Average Error: 2.2 → 2.2
Time: 4.4s
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 r250951 = a;
        double r250952 = k;
        double r250953 = m;
        double r250954 = pow(r250952, r250953);
        double r250955 = r250951 * r250954;
        double r250956 = 1.0;
        double r250957 = 10.0;
        double r250958 = r250957 * r250952;
        double r250959 = r250956 + r250958;
        double r250960 = r250952 * r250952;
        double r250961 = r250959 + r250960;
        double r250962 = r250955 / r250961;
        return r250962;
}
↓
double f(double a, double k, double m) {
        double r250963 = k;
        double r250964 = m;
        double r250965 = pow(r250963, r250964);
        double r250966 = 10.0;
        double r250967 = r250966 + r250963;
        double r250968 = r250963 * r250967;
        double r250969 = 1.0;
        double r250970 = r250968 + r250969;
        double r250971 = r250965 / r250970;
        double r250972 = a;
        double r250973 = r250971 * r250972;
        return r250973;
}

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 2.2

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

  2. Simplified2.2

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

  3. Final simplification2.2

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

Reproduce

herbie shell --seed 2020018 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))