Average Error: 2.2 → 2.2
Time: 3.6s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
double f(double a, double k, double m) {
        double r350944 = a;
        double r350945 = k;
        double r350946 = m;
        double r350947 = pow(r350945, r350946);
        double r350948 = r350944 * r350947;
        double r350949 = 1.0;
        double r350950 = 10.0;
        double r350951 = r350950 * r350945;
        double r350952 = r350949 + r350951;
        double r350953 = r350945 * r350945;
        double r350954 = r350952 + r350953;
        double r350955 = r350948 / r350954;
        return r350955;
}
↓
double f(double a, double k, double m) {
        double r350956 = a;
        double r350957 = k;
        double r350958 = m;
        double r350959 = pow(r350957, r350958);
        double r350960 = r350956 * r350959;
        double r350961 = 1.0;
        double r350962 = 10.0;
        double r350963 = r350962 * r350957;
        double r350964 = r350961 + r350963;
        double r350965 = r350957 * r350957;
        double r350966 = r350964 + r350965;
        double r350967 = r350960 / r350966;
        return r350967;
}

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. Final simplification2.2

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

Reproduce

herbie shell --seed 2020001 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))