Details

analyze1.2s (8.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.8%	0.2%	0%	0%	0%	0
0%	0%	99.8%	0.2%	0%	0%	0%	1
0%	0%	99.8%	0.2%	0%	0%	0%	2
0%	0%	99.8%	0.2%	0%	0%	0%	3
0%	0%	99.8%	0.2%	0%	0%	0%	4
0%	0%	99.8%	0.2%	0%	0%	0%	5
0%	0%	99.8%	0.2%	0%	0%	0%	6
0%	0%	99.8%	0.2%	0%	0%	0%	7
0%	0%	99.8%	0.2%	0%	0%	0%	8
12.5%	12.5%	87.3%	0.2%	0%	0%	0%	9
12.5%	12.5%	87.3%	0.2%	0%	0%	0%	10
18.8%	18.7%	81.1%	0.2%	0%	0%	0%	11
18.8%	18.7%	81.1%	0.2%	0%	0%	0%	12

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample2.9s (19.7%)

Results

2.5s	8128×	body	256	valid
146.0ms	93×	body	1024	infinite
139.0ms	407×	body	256	infinite
37.0ms	63×	body	1024	valid
30.0ms	75×	body	512	infinite
27.0ms	65×	body	512	valid
19.0ms	21×	body	2048	infinite

Bogosity

preprocess63.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

557×	`exp-sum_binary64`
549×	`distribute-rgt-in_binary64`
428×	`fma-neg_binary64`
375×	`sub-neg_binary64`
349×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	154	495
1	433	495
2	1050	473
3	3771	473
0	5	5
1	5	5

Stop Event

1×	unsound
1×	node limit

Calls

Call 1

Inputs
0
1
2
3
4

Outputs
0
1
2
1
3
4

Call 2

Inputs
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 m (+.f64 K n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 K n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 K n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 n (+.f64 m K)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m K) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m K))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 M (+.f64 m n)) 2) K)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) K) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 l (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 K (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 n m)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 n m))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 M n)) 2) m)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 M n) 2) m) 2)) (-.f64 l (fabs.f64 (-.f64 M n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 l n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 l n) 2) M) 2)) (-.f64 m (fabs.f64 (-.f64 l n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m M)) 2) n)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m M) 2) n) 2)) (-.f64 l (fabs.f64 (-.f64 m M))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m l)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m l) 2) M) 2)) (-.f64 n (fabs.f64 (-.f64 m l))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) l)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) l) 2)) (-.f64 M (fabs.f64 (-.f64 m n))))))

Outputs
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K 2) (+.f64 m n)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(*.f64 (cos.f64 (fma.f64 (/.f64 K 2) (+.f64 m n) (neg.f64 M))) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2))))
(/.f64 (cos.f64 (fma.f64 (+.f64 m n) (/.f64 K 2) (neg.f64 M))) (exp.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 m (+.f64 K n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 K n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 K n))))))
(*.f64 (cos.f64 (-.f64 (/.f64 m (/.f64 2 (+.f64 K n))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 K n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 K n))))))
(.f64 (cos.f64 (-.f64 (.f64 (/.f64 m 2) (+.f64 K n)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 K n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 K n))))))
(.f64 (cos.f64 (-.f64 (.f64 (+.f64 K n) (/.f64 m 2)) M)) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 K n)) l) (pow.f64 (-.f64 (/.f64 (+.f64 K n) 2) M) 2))))
(/.f64 (cos.f64 (-.f64 (*.f64 (+.f64 K n) (/.f64 m 2)) M)) (exp.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 K n) 2) M) 2) (-.f64 l (fabs.f64 (-.f64 K n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 n (+.f64 m K)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m K) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m K))))))
(*.f64 (cos.f64 (-.f64 (/.f64 n (/.f64 2 (+.f64 K m))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 K m) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m K))))))
(.f64 (cos.f64 (-.f64 (.f64 (/.f64 n 2) (+.f64 K m)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 K m) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m K))))))
(.f64 (cos.f64 (-.f64 (.f64 (/.f64 (+.f64 K m) 2) n) M)) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m K)) l) (pow.f64 (-.f64 (/.f64 (+.f64 K m) 2) M) 2))))
(.f64 (cos.f64 (-.f64 (.f64 (/.f64 (+.f64 K m) 2) n) M)) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 K m)) l) (pow.f64 (-.f64 (/.f64 (+.f64 K m) 2) M) 2))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 M (+.f64 m n)) 2) K)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) K) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(*.f64 (cos.f64 (-.f64 (/.f64 M (/.f64 2 (+.f64 m n))) K)) (exp.f64 (+.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) K) 2)) l) (fabs.f64 (-.f64 m n)))))
(.f64 (cos.f64 (-.f64 (.f64 (/.f64 M 2) (+.f64 m n)) K)) (exp.f64 (+.f64 (fabs.f64 (-.f64 m n)) (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) K) 2)) l))))
(.f64 (cos.f64 (-.f64 (.f64 (+.f64 m n) (/.f64 M 2)) K)) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) K) 2))))
(/.f64 (cos.f64 (-.f64 (*.f64 (+.f64 m n) (/.f64 M 2)) K)) (exp.f64 (+.f64 (-.f64 l (fabs.f64 (-.f64 m n))) (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) K) 2))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 l (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 K (fabs.f64 (-.f64 m n))))))
(*.f64 (cos.f64 (-.f64 (/.f64 l (/.f64 2 (+.f64 m n))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 K (fabs.f64 (-.f64 m n))))))
(*.f64 (cos.f64 (-.f64 (/.f64 (+.f64 m n) (/.f64 2 l)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 K (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (.f64 (+.f64 m n) (/.f64 l 2)) M)) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) K) (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2))))
(/.f64 (cos.f64 (-.f64 (*.f64 (+.f64 m n) (/.f64 l 2)) M)) (exp.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) (-.f64 K (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 n m)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 n m) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 n m))))))
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K 2) (+.f64 m n)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(*.f64 (cos.f64 (fma.f64 (/.f64 K 2) (+.f64 m n) (neg.f64 M))) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2))))
(/.f64 (cos.f64 (fma.f64 (+.f64 m n) (/.f64 K 2) (neg.f64 M))) (exp.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 M n)) 2) m)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 M n) 2) m) 2)) (-.f64 l (fabs.f64 (-.f64 M n))))))
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 n M))) m)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 n M) 2) m) 2)) (-.f64 l (fabs.f64 (-.f64 M n))))))
(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K 2) (+.f64 n M)) m)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 n M) 2) m) 2)) (-.f64 l (fabs.f64 (-.f64 M n))))))
(.f64 (cos.f64 (-.f64 (.f64 (+.f64 n M) (/.f64 K 2)) m)) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 M n)) l) (pow.f64 (-.f64 (/.f64 (+.f64 n M) 2) m) 2))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 l n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 l n) 2) M) 2)) (-.f64 m (fabs.f64 (-.f64 l n))))))
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 n l))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 n l) 2) M) 2)) (-.f64 m (fabs.f64 (-.f64 n l))))))
(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K 2) (+.f64 n l)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 n l) 2) M) 2)) (-.f64 m (fabs.f64 (-.f64 n l))))))
(.f64 (cos.f64 (-.f64 (.f64 (+.f64 n l) (/.f64 K 2)) M)) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 l n)) m) (pow.f64 (-.f64 (/.f64 (+.f64 n l) 2) M) 2))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m M)) 2) n)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m M) 2) n) 2)) (-.f64 l (fabs.f64 (-.f64 m M))))))
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m M))) n)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m M) 2) n) 2)) (-.f64 l (fabs.f64 (-.f64 m M))))))
(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K 2) (+.f64 m M)) n)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m M) 2) n) 2)) (-.f64 l (fabs.f64 (-.f64 m M))))))
(.f64 (cos.f64 (-.f64 (.f64 (+.f64 m M) (/.f64 K 2)) n)) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m M)) l) (pow.f64 (-.f64 (/.f64 (+.f64 m M) 2) n) 2))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m l)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m l) 2) M) 2)) (-.f64 n (fabs.f64 (-.f64 m l))))))
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m l))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m l) 2) M) 2)) (-.f64 n (fabs.f64 (-.f64 l m))))))
(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K 2) (+.f64 m l)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m l) 2) M) 2)) (-.f64 n (fabs.f64 (-.f64 l m))))))
(.f64 (cos.f64 (-.f64 (.f64 (+.f64 m l) (/.f64 K 2)) M)) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m l)) n) (pow.f64 (-.f64 (/.f64 (+.f64 m l) 2) M) 2))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) l)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) l) 2)) (-.f64 M (fabs.f64 (-.f64 m n))))))
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) l)) (exp.f64 (+.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) l) 2)) M) (fabs.f64 (-.f64 m n)))))
(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K 2) (+.f64 m n)) l)) (exp.f64 (+.f64 (fabs.f64 (-.f64 m n)) (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) l) 2)) M))))
(*.f64 (cos.f64 (fma.f64 (/.f64 K 2) (+.f64 m n) (neg.f64 l))) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) M) (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) l) 2))))
(/.f64 (cos.f64 (fma.f64 (+.f64 m n) (/.f64 K 2) (neg.f64 l))) (exp.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) l) 2) (-.f64 M (fabs.f64 (-.f64 m n))))))

Symmetry

(sort m n)

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify53.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

598×	`exp-prod_binary64`
446×	`fma-neg_binary64`
371×	`associate-l_binary64`
308×	`associate-r_binary64`
249×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	58	45
2	135	43
3	442	43
4	1767	43
5	7431	43

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Outputs
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K 2) (+.f64 m n)) M)) (exp.f64 (+.f64 (fabs.f64 (-.f64 m n)) (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) l))))
(.f64 (cos.f64 (-.f64 (.f64 (+.f64 m n) (/.f64 K 2)) M)) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2))))
(/.f64 (cos.f64 (fma.f64 (+.f64 m n) (/.f64 K 2) (neg.f64 M))) (exp.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) (-.f64 l (fabs.f64 (-.f64 m n))))))
(*.f64 (cos.f64 (fma.f64 K (/.f64 (+.f64 m n) 2) (neg.f64 M))) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2))))

eval1.0ms (0%)

Compiler: Compiled 62 to 37 computations (40.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

15.2b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	15.2b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 34 to 23 computations (32.4% saved)

localize53.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
✓	0.0b	(*.f64 K (+.f64 m n))
✓	33.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 153 to 64 computations (58.2% saved)

series25.0ms (0.2%)

Counts

4 → 168

Calls

42 calls:

Time	Variable		Expression
2.0ms	K	@	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
2.0ms	M	@	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
1.0ms	K	@	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
1.0ms	m	@	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
1.0ms	n	@	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite193.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

