Average Error: 2.2 → 2.2
Time: 7.0s
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 r273081 = a;
        double r273082 = k;
        double r273083 = m;
        double r273084 = pow(r273082, r273083);
        double r273085 = r273081 * r273084;
        double r273086 = 1.0;
        double r273087 = 10.0;
        double r273088 = r273087 * r273082;
        double r273089 = r273086 + r273088;
        double r273090 = r273082 * r273082;
        double r273091 = r273089 + r273090;
        double r273092 = r273085 / r273091;
        return r273092;
}
↓
double f(double a, double k, double m) {
        double r273093 = a;
        double r273094 = k;
        double r273095 = m;
        double r273096 = pow(r273094, r273095);
        double r273097 = r273093 * r273096;
        double r273098 = 1.0;
        double r273099 = 10.0;
        double r273100 = r273099 * r273094;
        double r273101 = r273098 + r273100;
        double r273102 = r273094 * r273094;
        double r273103 = r273101 + r273102;
        double r273104 = r273097 / r273103;
        return r273104;
}

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 2020036 +o rules:numerics
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))