Average Error: 2.1 → 0.1
Time: 21.8s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 3.773758653310437 \cdot 10^{+141}:\\ \;\;\;\;\frac{{\left(\sqrt[3]{k}\right)}^{m} \cdot \left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right)}{\left(10 \cdot k + 1\right) + k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;e^{m \cdot \log k} \cdot \frac{\frac{a}{k}}{k} + \left(e^{m \cdot \log k} \cdot \frac{\frac{a}{k}}{k}\right) \cdot \left(\frac{99}{k \cdot k} - \frac{10}{k}\right)\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 3.773758653310437 \cdot 10^{+141}:\\
\;\;\;\;\frac{{\left(\sqrt[3]{k}\right)}^{m} \cdot \left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right)}{\left(10 \cdot k + 1\right) + k \cdot k}\\

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

\end{array}
double f(double a, double k, double m) {
        double r7687102 = a;
        double r7687103 = k;
        double r7687104 = m;
        double r7687105 = pow(r7687103, r7687104);
        double r7687106 = r7687102 * r7687105;
        double r7687107 = 1.0;
        double r7687108 = 10.0;
        double r7687109 = r7687108 * r7687103;
        double r7687110 = r7687107 + r7687109;
        double r7687111 = r7687103 * r7687103;
        double r7687112 = r7687110 + r7687111;
        double r7687113 = r7687106 / r7687112;
        return r7687113;
}
↓
double f(double a, double k, double m) {
        double r7687114 = k;
        double r7687115 = 3.773758653310437e+141;
        bool r7687116 = r7687114 <= r7687115;
        double r7687117 = cbrt(r7687114);
        double r7687118 = m;
        double r7687119 = pow(r7687117, r7687118);
        double r7687120 = a;
        double r7687121 = r7687117 * r7687117;
        double r7687122 = pow(r7687121, r7687118);
        double r7687123 = r7687120 * r7687122;
        double r7687124 = r7687119 * r7687123;
        double r7687125 = 10.0;
        double r7687126 = r7687125 * r7687114;
        double r7687127 = 1.0;
        double r7687128 = r7687126 + r7687127;
        double r7687129 = r7687114 * r7687114;
        double r7687130 = r7687128 + r7687129;
        double r7687131 = r7687124 / r7687130;
        double r7687132 = log(r7687114);
        double r7687133 = r7687118 * r7687132;
        double r7687134 = exp(r7687133);
        double r7687135 = r7687120 / r7687114;
        double r7687136 = r7687135 / r7687114;
        double r7687137 = r7687134 * r7687136;
        double r7687138 = 99.0;
        double r7687139 = r7687138 / r7687129;
        double r7687140 = r7687125 / r7687114;
        double r7687141 = r7687139 - r7687140;
        double r7687142 = r7687137 * r7687141;
        double r7687143 = r7687137 + r7687142;
        double r7687144 = r7687116 ? r7687131 : r7687143;
        return r7687144;
}

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 < 3.773758653310437e+141

    1. Initial program 0.1

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

    3. Applied add-cube-cbrt0.1

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

    4. Applied unpow-prod-down0.1

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

    5. Applied associate-*r*0.1

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

    if 3.773758653310437e+141 < k

    1. Initial program 9.7

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

    2. Taylor expanded around -inf 63.0

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

    3. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 3.773758653310437 \cdot 10^{+141}:\\ \;\;\;\;\frac{{\left(\sqrt[3]{k}\right)}^{m} \cdot \left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right)}{\left(10 \cdot k + 1\right) + k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;e^{m \cdot \log k} \cdot \frac{\frac{a}{k}}{k} + \left(e^{m \cdot \log k} \cdot \frac{\frac{a}{k}}{k}\right) \cdot \left(\frac{99}{k \cdot k} - \frac{10}{k}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019133 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))