Average Error: 2.2 → 2.1
Time: 3.9s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{{k}^{m}}{k \cdot \left(10 + k\right) + 1} \cdot a\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{{k}^{m}}{k \cdot \left(10 + k\right) + 1} \cdot a
double f(double a, double k, double m) {
        double r326721 = a;
        double r326722 = k;
        double r326723 = m;
        double r326724 = pow(r326722, r326723);
        double r326725 = r326721 * r326724;
        double r326726 = 1.0;
        double r326727 = 10.0;
        double r326728 = r326727 * r326722;
        double r326729 = r326726 + r326728;
        double r326730 = r326722 * r326722;
        double r326731 = r326729 + r326730;
        double r326732 = r326725 / r326731;
        return r326732;
}
↓
double f(double a, double k, double m) {
        double r326733 = k;
        double r326734 = m;
        double r326735 = pow(r326733, r326734);
        double r326736 = 10.0;
        double r326737 = r326736 + r326733;
        double r326738 = r326733 * r326737;
        double r326739 = 1.0;
        double r326740 = r326738 + r326739;
        double r326741 = r326735 / r326740;
        double r326742 = a;
        double r326743 = r326741 * r326742;
        return r326743;
}

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. Simplified2.1

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

  3. Final simplification2.1

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

Reproduce

herbie shell --seed 2020039 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))