914689 = r8914670 * r8914670;
        double r8914690 = r8914686 / r8914689;
        double r8914691 = r8914681 / r8914689;
        double r8914692 = r8914690 * r8914691;
        double r8914693 = 99.0;
        double r8914694 = r8914692 * r8914693;
        double r8914695 = r8914688 + r8914694;
        double r8914696 = r8914675 * r8914686;
        double r8914697 = r8914696 / r8914689;
        double r8914698 = r8914697 * r8914683;
        double r8914699 = r8914695 - r8914698;
        double r8914700 = r8914672 ? r8914682 : r8914699;
        return r8914700;
}

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 < 7.623829945060762e+19

    1. Initial program 0.1

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

    2. Simplified0.0

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

    if 7.623829945060762e+19 < k

    1. Initial program 5.7

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

    2. Simplified5.7

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

    4. Applied add-sqr-sqrt5.7

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

    5. Applied *-un-lft-identity5.7

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

    6. Applied times-frac5.7

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

    7. Applied associate-*l*5.7

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

    8. Taylor expanded around -inf 64.0

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

    9. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 76238299450607616000:\\ \;\;\;\;\frac{{k}^{m}}{k \cdot \left(10 + k\right) + 1} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k} + \left(\frac{e^{\log k \cdot m}}{k \cdot k} \cdot \frac{a}{k \cdot k}\right) \cdot 99\right) - \frac{10 \cdot e^{\log k \cdot m}}{k \cdot k} \cdot \frac{a}{k}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))