Average Error: 2.0 → 0.2
Time: 32.4s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 8.36290345728224 \cdot 10^{+141}:\\ \;\;\;\;\frac{a \cdot {k}^{m}}{k \cdot k + \left(k \cdot 10 + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{k}{a} \cdot \frac{k}{e^{m \cdot \log k}} + \left(\frac{\frac{k \cdot 10}{a}}{e^{m \cdot \log k}} + \frac{\frac{1}{e^{m \cdot \log k}}}{a}\right)}\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 8.36290345728224 \cdot 10^{+141}:\\
\;\;\;\;\frac{a \cdot {k}^{m}}{k \cdot k + \left(k \cdot 10 + 1\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{k}{a} \cdot \frac{k}{e^{m \cdot \log k}} + \left(\frac{\frac{k \cdot 10}{a}}{e^{m \cdot \log k}} + \frac{\frac{1}{e^{m \cdot \log k}}}{a}\right)}\\

\end{array}
double f(double a, double k, double m) {
        double r6391503 = a;
        double r6391504 = k;
        double r6391505 = m;
        double r6391506 = pow(r6391504, r6391505);
        double r6391507 = r6391503 * r6391506;
        double r6391508 = 1.0;
        double r6391509 = 10.0;
        double r6391510 = r6391509 * r6391504;
        double r6391511 = r6391508 + r6391510;
        double r6391512 = r6391504 * r6391504;
        double r6391513 = r6391511 + r6391512;
        double r6391514 = r6391507 / r6391513;
        return r6391514;
}
↓
double f(double a, double k, double m) {
        double r6391515 = k;
        double r6391516 = 8.36290345728224e+141;
        bool r6391517 = r6391515 <= r6391516;
        double r6391518 = a;
        double r6391519 = m;
        double r6391520 = pow(r6391515, r6391519);
        double r6391521 = r6391518 * r6391520;
        double r6391522 = r6391515 * r6391515;
        double r6391523 = 10.0;
        double r6391524 = r6391515 * r6391523;
        double r6391525 = 1.0;
        double r6391526 = r6391524 + r6391525;
        double r6391527 = r6391522 + r6391526;
        double r6391528 = r6391521 / r6391527;
        double r6391529 = r6391515 / r6391518;
        double r6391530 = log(r6391515);
        double r6391531 = r6391519 * r6391530;
        double r6391532 = exp(r6391531);
        double r6391533 = r6391515 / r6391532;
        double r6391534 = r6391529 * r6391533;
        double r6391535 = r6391524 / r6391518;
        double r6391536 = r6391535 / r6391532;
        double r6391537 = r6391525 / r6391532;
        double r6391538 = r6391537 / r6391518;
        double r6391539 = r6391536 + r6391538;
        double r6391540 = r6391534 + r6391539;
        double r6391541 = r6391525 / r6391540;
        double r6391542 = r6391517 ? r6391528 : r6391541;
        return r6391542;
}

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 < 8.36290345728224e+141

    1. Initial program 0.1

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

    if 8.36290345728224e+141 < k

    1. Initial program 9.8

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

    3. Applied clear-num9.8

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

    4. Simplified9.8

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

    5. Taylor expanded around inf 9.8

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

    6. Simplified0.5

      \[\leadsto \frac{1}{\color{blue}{\left(\frac{\frac{10 \cdot k}{a}}{e^{\left(-m\right) \cdot \left(-\log k\right)}} + \frac{\frac{1}{e^{\left(-m\right) \cdot \left(-\log k\right)}}}{a}\right) + \frac{k}{a} \cdot \frac{k}{e^{\left(-m\right) \cdot \left(-\log k\right)}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 8.36290345728224 \cdot 10^{+141}:\\ \;\;\;\;\frac{a \cdot {k}^{m}}{k \cdot k + \left(k \cdot 10 + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{k}{a} \cdot \frac{k}{e^{m \cdot \log k}} + \left(\frac{\frac{k \cdot 10}{a}}{e^{m \cdot \log k}} + \frac{\frac{1}{e^{m \cdot \log k}}}{a}\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019152 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))