Average Error: 1.9 → 1.9
Time: 10.7s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{\left(a \cdot \left(\sqrt[3]{{k}^{m}} \cdot \sqrt[3]{{k}^{m}}\right)\right) \cdot \sqrt[3]{{k}^{m}}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{\left(a \cdot \left(\sqrt[3]{{k}^{m}} \cdot \sqrt[3]{{k}^{m}}\right)\right) \cdot \sqrt[3]{{k}^{m}}}{\left(1 + 10 \cdot k\right) + k \cdot k}
double f(double a, double k, double m) {
        double r203207 = a;
        double r203208 = k;
        double r203209 = m;
        double r203210 = pow(r203208, r203209);
        double r203211 = r203207 * r203210;
        double r203212 = 1.0;
        double r203213 = 10.0;
        double r203214 = r203213 * r203208;
        double r203215 = r203212 + r203214;
        double r203216 = r203208 * r203208;
        double r203217 = r203215 + r203216;
        double r203218 = r203211 / r203217;
        return r203218;
}
↓
double f(double a, double k, double m) {
        double r203219 = a;
        double r203220 = k;
        double r203221 = m;
        double r203222 = pow(r203220, r203221);
        double r203223 = cbrt(r203222);
        double r203224 = r203223 * r203223;
        double r203225 = r203219 * r203224;
        double r203226 = r203225 * r203223;
        double r203227 = 1.0;
        double r203228 = 10.0;
        double r203229 = r203228 * r203220;
        double r203230 = r203227 + r203229;
        double r203231 = r203220 * r203220;
        double r203232 = r203230 + r203231;
        double r203233 = r203226 / r203232;
        return r203233;
}

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 1.9

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

  3. Applied add-cube-cbrt1.9

    \[\leadsto \frac{a \cdot \color{blue}{\left(\left(\sqrt[3]{{k}^{m}} \cdot \sqrt[3]{{k}^{m}}\right) \cdot \sqrt[3]{{k}^{m}}\right)}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

  4. Applied associate-*r*1.9

    \[\leadsto \frac{\color{blue}{\left(a \cdot \left(\sqrt[3]{{k}^{m}} \cdot \sqrt[3]{{k}^{m}}\right)\right) \cdot \sqrt[3]{{k}^{m}}}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

  5. Final simplification1.9

    \[\leadsto \frac{\left(a \cdot \left(\sqrt[3]{{k}^{m}} \cdot \sqrt[3]{{k}^{m}}\right)\right) \cdot \sqrt[3]{{k}^{m}}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

Reproduce

herbie shell --seed 2020042 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))