Average Error: 2.3 → 2.3
Time: 18.9s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{\left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot {\left(\sqrt[3]{k}\right)}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{\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}
double f(double a, double k, double m) {
        double r133295 = a;
        double r133296 = k;
        double r133297 = m;
        double r133298 = pow(r133296, r133297);
        double r133299 = r133295 * r133298;
        double r133300 = 1.0;
        double r133301 = 10.0;
        double r133302 = r133301 * r133296;
        double r133303 = r133300 + r133302;
        double r133304 = r133296 * r133296;
        double r133305 = r133303 + r133304;
        double r133306 = r133299 / r133305;
        return r133306;
}
↓
double f(double a, double k, double m) {
        double r133307 = a;
        double r133308 = k;
        double r133309 = cbrt(r133308);
        double r133310 = r133309 * r133309;
        double r133311 = m;
        double r133312 = pow(r133310, r133311);
        double r133313 = r133307 * r133312;
        double r133314 = pow(r133309, r133311);
        double r133315 = r133313 * r133314;
        double r133316 = 1.0;
        double r133317 = 10.0;
        double r133318 = r133317 * r133308;
        double r133319 = r133316 + r133318;
        double r133320 = r133308 * r133308;
        double r133321 = r133319 + r133320;
        double r133322 = r133315 / r133321;
        return r133322;
}

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

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

Reproduce

herbie shell --seed 2019304 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))