634×	`fma-def_binary64`
331×	`fma-neg_binary64`
309×	`expm1-udef_binary64`
309×	`log1p-udef_binary64`
247×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	48
1	336	48
2	4968	48

Stop Event

1×	node limit

Counts

4 → 233

Calls

Call 1

Inputs
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
(*.f64 K (+.f64 m n))
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Outputs
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(neg.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 K 2) (+.f64 m n) (.f64 (neg.f64 M) 1))))))
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M) (.f64 (pow.f64 (+.f64 m n) 2) 1/4)) (fma.f64 (+.f64 m n) 1/2 M)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (.f64 (pow.f64 (+.f64 m n) 3) 1/8) (pow.f64 M 3)) (fma.f64 (+.f64 m n) 1/2 (neg.f64 M))) (fma.f64 M (fma.f64 (+.f64 m n) 1/2 M) (.f64 (pow.f64 (+.f64 m n) 2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 (pow.f64 (+.f64 m n) 2) 1/4 (neg.f64 (.f64 M M))) (fma.f64 (+.f64 m n) 1/2 (neg.f64 M))) (fma.f64 (+.f64 m n) 1/2 M))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 (+.f64 m n) 1/2 (neg.f64 M)) (-.f64 (.f64 (pow.f64 (+.f64 m n) 3) 1/8) (pow.f64 M 3))) (fma.f64 M (fma.f64 (+.f64 m n) 1/2 M) (.f64 (pow.f64 (+.f64 m n) 2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 (+.f64 m n) 1/2 (neg.f64 M)) (fma.f64 (pow.f64 (+.f64 m n) 2) 1/4 (neg.f64 (.f64 M M)))) (fma.f64 (+.f64 m n) 1/2 M))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (+.f64 m n) 1/2 (neg.f64 M)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (fma.f64 (+.f64 m n) 1/2 (neg.f64 M)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (fma.f64 (+.f64 m n) 1/2 (neg.f64 M)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (+.f64 m n) 1/2 (neg.f64 M)) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (fma.f64 (+.f64 m n) 1/2 (neg.f64 M)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (fma.f64 (+.f64 m n) 1/2 (neg.f64 M)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 2 (log.f64 (fma.f64 (+.f64 m n) 1/2 (neg.f64 M)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (fma.f64 (+.f64 m n) 1/2 (neg.f64 M)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 m n) 1/2) (fma.f64 (+.f64 m n) 1/2 (neg.f64 M)) (.f64 (neg.f64 M) (fma.f64 (+.f64 m n) 1/2 (neg.f64 M))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (+.f64 m n) 1/2 (neg.f64 M)) (.f64 (+.f64 m n) 1/2) (.f64 (fma.f64 (+.f64 m n) 1/2 (neg.f64 M)) (neg.f64 M)))))))

simplify90.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-def_binary64`
652×	`distribute-rgt-neg-out_binary64`
586×	`distribute-lft-neg-out_binary64`
382×	`*-commutative_binary64`
343×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	2669
1	417	2628
2	1279	2506
3	4078	2506

Stop Event

1×	node limit

Counts

401 → 320

Calls

Call 1

Inputs
(cos.f64 (neg.f64 M))
(+.f64 (cos.f64 (neg.f64 M)) (.f64 -1/2 (.f64 K (*.f64 (sin.f64 (neg.f64 M)) (+.f64 n m)))))
(+.f64 (cos.f64 (neg.f64 M)) (+.f64 (.f64 -1/8 (.f64 (cos.f64 (neg.f64 M)) (.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2)))) (.f64 -1/2 (.f64 K (.f64 (sin.f64 (neg.f64 M)) (+.f64 n m))))))
(+.f64 (cos.f64 (neg.f64 M)) (+.f64 (.f64 1/48 (.f64 (pow.f64 K 3) (.f64 (sin.f64 (neg.f64 M)) (pow.f64 (+.f64 n m) 3)))) (+.f64 (.f64 -1/8 (.f64 (cos.f64 (neg.f64 M)) (.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2)))) (.f64 -1/2 (.f64 K (*.f64 (sin.f64 (neg.f64 M)) (+.f64 n m)))))))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 -1/2 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (*.f64 K m))))
(+.f64 (.f64 -1/8 (.f64 (pow.f64 K 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (pow.f64 m 2)))) (+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 -1/2 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 K m)))))
(+.f64 (.f64 -1/8 (.f64 (pow.f64 K 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (pow.f64 m 2)))) (+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (+.f64 (.f64 1/48 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 (pow.f64 K 3) (pow.f64 m 3)))) (.f64 -1/2 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (*.f64 K m))))))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))
(+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)))
(+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))) (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (pow.f64 K 2)))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))
(+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))) (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (pow.f64 K 2)))) (+.f64 (.f64 1/48 (.f64 (pow.f64 n 3) (.f64 (pow.f64 K 3) (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)))))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))) M))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(+.f64 (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) M) (cos.f64 (.f64 1/2 (*.f64 K (+.f64 n m)))))
(+.f64 (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) M) (+.f64 (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 -1/2 (.f64 (cos.f64 (.f64 1/2 (*.f64 K (+.f64 n m)))) (pow.f64 M 2)))))
(+.f64 (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) M) (+.f64 (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (+.f64 (.f64 -1/6 (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (pow.f64 M 3))) (.f64 -1/2 (.f64 (cos.f64 (.f64 1/2 (*.f64 K (+.f64 n m)))) (pow.f64 M 2))))))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m)))))
(cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m)))))
(cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m)))))
(cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m)))))
(*.f64 K (+.f64 n m))
(*.f64 K (+.f64 n m))
(*.f64 K (+.f64 n m))
(*.f64 K (+.f64 n m))
(*.f64 K (+.f64 n m))
(*.f64 K (+.f64 n m))
(*.f64 K (+.f64 n m))
(*.f64 K (+.f64 n m))
(*.f64 K (+.f64 n m))
(*.f64 K (+.f64 n m))
(*.f64 K (+.f64 n m))
(*.f64 K (+.f64 n m))
(*.f64 n K)
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(*.f64 K m)
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(*.f64 K m)
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(*.f64 K m)
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(*.f64 n K)
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(*.f64 n K)
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(*.f64 -1 M)
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(.f64 1/2 (.f64 K (+.f64 n m)))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(.f64 1/2 (.f64 K (+.f64 n m)))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(-.f64 (.f64 1/2 (.f64 n K)) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(.f64 1/2 (.f64 K m))
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(.f64 1/2 (.f64 K m))
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (.f64 1/2 (.f64 K m)) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(.f64 1/2 (.f64 n K))
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(.f64 1/2 (.f64 n K))
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(.f64 1/2 (.f64 K (+.f64 n m)))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(*.f64 -1 M)
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(*.f64 -1 M)
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
(pow.f64 (-.f64 (*.f64 1/2 n) M) 2)
(+.f64 (.f64 (-.f64 (.f64 1/2 n) M) m) (pow.f64 (-.f64 (*.f64 1/2 n) M) 2))
(+.f64 (.f64 (-.f64 (.f64 1/2 n) M) m) (+.f64 (pow.f64 (-.f64 (.f64 1/2 n) M) 2) (.f64 1/4 (pow.f64 m 2))))
(+.f64 (.f64 (-.f64 (.f64 1/2 n) M) m) (+.f64 (pow.f64 (-.f64 (.f64 1/2 n) M) 2) (.f64 1/4 (pow.f64 m 2))))
(*.f64 1/4 (pow.f64 m 2))
(+.f64 (.f64 (-.f64 (.f64 1/2 n) M) m) (*.f64 1/4 (pow.f64 m 2)))
(+.f64 (.f64 (-.f64 (.f64 1/2 n) M) m) (+.f64 (pow.f64 (-.f64 (.f64 1/2 n) M) 2) (.f64 1/4 (pow.f64 m 2))))
(+.f64 (.f64 (-.f64 (.f64 1/2 n) M) m) (+.f64 (pow.f64 (-.f64 (.f64 1/2 n) M) 2) (.f64 1/4 (pow.f64 m 2))))
(*.f64 1/4 (pow.f64 m 2))
(+.f64 (.f64 (-.f64 (.f64 1/2 n) M) m) (*.f64 1/4 (pow.f64 m 2)))
(+.f64 (.f64 (-.f64 (.f64 1/2 n) M) m) (+.f64 (pow.f64 (-.f64 (.f64 1/2 n) M) 2) (.f64 1/4 (pow.f64 m 2))))
(+.f64 (.f64 (-.f64 (.f64 1/2 n) M) m) (+.f64 (pow.f64 (-.f64 (.f64 1/2 n) M) 2) (.f64 1/4 (pow.f64 m 2))))
(pow.f64 (-.f64 (*.f64 1/2 m) M) 2)
(+.f64 (pow.f64 (-.f64 (.f64 1/2 m) M) 2) (.f64 n (-.f64 (*.f64 1/2 m) M)))
(+.f64 (pow.f64 (-.f64 (.f64 1/2 m) M) 2) (+.f64 (.f64 n (-.f64 (.f64 1/2 m) M)) (.f64 1/4 (pow.f64 n 2))))
(+.f64 (pow.f64 (-.f64 (.f64 1/2 m) M) 2) (+.f64 (.f64 n (-.f64 (.f64 1/2 m) M)) (.f64 1/4 (pow.f64 n 2))))
(*.f64 1/4 (pow.f64 n 2))
(+.f64 (.f64 n (-.f64 (.f64 1/2 m) M)) (*.f64 1/4 (pow.f64 n 2)))
(+.f64 (pow.f64 (-.f64 (.f64 1/2 m) M) 2) (+.f64 (.f64 n (-.f64 (.f64 1/2 m) M)) (.f64 1/4 (pow.f64 n 2))))
(+.f64 (pow.f64 (-.f64 (.f64 1/2 m) M) 2) (+.f64 (.f64 n (-.f64 (.f64 1/2 m) M)) (.f64 1/4 (pow.f64 n 2))))
(*.f64 1/4 (pow.f64 n 2))
(+.f64 (.f64 n (-.f64 (.f64 1/2 m) M)) (*.f64 1/4 (pow.f64 n 2)))
(+.f64 (pow.f64 (-.f64 (.f64 1/2 m) M) 2) (+.f64 (.f64 n (-.f64 (.f64 1/2 m) M)) (.f64 1/4 (pow.f64 n 2))))
(+.f64 (pow.f64 (-.f64 (.f64 1/2 m) M) 2) (+.f64 (.f64 n (-.f64 (.f64 1/2 m) M)) (.f64 1/4 (pow.f64 n 2))))
(*.f64 1/4 (pow.f64 (+.f64 n m) 2))
(+.f64 (.f64 -1 (.f64 (+.f64 n m) M)) (*.f64 1/4 (pow.f64 (+.f64 n m) 2)))
(+.f64 (.f64 -1 (.f64 (+.f64 n m) M)) (+.f64 (*.f64 1/4 (pow.f64 (+.f64 n m) 2)) (pow.f64 M 2)))
(+.f64 (.f64 -1 (.f64 (+.f64 n m) M)) (+.f64 (*.f64 1/4 (pow.f64 (+.f64 n m) 2)) (pow.f64 M 2)))
(pow.f64 M 2)
(+.f64 (.f64 -1 (.f64 (+.f64 n m) M)) (pow.f64 M 2))
(+.f64 (.f64 -1 (.f64 (+.f64 n m) M)) (+.f64 (*.f64 1/4 (pow.f64 (+.f64 n m) 2)) (pow.f64 M 2)))
(+.f64 (.f64 -1 (.f64 (+.f64 n m) M)) (+.f64 (*.f64 1/4 (pow.f64 (+.f64 n m) 2)) (pow.f64 M 2)))
(pow.f64 M 2)
(+.f64 (.f64 -1 (.f64 (+.f64 n m) M)) (pow.f64 M 2))
(+.f64 (.f64 -1 (.f64 (+.f64 n m) M)) (+.f64 (*.f64 1/4 (pow.f64 (+.f64 n m) 2)) (pow.f64 M 2)))
(+.f64 (.f64 -1 (.f64 (+.f64 n m) M)) (+.f64 (*.f64 1/4 (pow.f64 (+.f64 n m) 2)) (pow.f64 M 2)))

