Average Error: 1.9 → 1.9
Time: 48.0s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{\left(a \cdot \left(\sqrt[3]{{k}^{m}} \cdot \sqrt[3]{{k}^{m}}\right)\right) \cdot \sqrt[3]{{k}^{m}}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{\left(a \cdot \left(\sqrt[3]{{k}^{m}} \cdot \sqrt[3]{{k}^{m}}\right)\right) \cdot \sqrt[3]{{k}^{m}}}{\left(1 + 10 \cdot k\right) + k \cdot k}
double f(double a, double k, double m) {
        double r439404 = a;
        double r439405 = k;
        double r439406 = m;
        double r439407 = pow(r439405, r439406);
        double r439408 = r439404 * r439407;
        double r439409 = 1.0;
        double r439410 = 10.0;
        double r439411 = r439410 * r439405;
        double r439412 = r439409 + r439411;
        double r439413 = r439405 * r439405;
        double r439414 = r439412 + r439413;
        double r439415 = r439408 / r439414;
        return r439415;
}
↓
double f(double a, double k, double m) {
        double r439416 = a;
        double r439417 = k;
        double r439418 = m;
        double r439419 = pow(r439417, r439418);
        double r439420 = cbrt(r439419);
        double r439421 = r439420 * r439420;
        double r439422 = r439416 * r439421;
        double r439423 = r439422 * r439420;
        double r439424 = 1.0;
        double r439425 = 10.0;
        double r439426 = r439425 * r439417;
        double r439427 = r439424 + r439426;
        double r439428 = r439417 * r439417;
        double r439429 = r439427 + r439428;
        double r439430 = r439423 / r439429;
        return r439430;
}

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. Initial program 1.9

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

  3. Applied add-cube-cbrt1.9

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

  4. Applied associate-*r*1.9

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

  5. Final simplification1.9

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))