Average Error: 2.1 → 2.1
Time: 4.4s
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 r292961 = a;
        double r292962 = k;
        double r292963 = m;
        double r292964 = pow(r292962, r292963);
        double r292965 = r292961 * r292964;
        double r292966 = 1.0;
        double r292967 = 10.0;
        double r292968 = r292967 * r292962;
        double r292969 = r292966 + r292968;
        double r292970 = r292962 * r292962;
        double r292971 = r292969 + r292970;
        double r292972 = r292965 / r292971;
        return r292972;
}
↓
double f(double a, double k, double m) {
        double r292973 = a;
        double r292974 = k;
        double r292975 = m;
        double r292976 = pow(r292974, r292975);
        double r292977 = r292973 * r292976;
        double r292978 = 1.0;
        double r292979 = 10.0;
        double r292980 = r292979 * r292974;
        double r292981 = r292978 + r292980;
        double r292982 = r292974 * r292974;
        double r292983 = r292981 + r292982;
        double r292984 = r292977 / r292983;
        return r292984;
}

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. Final simplification2.1

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

Reproduce

herbie shell --seed 2020062 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))