Outputs
(cos.f64 (neg.f64 M))
(cos.f64 M)
(+.f64 (cos.f64 (neg.f64 M)) (.f64 -1/2 (.f64 K (*.f64 (sin.f64 (neg.f64 M)) (+.f64 n m)))))
(+.f64 (cos.f64 M) (.f64 (.f64 -1/2 K) (*.f64 (neg.f64 (sin.f64 M)) (+.f64 n m))))
(fma.f64 -1/2 (.f64 K (.f64 (neg.f64 (sin.f64 M)) (+.f64 n m))) (cos.f64 M))
(fma.f64 -1/2 (.f64 (neg.f64 (sin.f64 M)) (.f64 K (+.f64 n m))) (cos.f64 M))
(+.f64 (cos.f64 (neg.f64 M)) (+.f64 (.f64 -1/8 (.f64 (cos.f64 (neg.f64 M)) (.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2)))) (.f64 -1/2 (.f64 K (.f64 (sin.f64 (neg.f64 M)) (+.f64 n m))))))
(+.f64 (cos.f64 M) (fma.f64 -1/8 (.f64 (.f64 (cos.f64 M) (.f64 K K)) (pow.f64 (+.f64 n m) 2)) (.f64 (.f64 -1/2 K) (.f64 (neg.f64 (sin.f64 M)) (+.f64 n m)))))
(+.f64 (cos.f64 M) (fma.f64 -1/2 (.f64 K (.f64 (neg.f64 (sin.f64 M)) (+.f64 n m))) (.f64 -1/8 (.f64 (.f64 K K) (.f64 (pow.f64 (+.f64 n m) 2) (cos.f64 M))))))
(fma.f64 -1/2 (.f64 K (.f64 (neg.f64 (sin.f64 M)) (+.f64 n m))) (fma.f64 (.f64 -1/8 (.f64 (cos.f64 M) (*.f64 K K))) (pow.f64 (+.f64 n m) 2) (cos.f64 M)))
(fma.f64 -1/2 (.f64 (neg.f64 (sin.f64 M)) (.f64 K (+.f64 n m))) (fma.f64 (.f64 K (.f64 K (pow.f64 (+.f64 n m) 2))) (*.f64 (cos.f64 M) -1/8) (cos.f64 M)))
(+.f64 (cos.f64 (neg.f64 M)) (+.f64 (.f64 1/48 (.f64 (pow.f64 K 3) (.f64 (sin.f64 (neg.f64 M)) (pow.f64 (+.f64 n m) 3)))) (+.f64 (.f64 -1/8 (.f64 (cos.f64 (neg.f64 M)) (.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2)))) (.f64 -1/2 (.f64 K (*.f64 (sin.f64 (neg.f64 M)) (+.f64 n m)))))))
(+.f64 (cos.f64 M) (fma.f64 1/48 (.f64 (.f64 (pow.f64 K 3) (neg.f64 (sin.f64 M))) (pow.f64 (+.f64 n m) 3)) (fma.f64 -1/8 (.f64 (.f64 (cos.f64 M) (.f64 K K)) (pow.f64 (+.f64 n m) 2)) (.f64 (.f64 -1/2 K) (.f64 (neg.f64 (sin.f64 M)) (+.f64 n m))))))
(+.f64 (fma.f64 1/48 (.f64 (pow.f64 (+.f64 n m) 3) (.f64 (neg.f64 (sin.f64 M)) (pow.f64 K 3))) (.f64 -1/8 (.f64 (.f64 K K) (.f64 (pow.f64 (+.f64 n m) 2) (cos.f64 M))))) (fma.f64 -1/2 (.f64 K (.f64 (neg.f64 (sin.f64 M)) (+.f64 n m))) (cos.f64 M)))
(+.f64 (fma.f64 (.f64 -1/8 (.f64 (cos.f64 M) (.f64 K K))) (pow.f64 (+.f64 n m) 2) (cos.f64 M)) (.f64 (neg.f64 (sin.f64 M)) (+.f64 (.f64 (pow.f64 (+.f64 n m) 3) (.f64 1/48 (pow.f64 K 3))) (.f64 (+.f64 n m) (.f64 -1/2 K)))))
(+.f64 (fma.f64 (.f64 K (.f64 K (pow.f64 (+.f64 n m) 2))) (.f64 (cos.f64 M) -1/8) (cos.f64 M)) (.f64 (neg.f64 (sin.f64 M)) (+.f64 (.f64 (pow.f64 (+.f64 n m) 3) (.f64 1/48 (pow.f64 K 3))) (.f64 (+.f64 n m) (.f64 -1/2 K)))))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K n) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 n (.f64 K 1/2)) M))
(cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))
(cos.f64 (fma.f64 K (*.f64 n 1/2) (neg.f64 M)))
(+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 -1/2 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (*.f64 K m))))
(+.f64 (cos.f64 (fma.f64 1/2 (.f64 K n) (neg.f64 M))) (.f64 -1/2 (.f64 (sin.f64 (fma.f64 1/2 (.f64 K n) (neg.f64 M))) (*.f64 K m))))
(fma.f64 -1/2 (.f64 K (.f64 m (sin.f64 (-.f64 (.f64 n (.f64 K 1/2)) M)))) (cos.f64 (-.f64 (.f64 n (.f64 K 1/2)) M)))
(fma.f64 (sin.f64 (-.f64 (.f64 K (.f64 n 1/2)) M)) (.f64 -1/2 (.f64 K m)) (cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M)))
(fma.f64 -1/2 (.f64 K (.f64 m (sin.f64 (fma.f64 K (.f64 n 1/2) (neg.f64 M))))) (cos.f64 (fma.f64 K (.f64 n 1/2) (neg.f64 M))))
(+.f64 (.f64 -1/8 (.f64 (pow.f64 K 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (pow.f64 m 2)))) (+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 -1/2 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 K m)))))
(fma.f64 -1/8 (.f64 (.f64 K K) (.f64 (cos.f64 (fma.f64 1/2 (.f64 K n) (neg.f64 M))) (.f64 m m))) (+.f64 (cos.f64 (fma.f64 1/2 (.f64 K n) (neg.f64 M))) (.f64 -1/2 (.f64 (sin.f64 (fma.f64 1/2 (.f64 K n) (neg.f64 M))) (.f64 K m)))))
(fma.f64 -1/8 (.f64 (cos.f64 (-.f64 (.f64 n (.f64 K 1/2)) M)) (.f64 (.f64 m m) (.f64 K K))) (fma.f64 -1/2 (.f64 K (.f64 m (sin.f64 (-.f64 (.f64 n (.f64 K 1/2)) M)))) (cos.f64 (-.f64 (.f64 n (.f64 K 1/2)) M))))
(fma.f64 -1/2 (.f64 K (.f64 m (sin.f64 (-.f64 (.f64 K (.f64 n 1/2)) M)))) (.f64 (+.f64 (.f64 (.f64 m m) (.f64 K (.f64 K -1/8))) 1) (cos.f64 (-.f64 (.f64 K (*.f64 n 1/2)) M))))
(fma.f64 -1/2 (.f64 K (.f64 m (sin.f64 (fma.f64 K (.f64 n 1/2) (neg.f64 M))))) (.f64 (+.f64 (.f64 (.f64 m m) (.f64 K (.f64 K -1/8))) 1) (cos.f64 (fma.f64 K (*.f64 n 1/2) (neg.f64 M)))))
(+.f64 (.f64 -1/8 (.f64 (pow.f64 K 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (pow.f64 m 2)))) (+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (+.f64 (.f64 1/48 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 (pow.f64 K 3) (pow.f64 m 3)))) (.f64 -1/2 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (*.f64 K m))))))
(fma.f64 -1/8 (.f64 (.f64 K K) (.f64 (cos.f64 (fma.f64 1/2 (.f64 K n) (neg.f64 M))) (.f64 m m))) (+.f64 (cos.f64 (fma.f64 1/2 (.f64 K n) (neg.f64 M))) (fma.f64 1/48 (.f64 (sin.f64 (fma.f64 1/2 (.f64 K n) (neg.f64 M))) (.f64 (pow.f64 K 3) (pow.f64 m 3))) (.f64 -1/2 (.f64 (sin.f64 (fma.f64 1/2 (.f64 K n) (neg.f64 M))) (*.f64 K m))))))
(+.f64 (fma.f64 -1/8 (.f64 (cos.f64 (-.f64 (.f64 n (.f64 K 1/2)) M)) (.f64 (.f64 m m) (.f64 K K))) (fma.f64 -1/2 (.f64 K (.f64 m (sin.f64 (-.f64 (.f64 n (.f64 K 1/2)) M)))) (cos.f64 (-.f64 (.f64 n (.f64 K 1/2)) M)))) (.f64 (sin.f64 (-.f64 (.f64 n (.f64 K 1/2)) M)) (.f64 (*.f64 (pow.f64 K 3) (pow.f64 m 3)) 1/48)))
(+.f64 (.f64 (sin.f64 (-.f64 (.f64 K (.f64 n 1/2)) M)) (+.f64 (.f64 -1/2 (.f64 K m)) (.f64 1/48 (.f64 (pow.f64 K 3) (pow.f64 m 3))))) (.f64 (+.f64 (.f64 (.f64 m m) (.f64 K (.f64 K -1/8))) 1) (cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))))
(+.f64 (.f64 (sin.f64 (fma.f64 K (.f64 n 1/2) (neg.f64 M))) (+.f64 (.f64 -1/2 (.f64 K m)) (.f64 1/48 (.f64 (pow.f64 K 3) (pow.f64 m 3))))) (.f64 (+.f64 (.f64 (.f64 m m) (.f64 K (.f64 K -1/8))) 1) (cos.f64 (fma.f64 K (.f64 n 1/2) (neg.f64 M)))))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(cos.f64 (-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))) M))
(cos.f64 (-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))) M))
(cos.f64 (-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M))
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(cos.f64 (-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M))
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(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
(fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M))
(-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
(fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M))
(-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
(fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M))
(-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M)
(-.f64 (.f64 1/2 (.f64 K m)) M)
(fma.f64 1/2 (*.f64 K m) (neg.f64 M))
(fma.f64 K (*.f64 m 1/2) (neg.f64 M))
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
(fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M))
(-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
(fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M))
(-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M)
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
(fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M))
(-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M)
(.f64 1/2 (.f64 n K))
(.f64 1/2 (.f64 K n))
(.f64 n (.f64 K 1/2))
(.f64 K (.f64 n 1/2))
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
(fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M))
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(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
(fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M))
(-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M)
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(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
(fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M))
(-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M)
