(sqrt (+ (* (- c) (+ (+ (cos p) (* (sin p) (sqrt 3))) 2.0)) (* m m)))

Average Error: 21.2 → 21.2

Time: 2.7s

Precision: binary64

Math

\[\sqrt{\left(-c\right) \cdot \left(\left(\cos p + \sin p \cdot \sqrt{3}\right) + 2\right) + m \cdot m}\]

↓

\[\sqrt{\left(-c\right) \cdot \left(\left(\cos p + \sin p \cdot \sqrt{3}\right) + 2\right) + m \cdot m}\]

Error

Bits error versus c

Bits error versus p

Bits error versus m

Derivation

1. Initial program 21.2

   \[\sqrt{\left(-c\right) \cdot \left(\left(\cos p + \sin p \cdot \sqrt{3}\right) + 2\right) + m \cdot m}\]

2. Final simplification 21.2

   \[\leadsto \sqrt{\left(-c\right) \cdot \left(\left(\cos p + \sin p \cdot \sqrt{3}\right) + 2\right) + m \cdot m}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (c p m)
  :name "(sqrt (+ (* (- c) (+ (+ (cos p) (* (sin p) (sqrt 3))) 2.0)) (* m m)))"
  :precision binary64
  (sqrt (+ (* (neg c) (+ (+ (cos p) (* (sin p) (sqrt 3.0))) 2.0)) (* m m))))