(+ (+ (+ (+ (+ (- a n) (- b n)) (- c n)) (- d n)) (- e n)) (- f n))

Average Error: 0.1 → 0.1

Time: 1.5s

Precision: binary64

Math

\[\left(\left(\left(\left(\left(a - n\right) + \left(b - n\right)\right) + \left(c - n\right)\right) + \left(d - n\right)\right) + \left(e - n\right)\right) + \left(f - n\right)\]

↓

\[\left(\left(\left(\left(\left(a - n\right) + \left(b - n\right)\right) + \left(c - n\right)\right) + \left(d - n\right)\right) + \left(e - n\right)\right) + \left(f - n\right)\]

C

double code(double a, double n, double b, double c, double d, double e, double f) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (a - n)) + ((double) (b - n)))) + ((double) (c - n)))) + ((double) (d - n)))) + ((double) (e - n)))) + ((double) (f - n))));
}

↓

double code(double a, double n, double b, double c, double d, double e, double f) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (a - n)) + ((double) (b - n)))) + ((double) (c - n)))) + ((double) (d - n)))) + ((double) (e - n)))) + ((double) (f - n))));
}

Error

Bits error versus a

Bits error versus n

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Bits error versus f

Derivation

1. Initial program 0.1

   \[\left(\left(\left(\left(\left(a - n\right) + \left(b - n\right)\right) + \left(c - n\right)\right) + \left(d - n\right)\right) + \left(e - n\right)\right) + \left(f - n\right)\]

2. Final simplification 0.1

   \[\leadsto \left(\left(\left(\left(\left(a - n\right) + \left(b - n\right)\right) + \left(c - n\right)\right) + \left(d - n\right)\right) + \left(e - n\right)\right) + \left(f - n\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a n b c d e f)
  :name "(+ (+ (+ (+ (+ (- a n) (- b n)) (- c n)) (- d n)) (- e n)) (- f n))"
  :precision binary64
  (+ (+ (+ (+ (+ (- a n) (- b n)) (- c n)) (- d n)) (- e n)) (- f n)))