(.f64 1/2 (.f64 n K))
(.f64 1/2 (.f64 K n))
(.f64 n (.f64 K 1/2))
(.f64 K (.f64 n 1/2))
(-.f64 (+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K))) M)
(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
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(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
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(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
(fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M))
(-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M)
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 (.f64 1/2 K) (+.f64 n m))
(.f64 K (.f64 (+.f64 n m) 1/2))
(+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))
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(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
(fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M))
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(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
(fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M))
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(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
(fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M))
(-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M)
(*.f64 -1 M)
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(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
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(-.f64 (.f64 (.f64 1/2 K) (+.f64 n m)) M)
(fma.f64 1/2 (*.f64 K (+.f64 n m)) (neg.f64 M))
(-.f64 (.f64 K (.f64 (+.f64 n m) 1/2)) M)
(pow.f64 (-.f64 (*.f64 1/2 n) M) 2)
(pow.f64 (-.f64 (*.f64 n 1/2) M) 2)
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(.f64 (-.f64 (.f64 n 1/2) M) (+.f64 m (-.f64 (*.f64 n 1/2) M)))
(.f64 (-.f64 (.f64 n 1/2) M) (+.f64 (-.f64 m M) (*.f64 n 1/2)))
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(fma.f64 m (.f64 m 1/4) (.f64 (-.f64 (.f64 n 1/2) M) (+.f64 m (-.f64 (.f64 n 1/2) M))))
(fma.f64 (-.f64 (.f64 n 1/2) M) (+.f64 (-.f64 m M) (.f64 n 1/2)) (.f64 m (.f64 m 1/4)))
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(fma.f64 m (.f64 m 1/4) (.f64 (-.f64 (.f64 n 1/2) M) (+.f64 m (-.f64 (.f64 n 1/2) M))))
(fma.f64 (-.f64 (.f64 n 1/2) M) (+.f64 (-.f64 m M) (.f64 n 1/2)) (.f64 m (.f64 m 1/4)))
(*.f64 1/4 (pow.f64 m 2))
(.f64 (.f64 m m) 1/4)
(.f64 m (.f64 m 1/4))
(+.f64 (.f64 (-.f64 (.f64 1/2 n) M) m) (*.f64 1/4 (pow.f64 m 2)))
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(fma.f64 m (-.f64 (.f64 n 1/2) M) (.f64 m (*.f64 m 1/4)))
(.f64 m (+.f64 (-.f64 (.f64 n 1/2) M) (*.f64 m 1/4)))
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(fma.f64 m (.f64 m 1/4) (.f64 (-.f64 (.f64 n 1/2) M) (+.f64 m (-.f64 (.f64 n 1/2) M))))
(fma.f64 (-.f64 (.f64 n 1/2) M) (+.f64 (-.f64 m M) (.f64 n 1/2)) (.f64 m (.f64 m 1/4)))
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(fma.f64 m (.f64 m 1/4) (.f64 (-.f64 (.f64 n 1/2) M) (+.f64 m (-.f64 (.f64 n 1/2) M))))
(fma.f64 (-.f64 (.f64 n 1/2) M) (+.f64 (-.f64 m M) (.f64 n 1/2)) (.f64 m (.f64 m 1/4)))
(*.f64 1/4 (pow.f64 m 2))
(.f64 (.f64 m m) 1/4)
(.f64 m (.f64 m 1/4))
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(fma.f64 (-.f64 (.f64 n 1/2) M) m (.f64 (*.f64 m m) 1/4))
(fma.f64 m (-.f64 (.f64 n 1/2) M) (.f64 m (*.f64 m 1/4)))
(.f64 m (+.f64 (-.f64 (.f64 n 1/2) M) (*.f64 m 1/4)))
(+.f64 (.f64 (-.f64 (.f64 1/2 n) M) m) (+.f64 (pow.f64 (-.f64 (.f64 1/2 n) M) 2) (.f64 1/4 (pow.f64 m 2))))
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(fma.f64 m (-.f64 (.f64 n 1/2) M) (fma.f64 (.f64 m m) 1/4 (pow.f64 (-.f64 (*.f64 n 1/2) M) 2)))
(fma.f64 m (.f64 m 1/4) (.f64 (-.f64 (.f64 n 1/2) M) (+.f64 m (-.f64 (.f64 n 1/2) M))))
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(fma.f64 m (.f64 m 1/4) (.f64 (-.f64 (.f64 n 1/2) M) (+.f64 m (-.f64 (.f64 n 1/2) M))))
(fma.f64 (-.f64 (.f64 n 1/2) M) (+.f64 (-.f64 m M) (.f64 n 1/2)) (.f64 m (.f64 m 1/4)))
(pow.f64 (-.f64 (*.f64 1/2 m) M) 2)
(pow.f64 (-.f64 (*.f64 m 1/2) M) 2)
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(.f64 (-.f64 (.f64 m 1/2) M) (+.f64 (-.f64 (*.f64 m 1/2) M) n))
(.f64 (-.f64 (.f64 m 1/2) M) (+.f64 n (-.f64 (*.f64 m 1/2) M)))
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(fma.f64 (-.f64 (.f64 m 1/2) M) (+.f64 n (-.f64 (.f64 m 1/2) M)) (.f64 n (.f64 n 1/4)))
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(fma.f64 (-.f64 (.f64 m 1/2) M) (+.f64 n (-.f64 (.f64 m 1/2) M)) (.f64 n (.f64 n 1/4)))
(*.f64 1/4 (pow.f64 n 2))
(.f64 (.f64 n n) 1/4)
(.f64 n (.f64 n 1/4))
(+.f64 (.f64 n (-.f64 (.f64 1/2 m) M)) (*.f64 1/4 (pow.f64 n 2)))
(fma.f64 n (-.f64 (.f64 m 1/2) M) (.f64 (*.f64 n n) 1/4))
(.f64 n (+.f64 (-.f64 (.f64 m 1/2) M) (*.f64 n 1/4)))
(+.f64 (pow.f64 (-.f64 (.f64 1/2 m) M) 2) (+.f64 (.f64 n (-.f64 (.f64 1/2 m) M)) (.f64 1/4 (pow.f64 n 2))))
(+.f64 (pow.f64 (-.f64 (.f64 m 1/2) M) 2) (fma.f64 n (-.f64 (.f64 m 1/2) M) (.f64 (.f64 n n) 1/4)))
(+.f64 (.f64 (-.f64 (.f64 m 1/2) M) (+.f64 (-.f64 (.f64 m 1/2) M) n)) (.f64 (*.f64 n n) 1/4))
(fma.f64 (-.f64 (.f64 m 1/2) M) (+.f64 n (-.f64 (.f64 m 1/2) M)) (.f64 n (.f64 n 1/4)))
(+.f64 (pow.f64 (-.f64 (.f64 1/2 m) M) 2) (+.f64 (.f64 n (-.f64 (.f64 1/2 m) M)) (.f64 1/4 (pow.f64 n 2))))
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(fma.f64 (-.f64 (.f64 m 1/2) M) (+.f64 n (-.f64 (.f64 m 1/2) M)) (.f64 n (.f64 n 1/4)))
(*.f64 1/4 (pow.f64 n 2))
(.f64 (.f64 n n) 1/4)
(.f64 n (.f64 n 1/4))
(+.f64 (.f64 n (-.f64 (.f64 1/2 m) M)) (*.f64 1/4 (pow.f64 n 2)))
(fma.f64 n (-.f64 (.f64 m 1/2) M) (.f64 (*.f64 n n) 1/4))
(.f64 n (+.f64 (-.f64 (.f64 m 1/2) M) (*.f64 n 1/4)))
(+.f64 (pow.f64 (-.f64 (.f64 1/2 m) M) 2) (+.f64 (.f64 n (-.f64 (.f64 1/2 m) M)) (.f64 1/4 (pow.f64 n 2))))
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(+.f64 (.f64 (-.f64 (.f64 m 1/2) M) (+.f64 (-.f64 (.f64 m 1/2) M) n)) (.f64 (*.f64 n n) 1/4))
(fma.f64 (-.f64 (.f64 m 1/2) M) (+.f64 n (-.f64 (.f64 m 1/2) M)) (.f64 n (.f64 n 1/4)))
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(-.f64 (.f64 (pow.f64 (+.f64 n m) 2) 1/4) (.f64 M (+.f64 n m)))
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(fma.f64 M M (.f64 (+.f64 n m) (-.f64 (.f64 (+.f64 n m) 1/4) M)))
(pow.f64 M 2)
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(-.f64 (fma.f64 M M (.f64 (pow.f64 (+.f64 n m) 2) 1/4)) (.f64 M (+.f64 n m)))
(fma.f64 M (-.f64 M (+.f64 n m)) (*.f64 (pow.f64 (+.f64 n m) 2) 1/4))
(fma.f64 M M (.f64 (+.f64 n m) (-.f64 (.f64 (+.f64 n m) 1/4) M)))
(+.f64 (.f64 -1 (.f64 (+.f64 n m) M)) (+.f64 (*.f64 1/4 (pow.f64 (+.f64 n m) 2)) (pow.f64 M 2)))
(fma.f64 -1 (.f64 M (+.f64 n m)) (fma.f64 1/4 (pow.f64 (+.f64 n m) 2) (.f64 M M)))
(-.f64 (fma.f64 M M (.f64 (pow.f64 (+.f64 n m) 2) 1/4)) (.f64 M (+.f64 n m)))
(fma.f64 M (-.f64 M (+.f64 n m)) (*.f64 (pow.f64 (+.f64 n m) 2) 1/4))
(fma.f64 M M (.f64 (+.f64 n m) (-.f64 (.f64 (+.f64 n m) 1/4) M)))
(pow.f64 M 2)
(*.f64 M M)
(+.f64 (.f64 -1 (.f64 (+.f64 n m) M)) (pow.f64 M 2))
(fma.f64 -1 (.f64 M (+.f64 n m)) (.f64 M M))
(*.f64 M (+.f64 M (neg.f64 (+.f64 n m))))
(*.f64 M (-.f64 M (+.f64 n m)))
(+.f64 (.f64 -1 (.f64 (+.f64 n m) M)) (+.f64 (*.f64 1/4 (pow.f64 (+.f64 n m) 2)) (pow.f64 M 2)))
(fma.f64 -1 (.f64 M (+.f64 n m)) (fma.f64 1/4 (pow.f64 (+.f64 n m) 2) (.f64 M M)))
(-.f64 (fma.f64 M M (.f64 (pow.f64 (+.f64 n m) 2) 1/4)) (.f64 M (+.f64 n m)))
(fma.f64 M (-.f64 M (+.f64 n m)) (*.f64 (pow.f64 (+.f64 n m) 2) 1/4))
(fma.f64 M M (.f64 (+.f64 n m) (-.f64 (.f64 (+.f64 n m) 1/4) M)))
(+.f64 (.f64 -1 (.f64 (+.f64 n m) M)) (+.f64 (*.f64 1/4 (pow.f64 (+.f64 n m) 2)) (pow.f64 M 2)))
(fma.f64 -1 (.f64 M (+.f64 n m)) (fma.f64 1/4 (pow.f64 (+.f64 n m) 2) (.f64 M M)))
(-.f64 (fma.f64 M M (.f64 (pow.f64 (+.f64 n m) 2) 1/4)) (.f64 M (+.f64 n m)))
(fma.f64 M (-.f64 M (+.f64 n m)) (*.f64 (pow.f64 (+.f64 n m) 2) 1/4))
(fma.f64 M M (.f64 (+.f64 n m) (-.f64 (.f64 (+.f64 n m) 1/4) M)))

