Bouland and Aaronson, Equation (24)

Average Error: 0.2 → 0.2

Time: 3.7s

Precision: binary64

Math

\[\]

↓

\[\]

C

double code(double a, double b) {
	return ((double) (((double) (((double) pow(((double) (((double) (a * a)) + ((double) (b * b)))), 2.0)) + ((double) (4.0 * ((double) (((double) (((double) (a * a)) * ((double) (1.0 - a)))) + ((double) (((double) (b * b)) * ((double) (3.0 + a)))))))))) - 1.0));
}

↓

double code(double a, double b) {
	return ((double) (((double) (((double) pow(((double) (((double) (a * a)) + ((double) (b * b)))), 2.0)) + ((double) (4.0 * ((double) (((double) (((double) (a * a)) * ((double) (1.0 - a)))) + ((double) (((double) (b * b)) * ((double) (a + 3.0)))))))))) - 1.0));
}

Error

Bits error versus a

Bits error versus b

Derivation

1. Initial program 0.2

   \[\]

2. Final simplification 0.2

   \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 1.0))