Average Error: 2.1 → 2.1
Time: 3.3s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{a}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}} \cdot \frac{{k}^{m}}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{a}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}} \cdot \frac{{k}^{m}}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}
double f(double a, double k, double m) {
        double r330178 = a;
        double r330179 = k;
        double r330180 = m;
        double r330181 = pow(r330179, r330180);
        double r330182 = r330178 * r330181;
        double r330183 = 1.0;
        double r330184 = 10.0;
        double r330185 = r330184 * r330179;
        double r330186 = r330183 + r330185;
        double r330187 = r330179 * r330179;
        double r330188 = r330186 + r330187;
        double r330189 = r330182 / r330188;
        return r330189;
}
↓
double f(double a, double k, double m) {
        double r330190 = a;
        double r330191 = 1.0;
        double r330192 = 10.0;
        double r330193 = k;
        double r330194 = r330192 * r330193;
        double r330195 = r330191 + r330194;
        double r330196 = r330193 * r330193;
        double r330197 = r330195 + r330196;
        double r330198 = sqrt(r330197);
        double r330199 = r330190 / r330198;
        double r330200 = m;
        double r330201 = pow(r330193, r330200);
        double r330202 = r330201 / r330198;
        double r330203 = r330199 * r330202;
        return r330203;
}

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 2.1

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

  3. Applied add-sqr-sqrt2.1

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

  4. Applied times-frac2.1

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

  5. Final simplification2.1

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

Reproduce

herbie shell --seed 2020033 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))