eval325.0ms (2.2%)

Compiler: Compiled 12435 to 5925 computations (52.4% saved)

prune99.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	315	5	320
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	316	5	321

Error

0.4b

Counts

321 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	35.9b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 n (.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	34.7b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (*.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	33.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 m (.f64 m 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	38.1b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (.f64 n n)) K) (-.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 312 to 214 computations (31.4% saved)

localize211.0ms (1.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 115 to 51 computations (55.7% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(-.f64 (neg.f64 (*.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))
	33.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 111 to 29 computations (73.9% saved)

series6.0ms (0%)

Counts

1 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	m	@	0	(-.f64 (neg.f64 (*.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))
1.0ms	M	@	0	(-.f64 (neg.f64 (*.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))
1.0ms	M	@	inf	(-.f64 (neg.f64 (*.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))
0.0ms	l	@	0	(-.f64 (neg.f64 (*.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))
0.0ms	l	@	inf	(-.f64 (neg.f64 (*.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))

rewrite81.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

757×	`fma-def_binary64`
577×	`log-prod_binary64`
382×	`fma-neg_binary64`
213×	`pow1/3_binary64`
213×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	261	13
2	4183	13

Stop Event

1×	node limit

Counts

1 → 160

Calls

Call 1

Inputs
(-.f64 (neg.f64 (*.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 M M) (neg.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 M M) (.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 m n) (-.f64 (.f64 M M) l))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l)) (fma.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l)) (fma.f64 (neg.f64 (cbrt.f64 (-.f64 l (-.f64 m n)))) (pow.f64 (cbrt.f64 (-.f64 l (-.f64 m n))) 2) (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l)) (+.f64 (neg.f64 (-.f64 l (-.f64 m n))) (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (-.f64 l (-.f64 m n))) (.f64 M M))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (.f64 M M) l) (-.f64 m n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (-.f64 (.f64 M M) l) 1) (-.f64 m n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l)))) (cbrt.f64 (exp.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l)))))) (log.f64 (cbrt.f64 (exp.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l))))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l))) (pow.f64 (cbrt.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l))) 2) (cbrt.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 M (sqrt.f64 (neg.f64 (-.f64 l (-.f64 m n))))) (hypot.f64 M (sqrt.f64 (neg.f64 (-.f64 l (-.f64 m n))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (.f64 M M) 3) (pow.f64 (-.f64 l (-.f64 m n)) 3)) (/.f64 1 (fma.f64 (-.f64 l (-.f64 m n)) (-.f64 (fma.f64 M M l) (-.f64 m n)) (pow.f64 M 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 M 4) (pow.f64 (-.f64 l (-.f64 m n)) 2)) (/.f64 1 (-.f64 (fma.f64 M M l) (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 M (sqrt.f64 (-.f64 l (-.f64 m n)))) (-.f64 M (sqrt.f64 (-.f64 l (-.f64 m n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (-.f64 l (-.f64 m n)) (-.f64 (fma.f64 M M l) (-.f64 m n)) (pow.f64 M 4)) (-.f64 (pow.f64 (.f64 M M) 3) (pow.f64 (-.f64 l (-.f64 m n)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 M M l) (-.f64 m n)) (-.f64 (pow.f64 M 4) (pow.f64 (-.f64 l (-.f64 m n)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 M M) 3) (pow.f64 (-.f64 l (-.f64 m n)) 3)) (fma.f64 (-.f64 l (-.f64 m n)) (-.f64 (fma.f64 M M l) (-.f64 m n)) (pow.f64 M 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 M 4) (pow.f64 (-.f64 l (-.f64 m n)) 2)) (-.f64 (fma.f64 M M l) (-.f64 m n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (.f64 M M) 3) (pow.f64 (-.f64 l (-.f64 m n)) 3))) (neg.f64 (fma.f64 (-.f64 l (-.f64 m n)) (-.f64 (fma.f64 M M l) (-.f64 m n)) (pow.f64 M 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 M 4) (pow.f64 (-.f64 l (-.f64 m n)) 2))) (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 M M) 3) (pow.f64 (neg.f64 (-.f64 l (-.f64 m n))) 3)) (+.f64 (pow.f64 M 4) (-.f64 (.f64 (neg.f64 (-.f64 l (-.f64 m n))) (neg.f64 (-.f64 l (-.f64 m n)))) (.f64 (.f64 M M) (neg.f64 (-.f64 l (-.f64 m n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (-.f64 (.f64 M M) l) 3) (pow.f64 (-.f64 m n) 3)) (fma.f64 (-.f64 (.f64 M M) l) (-.f64 (.f64 M M) l) (-.f64 (pow.f64 (-.f64 m n) 2) (.f64 (-.f64 (.f64 M M) l) (-.f64 m n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 M 4) (.f64 (neg.f64 (-.f64 l (-.f64 m n))) (neg.f64 (-.f64 l (-.f64 m n))))) (-.f64 (.f64 M M) (neg.f64 (-.f64 l (-.f64 m n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (-.f64 (.f64 M M) l) (-.f64 (.f64 M M) l)) (pow.f64 (-.f64 m n) 2)) (-.f64 (-.f64 (.f64 M M) l) (-.f64 m n)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 M (sqrt.f64 (neg.f64 (-.f64 l (-.f64 m n))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (-.f64 l (-.f64 m n)) (-.f64 (fma.f64 M M l) (-.f64 m n)) (pow.f64 M 4)) (-.f64 (pow.f64 (.f64 M M) 3) (pow.f64 (-.f64 l (-.f64 m n)) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (fma.f64 M M l) (-.f64 m n)) (-.f64 (pow.f64 M 4) (pow.f64 (-.f64 l (-.f64 m n)) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (fma.f64 M M l) (-.f64 m n)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 1 (exp.f64 (-.f64 (fma.f64 M M l) (-.f64 m n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 1 (.f64 (exp.f64 (.f64 M M)) (exp.f64 (-.f64 l (-.f64 m n))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (.f64 M M))) (exp.f64 (-.f64 l (-.f64 m n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (exp.f64 (.f64 M M)) (+.f64 1 (expm1.f64 (-.f64 l (-.f64 m n))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (.f64 M M))) (+.f64 1 (expm1.f64 (-.f64 l (-.f64 m n))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (exp.f64 (-.f64 (.f64 M M) l)) (exp.f64 (neg.f64 (-.f64 m n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (/.f64 (exp.f64 (.f64 M M)) (exp.f64 l)) (exp.f64 (neg.f64 (-.f64 m n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (exp.f64 (-.f64 (.f64 M M) l)) (/.f64 1 (exp.f64 (-.f64 m n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (/.f64 (exp.f64 (.f64 M M)) (exp.f64 l)) (/.f64 1 (exp.f64 (-.f64 m n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 M M))) (exp.f64 (neg.f64 (-.f64 l (-.f64 m n))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 M M)) (/.f64 1 (exp.f64 (-.f64 l (-.f64 m n))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 M M))) (/.f64 1 (exp.f64 (-.f64 l (-.f64 m n))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (-.f64 m n)) (exp.f64 (-.f64 (.f64 M M) l))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (-.f64 m n))) (exp.f64 (-.f64 (.f64 M M) l))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (-.f64 m n)) (/.f64 (exp.f64 (.f64 M M)) (exp.f64 l))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (-.f64 m n))) (/.f64 (exp.f64 (.f64 M M)) (exp.f64 l))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (neg.f64 (-.f64 l (-.f64 m n)))) (exp.f64 (.f64 M M))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (/.f64 1 (exp.f64 (-.f64 l (-.f64 m n)))) (exp.f64 (.f64 M M))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (neg.f64 (-.f64 l (-.f64 m n)))) (+.f64 1 (expm1.f64 (.f64 M M)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (/.f64 1 (exp.f64 (-.f64 l (-.f64 m n)))) (+.f64 1 (expm1.f64 (.f64 M M)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (/.f64 (exp.f64 (.f64 M M)) (exp.f64 l)) (exp.f64 (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (-.f64 (.f64 M M) l)) (+.f64 1 (expm1.f64 (-.f64 m n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (/.f64 (exp.f64 (.f64 M M)) (exp.f64 l)) (+.f64 1 (expm1.f64 (-.f64 m n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 M M) l)) 3))))) (#(struct:change #<rule 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Outputs

