(sqrt (+ (* e e) q))

Average Error: 21.4 → 21.4

Time: 773.0ms

Precision: binary64

Math

\[\sqrt{e \cdot e + q}\]

↓

\[\sqrt{e \cdot e + q}\]

C

double code(double e, double q) {
	return ((double) sqrt(((double) (((double) (e * e)) + q))));
}

↓

double code(double e, double q) {
	return ((double) sqrt(((double) (((double) (e * e)) + q))));
}

Error

Bits error versus e

Bits error versus q

Derivation

1. Initial program 21.4

   \[\sqrt{e \cdot e + q}\]

2. Final simplification 21.4

   \[\leadsto \sqrt{e \cdot e + q}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (e q)
  :name "(sqrt (+ (* e e) q))"
  :precision binary64
  (sqrt (+ (* e e) q)))