Average Error: 2.0 → 2.0
Time: 10.4s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\left(\frac{a}{k \cdot \left(10 + k\right) + 1} \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot {\left(\sqrt[3]{k}\right)}^{m}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\left(\frac{a}{k \cdot \left(10 + k\right) + 1} \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot {\left(\sqrt[3]{k}\right)}^{m}
double f(double a, double k, double m) {
        double r347025 = a;
        double r347026 = k;
        double r347027 = m;
        double r347028 = pow(r347026, r347027);
        double r347029 = r347025 * r347028;
        double r347030 = 1.0;
        double r347031 = 10.0;
        double r347032 = r347031 * r347026;
        double r347033 = r347030 + r347032;
        double r347034 = r347026 * r347026;
        double r347035 = r347033 + r347034;
        double r347036 = r347029 / r347035;
        return r347036;
}
↓
double f(double a, double k, double m) {
        double r347037 = a;
        double r347038 = k;
        double r347039 = 10.0;
        double r347040 = r347039 + r347038;
        double r347041 = r347038 * r347040;
        double r347042 = 1.0;
        double r347043 = r347041 + r347042;
        double r347044 = r347037 / r347043;
        double r347045 = cbrt(r347038);
        double r347046 = r347045 * r347045;
        double r347047 = m;
        double r347048 = pow(r347046, r347047);
        double r347049 = r347044 * r347048;
        double r347050 = pow(r347045, r347047);
        double r347051 = r347049 * r347050;
        return r347051;
}

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 2.0

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

  2. Simplified2.0

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

  4. Applied add-cube-cbrt2.0

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

  5. Applied unpow-prod-down2.0

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

  6. Applied associate-*r*2.0

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

  7. Final simplification2.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))