Average Error: 2.1 → 2.1
Time: 5.2s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\left(\frac{{\left(\sqrt[3]{k}\right)}^{m}}{k \cdot \left(10 + k\right) + 1} \cdot a\right) \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\left(\frac{{\left(\sqrt[3]{k}\right)}^{m}}{k \cdot \left(10 + k\right) + 1} \cdot a\right) \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}
double f(double a, double k, double m) {
        double r325912 = a;
        double r325913 = k;
        double r325914 = m;
        double r325915 = pow(r325913, r325914);
        double r325916 = r325912 * r325915;
        double r325917 = 1.0;
        double r325918 = 10.0;
        double r325919 = r325918 * r325913;
        double r325920 = r325917 + r325919;
        double r325921 = r325913 * r325913;
        double r325922 = r325920 + r325921;
        double r325923 = r325916 / r325922;
        return r325923;
}
↓
double f(double a, double k, double m) {
        double r325924 = k;
        double r325925 = cbrt(r325924);
        double r325926 = m;
        double r325927 = pow(r325925, r325926);
        double r325928 = 10.0;
        double r325929 = r325928 + r325924;
        double r325930 = r325924 * r325929;
        double r325931 = 1.0;
        double r325932 = r325930 + r325931;
        double r325933 = r325927 / r325932;
        double r325934 = a;
        double r325935 = r325933 * r325934;
        double r325936 = r325925 * r325925;
        double r325937 = pow(r325936, r325926);
        double r325938 = r325935 * r325937;
        return r325938;
}

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. Simplified2.1

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

  4. Applied *-un-lft-identity2.1

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

  5. Applied add-cube-cbrt2.1

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

  6. Applied unpow-prod-down2.1

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

  7. Applied times-frac2.1

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

  8. Applied associate-*l*2.1

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

  9. Final simplification2.1

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

Reproduce

herbie shell --seed 2020060 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))