Average Error: 2.0 → 2.0
Time: 17.0s
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 r273770 = a;
        double r273771 = k;
        double r273772 = m;
        double r273773 = pow(r273771, r273772);
        double r273774 = r273770 * r273773;
        double r273775 = 1.0;
        double r273776 = 10.0;
        double r273777 = r273776 * r273771;
        double r273778 = r273775 + r273777;
        double r273779 = r273771 * r273771;
        double r273780 = r273778 + r273779;
        double r273781 = r273774 / r273780;
        return r273781;
}
↓
double f(double a, double k, double m) {
        double r273782 = a;
        double r273783 = k;
        double r273784 = m;
        double r273785 = pow(r273783, r273784);
        double r273786 = r273782 * r273785;
        double r273787 = 1.0;
        double r273788 = 10.0;
        double r273789 = r273788 * r273783;
        double r273790 = r273787 + r273789;
        double r273791 = r273783 * r273783;
        double r273792 = r273790 + r273791;
        double r273793 = r273786 / r273792;
        return r273793;
}

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))))