Average Error: 2.2 → 2.2
Time: 19.2s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{a}{\frac{-\left(1 + k \cdot \left(10 + k\right)\right)}{-{k}^{m}}}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{a}{\frac{-\left(1 + k \cdot \left(10 + k\right)\right)}{-{k}^{m}}}
double f(double a, double k, double m) {
        double r246811 = a;
        double r246812 = k;
        double r246813 = m;
        double r246814 = pow(r246812, r246813);
        double r246815 = r246811 * r246814;
        double r246816 = 1.0;
        double r246817 = 10.0;
        double r246818 = r246817 * r246812;
        double r246819 = r246816 + r246818;
        double r246820 = r246812 * r246812;
        double r246821 = r246819 + r246820;
        double r246822 = r246815 / r246821;
        return r246822;
}
↓
double f(double a, double k, double m) {
        double r246823 = a;
        double r246824 = 1.0;
        double r246825 = k;
        double r246826 = 10.0;
        double r246827 = r246826 + r246825;
        double r246828 = r246825 * r246827;
        double r246829 = r246824 + r246828;
        double r246830 = -r246829;
        double r246831 = m;
        double r246832 = pow(r246825, r246831);
        double r246833 = -r246832;
        double r246834 = r246830 / r246833;
        double r246835 = r246823 / r246834;
        return r246835;
}

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 2.2

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

  3. Applied associate-/l*2.2

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

  5. Applied frac-2neg2.2

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

  6. Simplified2.2

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

  7. Final simplification2.2

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

Reproduce

herbie shell --seed 2019297 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))