Average Error: 2.0 → 2.0
Time: 19.0s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[{k}^{\left(\frac{m}{2}\right)} \cdot \left({k}^{\left(\frac{m}{2}\right)} \cdot \frac{a}{1 + \left(k + 10\right) \cdot k}\right)\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
{k}^{\left(\frac{m}{2}\right)} \cdot \left({k}^{\left(\frac{m}{2}\right)} \cdot \frac{a}{1 + \left(k + 10\right) \cdot k}\right)
double f(double a, double k, double m) {
        double r6139402 = a;
        double r6139403 = k;
        double r6139404 = m;
        double r6139405 = pow(r6139403, r6139404);
        double r6139406 = r6139402 * r6139405;
        double r6139407 = 1.0;
        double r6139408 = 10.0;
        double r6139409 = r6139408 * r6139403;
        double r6139410 = r6139407 + r6139409;
        double r6139411 = r6139403 * r6139403;
        double r6139412 = r6139410 + r6139411;
        double r6139413 = r6139406 / r6139412;
        return r6139413;
}
↓
double f(double a, double k, double m) {
        double r6139414 = k;
        double r6139415 = m;
        double r6139416 = 2.0;
        double r6139417 = r6139415 / r6139416;
        double r6139418 = pow(r6139414, r6139417);
        double r6139419 = a;
        double r6139420 = 1.0;
        double r6139421 = 10.0;
        double r6139422 = r6139414 + r6139421;
        double r6139423 = r6139422 * r6139414;
        double r6139424 = r6139420 + r6139423;
        double r6139425 = r6139419 / r6139424;
        double r6139426 = r6139418 * r6139425;
        double r6139427 = r6139418 * r6139426;
        return r6139427;
}

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 2.0

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

  2. Simplified2.0

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

  4. Applied sqr-pow2.0

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

  5. Applied associate-*r*2.0

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

  6. Final simplification2.0

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

Reproduce

herbie shell --seed 2019128 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))