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(2) ((x fma.f64 (cbrt.f64 (pow.f64 M 4)) (cbrt.f64 (*.f64 M M)) (*.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 M 4)) (neg.f64 (cbrt.f64 (*.f64 M M))) (neg.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 M 4)) (neg.f64 (cbrt.f64 (*.f64 M M))) (*.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 M (sqrt.f64 (neg.f64 (-.f64 l (-.f64 m n))))) (hypot.f64 M (sqrt.f64 (neg.f64 (-.f64 l (-.f64 m n))))) (fma.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 M (sqrt.f64 (neg.f64 (-.f64 l (-.f64 m n))))) (hypot.f64 M (sqrt.f64 (neg.f64 (-.f64 l (-.f64 m n))))) (fma.f64 (neg.f64 (cbrt.f64 (-.f64 l (-.f64 m n)))) (pow.f64 (cbrt.f64 (-.f64 l (-.f64 m n))) 2) (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 M (sqrt.f64 (neg.f64 (-.f64 l (-.f64 m n))))) (hypot.f64 M (sqrt.f64 (neg.f64 (-.f64 l (-.f64 m n))))) (+.f64 (neg.f64 (-.f64 l (-.f64 m n))) (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 M) (*.f64 (sqrt.f64 M) (neg.f64 M)) (neg.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 M) (*.f64 (sqrt.f64 M) (neg.f64 M)) (*.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 M) (*.f64 (sqrt.f64 M) M) (neg.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 M) (*.f64 (sqrt.f64 M) M) (*.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 m n)) (sqrt.f64 (-.f64 m n)) (-.f64 (*.f64 M M) l))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 l (-.f64 m n))) (neg.f64 (sqrt.f64 (-.f64 l (-.f64 m n)))) (*.f64 M M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (*.f64 M M) 3) (pow.f64 (-.f64 l (-.f64 m n)) 3)) (/.f64 1 (fma.f64 (-.f64 l (-.f64 m n)) (-.f64 (fma.f64 M M l) (-.f64 m n)) (pow.f64 M 4))) (fma.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (*.f64 M M) 3) (pow.f64 (-.f64 l (-.f64 m n)) 3)) (/.f64 1 (fma.f64 (-.f64 l (-.f64 m n)) (-.f64 (fma.f64 M M l) (-.f64 m n)) (pow.f64 M 4))) (fma.f64 (neg.f64 (cbrt.f64 (-.f64 l (-.f64 m n)))) (pow.f64 (cbrt.f64 (-.f64 l (-.f64 m n))) 2) (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (*.f64 M M) 3) (pow.f64 (-.f64 l (-.f64 m n)) 3)) (/.f64 1 (fma.f64 (-.f64 l (-.f64 m n)) (-.f64 (fma.f64 M M l) (-.f64 m n)) (pow.f64 M 4))) (+.f64 (neg.f64 (-.f64 l (-.f64 m n))) (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 m 3) (pow.f64 n 3)) (/.f64 1 (fma.f64 n (+.f64 m n) (*.f64 m m))) (-.f64 (*.f64 M M) l))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (*.f64 M M) (neg.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (*.f64 M M) (*.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (-.f64 l (-.f64 m n)) (*.f64 M M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 M 4) (pow.f64 (-.f64 l (-.f64 m n)) 2)) (/.f64 1 (-.f64 (fma.f64 M M l) (-.f64 m n))) (fma.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 M 4) (pow.f64 (-.f64 l (-.f64 m n)) 2)) (/.f64 1 (-.f64 (fma.f64 M M l) (-.f64 m n))) (fma.f64 (neg.f64 (cbrt.f64 (-.f64 l (-.f64 m n)))) (pow.f64 (cbrt.f64 (-.f64 l (-.f64 m n))) 2) (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 M 4) (pow.f64 (-.f64 l (-.f64 m n)) 2)) (/.f64 1 (-.f64 (fma.f64 M M l) (-.f64 m n))) (+.f64 (neg.f64 (-.f64 l (-.f64 m n))) (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 m n) (-.f64 m n)) (/.f64 1 (+.f64 m n)) (-.f64 (*.f64 M M) l))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 M) M (neg.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 M) M (*.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (*.f64 M M) l) 1 (-.f64 m n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 M (sqrt.f64 M)) (sqrt.f64 M) (neg.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 M (sqrt.f64 M)) (sqrt.f64 M) (*.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (neg.f64 (-.f64 l (-.f64 m n)))) (cbrt.f64 (neg.f64 (-.f64 l (-.f64 m n))))) (cbrt.f64 (neg.f64 (-.f64 l (-.f64 m n)))) (*.f64 M M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 M M) l)) (cbrt.f64 (-.f64 (*.f64 M M) l))) (cbrt.f64 (-.f64 (*.f64 M M) l)) (-.f64 m n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 M M) l)) (cbrt.f64 (-.f64 (*.f64 M M) l))) (cbrt.f64 (-.f64 (*.f64 M M) l)) (neg.f64 (neg.f64 (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (neg.f64 (-.f64 l (-.f64 m n)))) (sqrt.f64 (neg.f64 (-.f64 l (-.f64 m n)))) (*.f64 M M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (*.f64 M M) l)) (sqrt.f64 (-.f64 (*.f64 M M) l)) (-.f64 m n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (*.f64 M M) l)) (sqrt.f64 (-.f64 (*.f64 M M) l)) (neg.f64 (neg.f64 (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sqrt.f64 (-.f64 l (-.f64 m n)))) (sqrt.f64 (-.f64 l (-.f64 m n))) (*.f64 M M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fabs.f64 (pow.f64 (cbrt.f64 (-.f64 m n)) 2)) (fabs.f64 (cbrt.f64 (-.f64 m n))) (-.f64 (*.f64 M M) l))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 m) (sqrt.f64 n)) (-.f64 (sqrt.f64 m) (sqrt.f64 n)) (-.f64 (*.f64 M M) l))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 M (sqrt.f64 (-.f64 l (-.f64 m n)))) (-.f64 M (sqrt.f64 (-.f64 l (-.f64 m n)))) (fma.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 M (sqrt.f64 (-.f64 l (-.f64 m n)))) (-.f64 M (sqrt.f64 (-.f64 l (-.f64 m n)))) (fma.f64 (neg.f64 (cbrt.f64 (-.f64 l (-.f64 m n)))) (pow.f64 (cbrt.f64 (-.f64 l (-.f64 m n))) 2) (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 M (sqrt.f64 (-.f64 l (-.f64 m n)))) (-.f64 M (sqrt.f64 (-.f64 l (-.f64 m n)))) (+.f64 (neg.f64 (-.f64 l (-.f64 m n))) (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 M (sqrt.f64 l)) (-.f64 M (sqrt.f64 l)) (-.f64 m n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 M (sqrt.f64 l)) (-.f64 M (sqrt.f64 l)) (neg.f64 (neg.f64 (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (pow.f64 M 4))) (cbrt.f64 (*.f64 M M)) (neg.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (pow.f64 M 4))) (cbrt.f64 (*.f64 M M)) (*.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (-.f64 l (-.f64 m n))) 2)) (cbrt.f64 (-.f64 l (-.f64 m n))) (*.f64 M M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1 (cbrt.f64 (pow.f64 M 4))) (cbrt.f64 (*.f64 M M)) (neg.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1 (cbrt.f64 (pow.f64 M 4))) (cbrt.f64 (*.f64 M M)) (*.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 M) 1) M (neg.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 M) 1) M (*.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 M) (cbrt.f64 (*.f64 M M))) (cbrt.f64 M) (neg.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 M) (cbrt.f64 (*.f64 M M))) (cbrt.f64 M) (*.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 M) (sqrt.f64 M)) (sqrt.f64 M) (neg.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 M) (sqrt.f64 M)) (sqrt.f64 M) (*.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 M (cbrt.f64 (*.f64 M M))) (cbrt.f64 M) (neg.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 M (cbrt.f64 (*.f64 M M))) (cbrt.f64 M) (*.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))))

simplify138.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

929×	`fma-neg_binary64`
532×	`unswap-sqr_binary64`
472×	`fma-def_binary64`
413×	`distribute-rgt-neg-in_binary64`
290×	`neg-sub0_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	29	669
1	78	585
2	143	585
3	291	585
4	590	585
5	1308	585
6	2304	585
7	4368	585
8	5753	579
9	6675	579
10	7233	579
11	7811	579

Stop Event

1×	node limit

Counts

208 → 174

Calls

Call 1

Inputs
(-.f64 (fabs.f64 (-.f64 m n)) l)
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(*.f64 -1 (pow.f64 M 2))
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(*.f64 -1 (pow.f64 M 2))
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (fabs.f64 (-.f64 m n)) (pow.f64 M 2))
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(*.f64 -1 l)
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(*.f64 -1 l)
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (*.f64 -1 m)))) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (*.f64 -1 m)))) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (*.f64 -1 m)))) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (*.f64 -1 m)))) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (+.f64 (*.f64 -1 n) m)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (+.f64 (*.f64 -1 n) m)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (+.f64 (*.f64 -1 n) m)) (+.f64 l (pow.f64 M 2)))
(-.f64 (fabs.f64 (+.f64 (*.f64 -1 n) m)) (+.f64 l (pow.f64 M 2)))

Outputs
(-.f64 (fabs.f64 (-.f64 m n)) l)
(-.f64 (fabs.f64 (-.f64 n m)) l)
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(*.f64 -1 (pow.f64 M 2))
(neg.f64 (*.f64 M M))
(*.f64 M (neg.f64 M))
(*.f64 M M)
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(*.f64 -1 (pow.f64 M 2))
(neg.f64 (*.f64 M M))
(*.f64 M (neg.f64 M))
(*.f64 M M)
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1 (pow.f64 M 2))) l)
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (pow.f64 M 2))
(-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M))
(fma.f64 M M (fabs.f64 (-.f64 n m)))
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(*.f64 -1 l)
(neg.f64 l)
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(*.f64 -1 l)
(neg.f64 l)
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (+.f64 (*.f64 -1 l) (fabs.f64 (-.f64 m n))) (pow.f64 M 2))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (*.f64 -1 m)))) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (*.f64 -1 m)))) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (*.f64 -1 m)))) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (*.f64 -1 m)))) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (+.f64 (*.f64 -1 n) m)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (+.f64 (*.f64 -1 n) m)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (+.f64 (*.f64 -1 n) m)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))
(-.f64 (fabs.f64 (+.f64 (*.f64 -1 n) m)) (+.f64 l (pow.f64 M 2)))
(-.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 M M)) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 M M l))

localize53.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 m (.f64 m 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
✓	0.0b	(-.f64 (neg.f64 (.f64 m (.f64 m 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))
	33.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 125 to 52 computations (58.4% saved)

series46.0ms (0.3%)

