Average Error: 2.0 → 2.0
Time: 6.9s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{{k}^{m}}{k \cdot \left(10 + k\right) + 1} \cdot a\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{{k}^{m}}{k \cdot \left(10 + k\right) + 1} \cdot a
double f(double a, double k, double m) {
        double r203860 = a;
        double r203861 = k;
        double r203862 = m;
        double r203863 = pow(r203861, r203862);
        double r203864 = r203860 * r203863;
        double r203865 = 1.0;
        double r203866 = 10.0;
        double r203867 = r203866 * r203861;
        double r203868 = r203865 + r203867;
        double r203869 = r203861 * r203861;
        double r203870 = r203868 + r203869;
        double r203871 = r203864 / r203870;
        return r203871;
}
↓
double f(double a, double k, double m) {
        double r203872 = k;
        double r203873 = m;
        double r203874 = pow(r203872, r203873);
        double r203875 = 10.0;
        double r203876 = r203875 + r203872;
        double r203877 = r203872 * r203876;
        double r203878 = 1.0;
        double r203879 = r203877 + r203878;
        double r203880 = r203874 / r203879;
        double r203881 = a;
        double r203882 = r203880 * r203881;
        return r203882;
}

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

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

  3. Final simplification2.0

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

Reproduce

herbie shell --seed 2020027 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))