Average Error: 2.2 → 2.2
Time: 3.9s
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 r178568 = a;
        double r178569 = k;
        double r178570 = m;
        double r178571 = pow(r178569, r178570);
        double r178572 = r178568 * r178571;
        double r178573 = 1.0;
        double r178574 = 10.0;
        double r178575 = r178574 * r178569;
        double r178576 = r178573 + r178575;
        double r178577 = r178569 * r178569;
        double r178578 = r178576 + r178577;
        double r178579 = r178572 / r178578;
        return r178579;
}
↓
double f(double a, double k, double m) {
        double r178580 = a;
        double r178581 = k;
        double r178582 = m;
        double r178583 = pow(r178581, r178582);
        double r178584 = r178580 * r178583;
        double r178585 = 1.0;
        double r178586 = 10.0;
        double r178587 = r178586 * r178581;
        double r178588 = r178585 + r178587;
        double r178589 = r178581 * r178581;
        double r178590 = r178588 + r178589;
        double r178591 = r178584 / r178590;
        return r178591;
}

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 2020001 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))