Counts

2 → 96

Calls

24 calls:

Time	Variable		Point	Expression
25.0ms	n	@	0	(-.f64 (neg.f64 (.f64 m (.f64 m 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))
3.0ms	n	@	inf	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 m (.f64 m 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
1.0ms	l	@	inf	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 m (.f64 m 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
1.0ms	m	@	0	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 m (.f64 m 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
1.0ms	l	@	0	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 m (.f64 m 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))

rewrite101.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

448×	`log1p-udef_binary64`
274×	`add-sqr-sqrt_binary64`
267×	`*-un-lft-identity_binary64`
267×	`pow1_binary64`
258×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	59
1	518	51
2	7880	51

Stop Event

1×	node limit

Counts

2 → 68

Calls

Call 1

Inputs

(-.f64 (neg.f64 (*.f64 m (*.f64 m 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))

(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (*.f64 m (*.f64 m 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 m (*.f64 m 1/4)) (neg.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 m (*.f64 m 1/4)) (*.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 m n) (-.f64 (*.f64 m (*.f64 m 1/4)) l))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 m (*.f64 m -1/4) (neg.f64 (-.f64 l (-.f64 m n)))) (fma.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 m (*.f64 m -1/4) (neg.f64 (-.f64 l (-.f64 m n)))) (fma.f64 (neg.f64 (cbrt.f64 (-.f64 l (-.f64 m n)))) (cbrt.f64 (pow.f64 (-.f64 l (-.f64 m n)) 2)) (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 m (*.f64 m -1/4) (neg.f64 (-.f64 l (-.f64 m n)))) (fma.f64 (neg.f64 (sqrt.f64 (-.f64 l (-.f64 m n)))) (sqrt.f64 (-.f64 l (-.f64 m n))) (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 m 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m (*.f64 m -1/4) (neg.f64 (-.f64 l (-.f64 m n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 m (*.f64 m -1/4) (neg.f64 (-.f64 l (-.f64 m n))))) (pow.f64 (cbrt.f64 (fma.f64 m (*.f64 m -1/4) (neg.f64 (-.f64 l (-.f64 m n))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 m (*.f64 m -1/4) (neg.f64 (-.f64 l (-.f64 m n))))) 2) (cbrt.f64 (fma.f64 m (*.f64 m -1/4) (neg.f64 (-.f64 l (-.f64 m n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 m (*.f64 m -1/4) (neg.f64 (-.f64 l (-.f64 m n))))) (sqrt.f64 (fma.f64 m (*.f64 m -1/4) (neg.f64 (-.f64 l (-.f64 m n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 m (*.f64 m 1/4)) 3) (pow.f64 (-.f64 l (-.f64 m n)) 3)) (/.f64 1 (+.f64 (pow.f64 (*.f64 m (*.f64 m 1/4)) 2) (*.f64 (-.f64 l (-.f64 m n)) (fma.f64 m (*.f64 m -1/4) (-.f64 l (-.f64 m n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 m (*.f64 m 1/4)) 2) 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simplify123.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

523×	`associate-*r/_binary64`
453×	`associate-*l/_binary64`
297×	`fma-neg_binary64`
294×	`unsub-neg_binary64`
235×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	184	3910
1	567	3769
2	1931	3381
3	6152	3373

Stop Event

1×	node limit

Counts

164 → 128

Calls

Call 1

Inputs
(-.f64 (fabs.f64 (-.f64 m n)) l)
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (-.f64 m n))) l)
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (-.f64 m n))) l)
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (-.f64 m n))) l)
(*.f64 -1/4 (pow.f64 m 2))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (-.f64 m n))) l)
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (-.f64 m n))) l)
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (-.f64 m n))) l)
(*.f64 -1/4 (pow.f64 m 2))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m))))) l)
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m))))) l)
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m))))) l)
(-.f64 (fabs.f64 (-.f64 m n)) (*.f64 1/4 (pow.f64 m 2)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(*.f64 -1 l)
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(*.f64 -1 l)
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))
(-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))
(-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))
(-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))
(-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (neg.f64 M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(+.f64 (.f64 -1/2 (.f64 K (.f64 (sin.f64 (neg.f64 M)) (.f64 (+.f64 n m) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))))) (.f64 (cos.f64 (neg.f64 M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2)))))))
(+.f64 (.f64 -1/2 (.f64 K (.f64 (sin.f64 (neg.f64 M)) (.f64 (+.f64 n m) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))))) (+.f64 (.f64 -1/8 (.f64 (cos.f64 (neg.f64 M)) (.f64 (pow.f64 K 2) (.f64 (pow.f64 (+.f64 n m) 2) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))))) (.f64 (cos.f64 (neg.f64 M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))))
(+.f64 (.f64 -1/2 (.f64 K (.f64 (sin.f64 (neg.f64 M)) (.f64 (+.f64 n m) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))))) (+.f64 (.f64 1/48 (.f64 (pow.f64 K 3) (.f64 (sin.f64 (neg.f64 M)) (.f64 (pow.f64 (+.f64 n m) 3) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))))) (+.f64 (.f64 -1/8 (.f64 (cos.f64 (neg.f64 M)) (.f64 (pow.f64 K 2) (.f64 (pow.f64 (+.f64 n m) 2) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))))) (.f64 (cos.f64 (neg.f64 M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2)))))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)))
(+.f64 (.f64 -1/2 (.f64 K (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m)))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M))))
(+.f64 (.f64 -1/2 (.f64 K (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m)))) (+.f64 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (.f64 (+.f64 (.f64 -1/4 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)))) (.f64 -1/8 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (.f64 (pow.f64 K 2) (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)))))) (pow.f64 m 2))))
(+.f64 (.f64 (pow.f64 m 3) (+.f64 (.f64 1/48 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (.f64 (pow.f64 K 3) (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))))) (.f64 1/8 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))))))) (+.f64 (.f64 -1/2 (.f64 K (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m)))) (+.f64 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (.f64 (+.f64 (.f64 -1/4 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)))) (.f64 -1/8 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (.f64 (pow.f64 K 2) (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)))))) (pow.f64 m 2)))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (.f64 -1 m)))) M)) (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (.f64 -1 m)))) M)) (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (.f64 -1 m)))) M)) (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (.f64 -1 m)))) M)) (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(+.f64 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2)))))) (.f64 -1/2 (.f64 n (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))))))))
(+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (.f64 (pow.f64 K 2) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))))) (+.f64 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2)))))) (.f64 -1/2 (.f64 n (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2)))))))))))
(+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (.f64 (pow.f64 K 2) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))))) (+.f64 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2)))))) (+.f64 (.f64 1/48 (.f64 (pow.f64 n 3) (.f64 (pow.f64 K 3) (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))))) (.f64 -1/2 (.f64 n (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))))))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (.f64 -1 n)))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (.f64 -1 n)))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (.f64 -1 n)))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (.f64 -1 n)))) M)))
(.f64 (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(+.f64 (.f64 (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2)))))) (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))) M)))
(+.f64 (.f64 (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2)))))) (+.f64 (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))) M)) (.f64 -1/2 (.f64 (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))) (pow.f64 M 2))))))
(+.f64 (.f64 -1/6 (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))) (pow.f64 M 3)))) (+.f64 (.f64 (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2)))))) (+.f64 (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))) M)) (.f64 -1/2 (.f64 (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))) (pow.f64 M 2)))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 m 2))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 m 2)))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(+.f64 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 m 2)))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))) (.f64 -1 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 m 2)))) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) l))))
(+.f64 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 m 2)))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))) (+.f64 (.f64 1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 m 2)))) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (pow.f64 l 2)))) (.f64 -1 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 m 2)))) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) l)))))
(+.f64 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 m 2)))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))) (+.f64 (.f64 1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 m 2)))) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (pow.f64 l 2)))) (+.f64 (.f64 -1 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 m 2)))) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) l))) (.f64 -1/6 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 m 2)))) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (pow.f64 l 3)))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))

Outputs
(-.f64 (fabs.f64 (-.f64 m n)) l)
(-.f64 (fabs.f64 (-.f64 n m)) l)
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
(*.f64 -1/4 (pow.f64 m 2))
(.f64 -1/4 (.f64 m m))
(.f64 m (.f64 m -1/4))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
(*.f64 -1/4 (pow.f64 m 2))
(.f64 -1/4 (.f64 m m))
(.f64 m (.f64 m -1/4))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m))))) l)
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m))))) l)
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 m 2)) (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m))))) l)
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
(-.f64 (fabs.f64 (-.f64 m n)) (*.f64 1/4 (pow.f64 m 2)))
(fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n)))
(fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 n m)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
(*.f64 -1 l)
(neg.f64 l)
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
(*.f64 -1 l)
(neg.f64 l)
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))
(-.f64 (fma.f64 -1/4 (*.f64 m m) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (*.f64 m m) 1/4 l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (*.f64 m 1/4) l))
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(fma.f64 (exp.f64 (fma.f64 -1/4 (.f64 m m) (fabs.f64 (-.f64 m n)))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 m n))) M)) (fma.f64 1/2 (.f64 (exp.f64 (fma.f64 -1/4 (.f64 m m) (fabs.f64 (-.f64 m n)))) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 m n))) M)) (.f64 l l))) (fma.f64 -1 (.f64 (exp.f64 (fma.f64 -1/4 (.f64 m m) (fabs.f64 (-.f64 m n)))) (.f64 l (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 m n))) M)))) (.f64 -1/6 (.f64 (exp.f64 (fma.f64 -1/4 (.f64 m m) (fabs.f64 (-.f64 m n)))) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 m n))) M)) (pow.f64 l 3)))))))
(fma.f64 (cos.f64 (fma.f64 1/2 (.f64 K (+.f64 m n)) (neg.f64 M))) (exp.f64 (fma.f64 -1/4 (.f64 m m) (fabs.f64 (-.f64 n m)))) (fma.f64 1/2 (.f64 (cos.f64 (fma.f64 1/2 (.f64 K (+.f64 m n)) (neg.f64 M))) (.f64 (exp.f64 (fma.f64 -1/4 (.f64 m m) (fabs.f64 (-.f64 n m)))) (.f64 l l))) (-.f64 (.f64 (.f64 (cos.f64 (fma.f64 1/2 (.f64 K (+.f64 m n)) (neg.f64 M))) (exp.f64 (fma.f64 -1/4 (.f64 m m) (fabs.f64 (-.f64 n m))))) (.f64 (pow.f64 l 3) -1/6)) (.f64 l (.f64 (cos.f64 (fma.f64 1/2 (.f64 K (+.f64 m n)) (neg.f64 M))) (exp.f64 (fma.f64 -1/4 (.f64 m m) (fabs.f64 (-.f64 n m)))))))))
(+.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (-.f64 (exp.f64 (fma.f64 -1/4 (.f64 m m) (fabs.f64 (-.f64 n m)))) (.f64 (exp.f64 (fma.f64 -1/4 (.f64 m m) (fabs.f64 (-.f64 n m)))) l))) (.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (fma.f64 -1/4 (.f64 m m) (fabs.f64 (-.f64 n m))))) (+.f64 (.f64 (.f64 l l) 1/2) (.f64 (pow.f64 l 3) -1/6))))
(fma.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (+.f64 (exp.f64 (fma.f64 -1/4 (.f64 m m) (fabs.f64 (-.f64 n m)))) (.f64 (.f64 1/2 (exp.f64 (fma.f64 -1/4 (.f64 m m) (fabs.f64 (-.f64 n m))))) (.f64 l l))) (.f64 (.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))) (exp.f64 (fma.f64 -1/4 (.f64 m m) (fabs.f64 (-.f64 n m))))) (-.f64 (*.f64 (pow.f64 l 3) -1/6) l)))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (.f64 m m)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (.f64 m 1/4) l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (.f64 m m)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (.f64 m 1/4) l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (.f64 m m)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (.f64 m 1/4) l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 m 2))))))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (.f64 m m)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (.f64 m 1/4) l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (.f64 m m)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (.f64 m 1/4) l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (.f64 m m)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (.f64 m 1/4) l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (.f64 m m)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (.f64 m 1/4) l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 m 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (.f64 m m)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (.f64 m m) 1/4 l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 m (.f64 m 1/4) l))) (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) 1/2) (neg.f64 M))))

