Average Error: 2.0 → 2.0
Time: 6.7s
Precision: binary64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{{k}^{m} \cdot \frac{a}{\sqrt{1 + k \cdot \left(k + 10\right)}}}{\sqrt{\left(1 + k \cdot 10\right) + k \cdot k}}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{{k}^{m} \cdot \frac{a}{\sqrt{1 + k \cdot \left(k + 10\right)}}}{\sqrt{\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
 (/
  (* (pow k m) (/ a (sqrt (+ 1.0 (* k (+ k 10.0))))))
  (sqrt (+ (+ 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 (pow(k, m) * (a / sqrt(1.0 + (k * (k + 10.0))))) / sqrt((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 2.0

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

  3. Applied add-sqr-sqrt_binary64_51822.0

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

  4. Applied associate-/r*_binary64_52602.0

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

  5. Simplified2.0

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

  6. Final simplification2.0

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

Reproduce

herbie shell --seed 2020270 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))