Average Error: 2.3 → 2.3
Time: 22.7s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{{\left(\sqrt[3]{k}\right)}^{m} \cdot \left({\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m} \cdot a\right)}{\left(10 \cdot k + 1\right) + k \cdot k}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{{\left(\sqrt[3]{k}\right)}^{m} \cdot \left({\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m} \cdot a\right)}{\left(10 \cdot k + 1\right) + k \cdot k}
double f(double a, double k, double m) {
        double r9018157 = a;
        double r9018158 = k;
        double r9018159 = m;
        double r9018160 = pow(r9018158, r9018159);
        double r9018161 = r9018157 * r9018160;
        double r9018162 = 1.0;
        double r9018163 = 10.0;
        double r9018164 = r9018163 * r9018158;
        double r9018165 = r9018162 + r9018164;
        double r9018166 = r9018158 * r9018158;
        double r9018167 = r9018165 + r9018166;
        double r9018168 = r9018161 / r9018167;
        return r9018168;
}
↓
double f(double a, double k, double m) {
        double r9018169 = k;
        double r9018170 = cbrt(r9018169);
        double r9018171 = m;
        double r9018172 = pow(r9018170, r9018171);
        double r9018173 = r9018170 * r9018170;
        double r9018174 = pow(r9018173, r9018171);
        double r9018175 = a;
        double r9018176 = r9018174 * r9018175;
        double r9018177 = r9018172 * r9018176;
        double r9018178 = 10.0;
        double r9018179 = r9018178 * r9018169;
        double r9018180 = 1.0;
        double r9018181 = r9018179 + r9018180;
        double r9018182 = r9018169 * r9018169;
        double r9018183 = r9018181 + r9018182;
        double r9018184 = r9018177 / r9018183;
        return r9018184;
}

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-cube-cbrt2.3

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

  4. Applied unpow-prod-down2.3

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

  5. Applied associate-*r*2.3

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

  6. Final simplification2.3

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))