Average Error: 2.0 → 2.0
Time: 17.4s
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 r155067 = a;
        double r155068 = k;
        double r155069 = m;
        double r155070 = pow(r155068, r155069);
        double r155071 = r155067 * r155070;
        double r155072 = 1.0;
        double r155073 = 10.0;
        double r155074 = r155073 * r155068;
        double r155075 = r155072 + r155074;
        double r155076 = r155068 * r155068;
        double r155077 = r155075 + r155076;
        double r155078 = r155071 / r155077;
        return r155078;
}
↓
double f(double a, double k, double m) {
        double r155079 = a;
        double r155080 = k;
        double r155081 = m;
        double r155082 = pow(r155080, r155081);
        double r155083 = r155079 * r155082;
        double r155084 = 1.0;
        double r155085 = 10.0;
        double r155086 = r155085 * r155080;
        double r155087 = r155084 + r155086;
        double r155088 = r155080 * r155080;
        double r155089 = r155087 + r155088;
        double r155090 = r155083 / r155089;
        return r155090;
}

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. Final simplification2.0

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

Reproduce

herbie shell --seed 2019325 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))