Average Error: 2.2 → 2.2
Time: 6.6s
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 r215279 = a;
        double r215280 = k;
        double r215281 = m;
        double r215282 = pow(r215280, r215281);
        double r215283 = r215279 * r215282;
        double r215284 = 1.0;
        double r215285 = 10.0;
        double r215286 = r215285 * r215280;
        double r215287 = r215284 + r215286;
        double r215288 = r215280 * r215280;
        double r215289 = r215287 + r215288;
        double r215290 = r215283 / r215289;
        return r215290;
}
↓
double f(double a, double k, double m) {
        double r215291 = a;
        double r215292 = k;
        double r215293 = m;
        double r215294 = pow(r215292, r215293);
        double r215295 = r215291 * r215294;
        double r215296 = 1.0;
        double r215297 = 10.0;
        double r215298 = r215297 * r215292;
        double r215299 = r215296 + r215298;
        double r215300 = r215292 * r215292;
        double r215301 = r215299 + r215300;
        double r215302 = r215295 / r215301;
        return r215302;
}

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