Average Error: 2.1 → 2.1
Time: 5.6s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{\frac{{k}^{m}}{\sqrt{k \cdot \left(10 + k\right) + 1}} \cdot a}{\sqrt{k \cdot \left(10 + k\right) + 1}}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{\frac{{k}^{m}}{\sqrt{k \cdot \left(10 + k\right) + 1}} \cdot a}{\sqrt{k \cdot \left(10 + k\right) + 1}}
double code(double a, double k, double m) {
	return ((a * pow(k, m)) / ((1.0 + (10.0 * k)) + (k * k)));
}
↓
double code(double a, double k, double m) {
	return (((pow(k, m) / sqrt(((k * (10.0 + k)) + 1.0))) * a) / sqrt(((k * (10.0 + k)) + 1.0)));
}

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 add-sqr-sqrt2.1

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

  5. Applied associate-/r*2.1

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

  7. Applied associate-*l/2.1

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

  8. Final simplification2.1

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

Reproduce

herbie shell --seed 2020058 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))