Average Error: 2.1 → 0.1
Time: 31.0s
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 r9091804 = a;
        double r9091805 = k;
        double r9091806 = m;
        double r9091807 = pow(r9091805, r9091806);
        double r9091808 = r9091804 * r9091807;
        double r9091809 = 1.0;
        double r9091810 = 10.0;
        double r9091811 = r9091810 * r9091805;
        double r9091812 = r9091809 + r9091811;
        double r9091813 = r9091805 * r9091805;
        double r9091814 = r9091812 + r9091813;
        double r9091815 = r9091808 / r9091814;
        return r9091815;
}
↓
double f(double a, double k, double m) {
        double r9091816 = k;
        double r9091817 = 7.623829945060762e+19;
        bool r9091818 = r9091816 <= r9091817;
        double r9091819 = m;
        double r9091820 = pow(r9091816, r9091819);
        double r9091821 = 10.0;
        double r9091822 = r9091821 + r9091816;
        double r9091823 = r9091816 * r9091822;
        double r9091824 = 1.0;
        double r9091825 = r9091823 + r9091824;
        double r9091826 = r9091820 / r9091825;
        double r9091827 = a;
        double r9091828 = r9091826 * r9091827;
        double r9091829 = r9091827 / r9091816;
        double r9091830 = log(r9091816);
        double r9091831 = r9091830 * r9091819;
        double r9091832 = exp(r9091831);
        double r9091833 = r9091832 / r9091816;
        double r9091834 = r9091829 * r9091833;
        double r9091835 = r9091816 * r9091816;
        double r9091836 = r9091832 / r9091835;
        double r9091837 = r9091827 / r9091835;
        double r9091838 = r9091836 * r9091837;
        double r9091839 = 99.0;
        double r9091840 = r9091838 * r9091839;
        double r9091841 = r9091834 + r9091840;
        double r9091842 = r9091821 * r9091832;
        double r9091843 = r9091842 / r9091835;
        double r9091844 = r9091843 * r9091829;
        double r9091845 = r9091841 - r9091844;
        double r9091846 = r9091818 ? r9091828 : r9091845;
        return r9091846;
}

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))))