Average Error: 1.9 → 1.9
Time: 5.8s
Precision: binary64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{\sqrt{{k}^{m}} \cdot \left(a \cdot \sqrt{{k}^{m}}\right)}{\left(1 + k \cdot 10\right) + k \cdot k}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{\sqrt{{k}^{m}} \cdot \left(a \cdot \sqrt{{k}^{m}}\right)}{\left(1 + k \cdot 10\right) + k \cdot k}
(FPCore (a k m)
 :precision binary64
 (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))
↓
(FPCore (a k m)
 :precision binary64
 (/
  (* (sqrt (pow k m)) (* a (sqrt (pow k m))))
  (+ (+ 1.0 (* k 10.0)) (* k k))))
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 (sqrt(pow(k, m)) * (a * sqrt(pow(k, m)))) / ((1.0 + (k * 10.0)) + (k * k));
}

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 1.9

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

  3. Applied add-sqr-sqrt_binary64_5591.9

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

  4. Applied associate-*r*_binary64_6331.9

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

  5. Final simplification1.9

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

Reproduce

herbie shell --seed 2020231 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))