Average Error: 0.2 → 0.2
Time: 2.9s
Precision: binary64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[{\left(a \cdot a + b \cdot b\right)}^{2} + \left(b \cdot \left(b \cdot 4\right) - 1\right)\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
{\left(a \cdot a + b \cdot b\right)}^{2} + \left(b \cdot \left(b \cdot 4\right) - 1\right)
double code(double a, double b) {
	return ((double) (((double) (((double) pow(((double) (((double) (a * a)) + ((double) (b * b)))), 2.0)) + ((double) (4.0 * ((double) (b * b)))))) - 1.0));
}
↓
double code(double a, double b) {
	return ((double) (((double) pow(((double) (((double) (a * a)) + ((double) (b * b)))), 2.0)) + ((double) (((double) (b * ((double) (b * 4.0)))) - 1.0))));
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]

  2. Simplified0.2

    \[\leadsto \color{blue}{{\left(a \cdot a + b \cdot b\right)}^{2} + \left(b \cdot \left(b \cdot 4\right) - 1\right)}\]

  3. Final simplification0.2

    \[\leadsto {\left(a \cdot a + b \cdot b\right)}^{2} + \left(b \cdot \left(b \cdot 4\right) - 1\right)\]

Reproduce

herbie shell --seed 2020185 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))