Average Error: 2.1 → 2.1
Time: 4.3s
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 r184194 = a;
        double r184195 = k;
        double r184196 = m;
        double r184197 = pow(r184195, r184196);
        double r184198 = r184194 * r184197;
        double r184199 = 1.0;
        double r184200 = 10.0;
        double r184201 = r184200 * r184195;
        double r184202 = r184199 + r184201;
        double r184203 = r184195 * r184195;
        double r184204 = r184202 + r184203;
        double r184205 = r184198 / r184204;
        return r184205;
}
↓
double f(double a, double k, double m) {
        double r184206 = a;
        double r184207 = k;
        double r184208 = m;
        double r184209 = pow(r184207, r184208);
        double r184210 = r184206 * r184209;
        double r184211 = 1.0;
        double r184212 = 10.0;
        double r184213 = r184212 * r184207;
        double r184214 = r184211 + r184213;
        double r184215 = r184207 * r184207;
        double r184216 = r184214 + r184215;
        double r184217 = r184210 / r184216;
        return r184217;
}

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))))