Average Error: 2.1 → 2.1
Time: 29.3s
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 r153498 = a;
        double r153499 = k;
        double r153500 = m;
        double r153501 = pow(r153499, r153500);
        double r153502 = r153498 * r153501;
        double r153503 = 1.0;
        double r153504 = 10.0;
        double r153505 = r153504 * r153499;
        double r153506 = r153503 + r153505;
        double r153507 = r153499 * r153499;
        double r153508 = r153506 + r153507;
        double r153509 = r153502 / r153508;
        return r153509;
}
↓
double f(double a, double k, double m) {
        double r153510 = a;
        double r153511 = k;
        double r153512 = 10.0;
        double r153513 = r153512 + r153511;
        double r153514 = r153511 * r153513;
        double r153515 = 1.0;
        double r153516 = r153514 + r153515;
        double r153517 = m;
        double r153518 = pow(r153511, r153517);
        double r153519 = r153516 / r153518;
        double r153520 = r153510 / r153519;
        return r153520;
}

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))))