Average Error: 2.0 → 0.1
Time: 29.0s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 7.732202330022239197363373519907478595424 \cdot 10^{109}:\\ \;\;\;\;\frac{a}{\frac{\frac{k \cdot \left(10 + k\right) + 1}{{\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}}}{{\left(\sqrt[3]{k}\right)}^{m}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k} - \frac{e^{\log k \cdot m} \cdot 10}{\frac{{k}^{3}}{a}}\right) + \frac{99 \cdot \left(a \cdot e^{\log k \cdot m}\right)}{{k}^{4}}\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 7.732202330022239197363373519907478595424 \cdot 10^{109}:\\
\;\;\;\;\frac{a}{\frac{\frac{k \cdot \left(10 + k\right) + 1}{{\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}}}{{\left(\sqrt[3]{k}\right)}^{m}}}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k} - \frac{e^{\log k \cdot m} \cdot 10}{\frac{{k}^{3}}{a}}\right) + \frac{99 \cdot \left(a \cdot e^{\log k \cdot m}\right)}{{k}^{4}}\\

\end{array}
double f(double a, double k, double m) {
        double r233365 = a;
        double r233366 = k;
        double r233367 = m;
        double r233368 = pow(r233366, r233367);
        double r233369 = r233365 * r233368;
        double r233370 = 1.0;
        double r233371 = 10.0;
        double r233372 = r233371 * r233366;
        double r233373 = r233370 + r233372;
        double r233374 = r233366 * r233366;
        double r233375 = r233373 + r233374;
        double r233376 = r233369 / r233375;
        return r233376;
}
↓
double f(double a, double k, double m) {
        double r233377 = k;
        double r233378 = 7.73220233002224e+109;
        bool r233379 = r233377 <= r233378;
        double r233380 = a;
        double r233381 = 10.0;
        double r233382 = r233381 + r233377;
        double r233383 = r233377 * r233382;
        double r233384 = 1.0;
        double r233385 = r233383 + r233384;
        double r233386 = cbrt(r233377);
        double r233387 = r233386 * r233386;
        double r233388 = m;
        double r233389 = pow(r233387, r233388);
        double r233390 = r233385 / r233389;
        double r233391 = pow(r233386, r233388);
        double r233392 = r233390 / r233391;
        double r233393 = r233380 / r233392;
        double r233394 = r233380 / r233377;
        double r233395 = log(r233377);
        double r233396 = r233395 * r233388;
        double r233397 = exp(r233396);
        double r233398 = r233397 / r233377;
        double r233399 = r233394 * r233398;
        double r233400 = r233397 * r233381;
        double r233401 = 3.0;
        double r233402 = pow(r233377, r233401);
        double r233403 = r233402 / r233380;
        double r233404 = r233400 / r233403;
        double r233405 = r233399 - r233404;
        double r233406 = 99.0;
        double r233407 = r233380 * r233397;
        double r233408 = r233406 * r233407;
        double r233409 = 4.0;
        double r233410 = pow(r233377, r233409);
        double r233411 = r233408 / r233410;
        double r233412 = r233405 + r233411;
        double r233413 = r233379 ? r233393 : r233412;
        return r233413;
}

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 < 7.73220233002224e+109

    1. Initial program 0.1

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

    2. Simplified0.1

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

    4. Applied add-cube-cbrt0.1

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

    5. Applied unpow-prod-down0.1

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

    6. Applied associate-/r*0.1

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

    7. Simplified0.1

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

    if 7.73220233002224e+109 < k

    1. Initial program 7.9

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

    2. Simplified7.9

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

    3. Taylor expanded around inf 7.9

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

    4. Simplified0.2

      \[\leadsto \color{blue}{\frac{99 \cdot \left(e^{-\left(-m \cdot \log k\right)} \cdot a\right)}{{k}^{4}} + \left(\frac{e^{-\left(-m \cdot \log k\right)}}{k} \cdot \frac{a}{k} - \frac{e^{-\left(-m \cdot \log k\right)} \cdot 10}{\frac{{k}^{3}}{a}}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 7.732202330022239197363373519907478595424 \cdot 10^{109}:\\ \;\;\;\;\frac{a}{\frac{\frac{k \cdot \left(10 + k\right) + 1}{{\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}}}{{\left(\sqrt[3]{k}\right)}^{m}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{k} \cdot \frac{e^{\log k \cdot m}}{k} - \frac{e^{\log k \cdot m} \cdot 10}{\frac{{k}^{3}}{a}}\right) + \frac{99 \cdot \left(a \cdot e^{\log k \cdot m}\right)}{{k}^{4}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))