Average Error: 1.9 → 1.9
Time: 10.6s
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 r226525 = a;
        double r226526 = k;
        double r226527 = m;
        double r226528 = pow(r226526, r226527);
        double r226529 = r226525 * r226528;
        double r226530 = 1.0;
        double r226531 = 10.0;
        double r226532 = r226531 * r226526;
        double r226533 = r226530 + r226532;
        double r226534 = r226526 * r226526;
        double r226535 = r226533 + r226534;
        double r226536 = r226529 / r226535;
        return r226536;
}
↓
double f(double a, double k, double m) {
        double r226537 = a;
        double r226538 = k;
        double r226539 = m;
        double r226540 = pow(r226538, r226539);
        double r226541 = cbrt(r226540);
        double r226542 = r226541 * r226541;
        double r226543 = r226537 * r226542;
        double r226544 = r226543 * r226541;
        double r226545 = 1.0;
        double r226546 = 10.0;
        double r226547 = r226546 * r226538;
        double r226548 = r226545 + r226547;
        double r226549 = r226538 * r226538;
        double r226550 = r226548 + r226549;
        double r226551 = r226544 / r226550;
        return r226551;
}

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 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))