Average Error: 2.1 → 2.1
Time: 28.3s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{a}{\frac{k \cdot \left(10 + k\right) + 1}{{k}^{m}}}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{a}{\frac{k \cdot \left(10 + k\right) + 1}{{k}^{m}}}
double f(double a, double k, double m) {
        double r189317 = a;
        double r189318 = k;
        double r189319 = m;
        double r189320 = pow(r189318, r189319);
        double r189321 = r189317 * r189320;
        double r189322 = 1.0;
        double r189323 = 10.0;
        double r189324 = r189323 * r189318;
        double r189325 = r189322 + r189324;
        double r189326 = r189318 * r189318;
        double r189327 = r189325 + r189326;
        double r189328 = r189321 / r189327;
        return r189328;
}
↓
double f(double a, double k, double m) {
        double r189329 = a;
        double r189330 = k;
        double r189331 = 10.0;
        double r189332 = r189331 + r189330;
        double r189333 = r189330 * r189332;
        double r189334 = 1.0;
        double r189335 = r189333 + r189334;
        double r189336 = m;
        double r189337 = pow(r189330, r189336);
        double r189338 = r189335 / r189337;
        double r189339 = r189329 / r189338;
        return r189339;
}

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 2.1

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

  2. Simplified2.1

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

  3. Final simplification2.1

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

Reproduce

herbie shell --seed 2019326 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))