Average Error: 2.3 → 2.3
Time: 4.9s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{\left(a \cdot \sqrt{{k}^{m}}\right) \cdot \sqrt{{k}^{m}}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{\left(a \cdot \sqrt{{k}^{m}}\right) \cdot \sqrt{{k}^{m}}}{\left(1 + 10 \cdot k\right) + k \cdot k}
double f(double a, double k, double m) {
        double r149599 = a;
        double r149600 = k;
        double r149601 = m;
        double r149602 = pow(r149600, r149601);
        double r149603 = r149599 * r149602;
        double r149604 = 1.0;
        double r149605 = 10.0;
        double r149606 = r149605 * r149600;
        double r149607 = r149604 + r149606;
        double r149608 = r149600 * r149600;
        double r149609 = r149607 + r149608;
        double r149610 = r149603 / r149609;
        return r149610;
}
↓
double f(double a, double k, double m) {
        double r149611 = a;
        double r149612 = k;
        double r149613 = m;
        double r149614 = pow(r149612, r149613);
        double r149615 = sqrt(r149614);
        double r149616 = r149611 * r149615;
        double r149617 = r149616 * r149615;
        double r149618 = 1.0;
        double r149619 = 10.0;
        double r149620 = r149619 * r149612;
        double r149621 = r149618 + r149620;
        double r149622 = r149612 * r149612;
        double r149623 = r149621 + r149622;
        double r149624 = r149617 / r149623;
        return r149624;
}

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 2.3

    \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt2.3

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

  4. Applied associate-*r*2.3

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

  5. Final simplification2.3

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

Reproduce

herbie shell --seed 2020065 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))