Average Error: 2.0 → 2.0
Time: 6.5s
Precision: binary64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\left(a \cdot {k}^{m}\right) \cdot \frac{1}{1 + k \cdot \left(k + 10\right)}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\left(a \cdot {k}^{m}\right) \cdot \frac{1}{1 + k \cdot \left(k + 10\right)}
(FPCore (a k m)
 :precision binary64
 (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))
↓
(FPCore (a k m)
 :precision binary64
 (* (* a (pow k m)) (/ 1.0 (+ 1.0 (* k (+ k 10.0))))))
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 (a * pow(k, m)) * (1.0 / (1.0 + (k * (k + 10.0))));
}

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 2.0

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

  2. Simplified2.0

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

  4. Applied div-inv_binary64_14522.0

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

  5. Final simplification2.0

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

Reproduce

herbie shell --seed 2020281 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))