Exception for (fabs (asin (sqrt (/ (- (- (- (+ (* (* 2 (+ (pow (* (sin f) (cos a)) 2) 1)) (pow (cos (/ pi n)) 2)) (* (* (* (* 2 (sqrt (+ (+ (* (- 2) (pow (* (sin f) (cos (/ pi n))) 2)) (cos c)) 1))) (sqrt 2)) (sin (/ pi n))) (cos a))) (* 2 (pow (cos a) 2))) (cos c)) 1) (* (+ (- (cos c)) 1) (cos (/ pi n)))))))

Math

\[\left|\sin^{-1} \left(\sqrt{\frac{\left(\left(\left(\left(2 \cdot \left({\left(\sin f \cdot \cos a\right)}^{2} + 1\right)\right) \cdot {\left(\cos \left(\frac{pi}{n}\right)\right)}^{2} + \left(\left(\left(2 \cdot \sqrt{\left(\left(-2\right) \cdot {\left(\sin f \cdot \cos \left(\frac{pi}{n}\right)\right)}^{2} + \cos c\right) + 1}\right) \cdot \sqrt{2}\right) \cdot \sin \left(\frac{pi}{n}\right)\right) \cdot \cos a\right) - 2 \cdot {\left(\cos a\right)}^{2}\right) - \cos c\right) - 1}{\left(\left(-\cos c\right) + 1\right) \cdot \cos \left(\frac{pi}{n}\right)}}\right)\right|\]

Reproduce

herbie shell --seed 2020152 
(FPCore (f a pi n c)
  :name "(fabs (asin (sqrt (/ (- (- (- (+ (* (* 2 (+ (pow (* (sin f) (cos a)) 2) 1)) (pow (cos (/ pi n)) 2)) (* (* (* (* 2 (sqrt (+ (+ (* (- 2) (pow (* (sin f) (cos (/ pi n))) 2)) (cos c)) 1))) (sqrt 2)) (sin (/ pi n))) (cos a))) (* 2 (pow (cos a) 2))) (cos c)) 1) (* (+ (- (cos c)) 1) (cos (/ pi n)))))))"
  :precision binary64
  (fabs (asin (sqrt (/ (- (- (- (+ (* (* 2.0 (+ (pow (* (sin f) (cos a)) 2.0) 1.0)) (pow (cos (/ pi n)) 2.0)) (* (* (* (* 2.0 (sqrt (+ (+ (* (neg 2.0) (pow (* (sin f) (cos (/ pi n))) 2.0)) (cos c)) 1.0))) (sqrt 2.0)) (sin (/ pi n))) (cos a))) (* 2.0 (pow (cos a) 2.0))) (cos c)) 1.0) (* (+ (neg (cos c)) 1.0) (cos (/ pi n))))))))