localize45.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(-.f64 (neg.f64 (.f64 n (.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))
✓	0.0b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 n (.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	33.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 125 to 52 computations (58.4% saved)

series19.0ms (0.1%)

Counts

2 → 96

Calls

24 calls:

Time	Variable		Point	Expression
2.0ms	K	@	0	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 n (.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
1.0ms	n	@	inf	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 n (.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
1.0ms	n	@	0	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 n (.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
1.0ms	m	@	0	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 n (.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
1.0ms	K	@	inf	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 n (.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))

rewrite94.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

446×	`log1p-udef_binary64`
273×	`add-sqr-sqrt_binary64`
266×	`*-un-lft-identity_binary64`
266×	`pow1_binary64`
257×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	59
1	517	51
2	7858	51

Stop Event

1×	node limit

Counts

2 → 68

Calls

Call 1

Inputs

(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (*.f64 n (*.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))

(-.f64 (neg.f64 (*.f64 n (*.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 n (*.f64 n -1/4)) (neg.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 n (*.f64 n -1/4)) (*.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n -1/4)) l))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n -1/4)) l)) (fma.f64 (neg.f64 (-.f64 l (-.f64 m n))) 1 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n -1/4)) l)) (fma.f64 (neg.f64 (cbrt.f64 (-.f64 l (-.f64 m n)))) (pow.f64 (cbrt.f64 (-.f64 l (-.f64 m n))) 2) (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n -1/4)) l)) (fma.f64 (neg.f64 (sqrt.f64 (-.f64 l (-.f64 m n)))) (sqrt.f64 (-.f64 l (-.f64 m n))) (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (-.f64 m n) 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simplify121.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

415×	`associate-*l/_binary64`
361×	`unsub-neg_binary64`
338×	`associate-*r/_binary64`
288×	`fma-neg_binary64`
246×	`neg-sub0_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	3912
1	572	3744
2	2025	3392
3	6023	3390

Stop Event

1×	node limit

Counts

164 → 129

Calls

Call 1

Inputs
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (neg.f64 M)))
(+.f64 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (neg.f64 M))) (.f64 -1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 K (*.f64 (sin.f64 (neg.f64 M)) (+.f64 n m))))))
(+.f64 (.f64 -1/8 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 (cos.f64 (neg.f64 M)) (.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2))))) (+.f64 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (neg.f64 M))) (.f64 -1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 K (.f64 (sin.f64 (neg.f64 M)) (+.f64 n m)))))))
(+.f64 (.f64 -1/8 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 (cos.f64 (neg.f64 M)) (.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2))))) (+.f64 (.f64 1/48 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 (pow.f64 K 3) (.f64 (sin.f64 (neg.f64 M)) (pow.f64 (+.f64 n m) 3))))) (+.f64 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (neg.f64 M))) (.f64 -1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 K (*.f64 (sin.f64 (neg.f64 M)) (+.f64 n m))))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 K m)))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M))))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 K m)))) (+.f64 (.f64 -1/8 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 (pow.f64 K 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (pow.f64 m 2))))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)))))
(+.f64 (.f64 1/48 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 (pow.f64 K 3) (pow.f64 m 3))))) (+.f64 (.f64 -1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 K m)))) (+.f64 (.f64 -1/8 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 (pow.f64 K 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (pow.f64 m 2))))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (.f64 -1 m)))) M)) (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 n 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (.f64 -1 m)))) M)) (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 n 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (.f64 -1 m)))) M)) (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 n 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (.f64 -1 m)))) M)) (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 n 2))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)))
(+.f64 (.f64 -1/2 (.f64 n (.f64 K (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l))))
(+.f64 (.f64 (pow.f64 n 2) (+.f64 (.f64 -1/8 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (pow.f64 K 2)))) (.f64 -1/4 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)))))) (+.f64 (.f64 -1/2 (.f64 n (.f64 K (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)))))
(+.f64 (.f64 (pow.f64 n 2) (+.f64 (.f64 -1/8 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (pow.f64 K 2)))) (.f64 -1/4 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)))))) (+.f64 (.f64 -1/2 (.f64 n (.f64 K (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (+.f64 (.f64 (pow.f64 n 3) (+.f64 (.f64 1/48 (.f64 (pow.f64 K 3) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))) (.f64 1/8 (.f64 K (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))))) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (.f64 -1 n)))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (.f64 -1 n)))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (.f64 -1 n)))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (.f64 -1 n)))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))))
(+.f64 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))) (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) M)))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (pow.f64 M 2)))) (+.f64 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))) (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) M))))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (pow.f64 M 2)))) (+.f64 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))) (+.f64 (.f64 -1/6 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (pow.f64 M 3)))) (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) M)))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (*.f64 K (+.f64 n m))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2)))))
(+.f64 (.f64 -1 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (.f64 l (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))))) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))))
(+.f64 (.f64 1/2 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (.f64 (pow.f64 l 2) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))))) (+.f64 (.f64 -1 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (.f64 l (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))))) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2)))))))
(+.f64 (.f64 1/2 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (.f64 (pow.f64 l 2) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))))) (+.f64 (.f64 -1 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (.f64 l (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))))) (+.f64 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))) (.f64 -1/6 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (.f64 (pow.f64 l 3) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(-.f64 (fabs.f64 (-.f64 m n)) l)
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) (fabs.f64 (-.f64 m n))) l)
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) (fabs.f64 (-.f64 m n))) l)
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) (fabs.f64 (-.f64 m n))) l)
(*.f64 -1/4 (pow.f64 n 2))
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1/4 (pow.f64 n 2))) l)
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1/4 (pow.f64 n 2))) l)
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1/4 (pow.f64 n 2))) l)
(*.f64 -1/4 (pow.f64 n 2))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (fabs.f64 (+.f64 (.f64 -1 n) m))) l)
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (fabs.f64 (+.f64 (.f64 -1 n) m))) l)
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (fabs.f64 (+.f64 (.f64 -1 n) m))) l)
(-.f64 (fabs.f64 (-.f64 m n)) (*.f64 1/4 (pow.f64 n 2)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(*.f64 -1 l)
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(*.f64 -1 l)
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 n 2))))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 n 2))))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 n 2))))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 n 2))))

Outputs
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (neg.f64 M)))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 (*.f64 n n) -1/4))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(+.f64 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (neg.f64 M))) (.f64 -1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 K (*.f64 (sin.f64 (neg.f64 M)) (+.f64 n m))))))
(fma.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 (.f64 n n) -1/4))) (cos.f64 M) (.f64 -1/2 (.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 (.f64 n n) -1/4))) (.f64 K (.f64 (neg.f64 (sin.f64 M)) (+.f64 m n))))))
(fma.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (.f64 (.f64 K (.f64 (neg.f64 (sin.f64 M)) (+.f64 m n))) -1/2)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (+.f64 (cos.f64 M) (.f64 -1/2 (.f64 K (*.f64 (neg.f64 (sin.f64 M)) (+.f64 m n))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (+.f64 (cos.f64 M) (.f64 -1/2 (.f64 K (*.f64 (neg.f64 (sin.f64 M)) (+.f64 m n))))))
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(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 (.f64 n n) -1/4))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 (-.f64 (.f64 K (.f64 1/2 (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 (-.f64 M (.f64 K (.f64 1/2 (+.f64 m n))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 (.f64 n n) -1/4))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 (-.f64 (.f64 K (.f64 1/2 (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 (-.f64 M (.f64 K (.f64 1/2 (+.f64 m n))))))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 (.f64 n n) -1/4))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 (-.f64 (.f64 K (.f64 1/2 (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 (-.f64 M (.f64 K (.f64 1/2 (+.f64 m n))))))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 (.f64 n n) -1/4))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 (-.f64 (.f64 K (.f64 1/2 (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 (-.f64 M (.f64 K (.f64 1/2 (+.f64 m n))))))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 (.f64 n n) -1/4))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 (-.f64 (.f64 K (.f64 1/2 (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 (-.f64 M (.f64 K (.f64 1/2 (+.f64 m n))))))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 (.f64 n n) -1/4))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 (-.f64 (.f64 K (.f64 1/2 (+.f64 m n))) M)))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 (-.f64 M (.f64 K (.f64 1/2 (+.f64 m n))))))
(-.f64 (fabs.f64 (-.f64 m n)) l)
(-.f64 (fabs.f64 (-.f64 n m)) l)
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(*.f64 -1/4 (pow.f64 n 2))
(.f64 (.f64 n n) -1/4)
(.f64 n (.f64 n -1/4))
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1/4 (pow.f64 n 2))) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1/4 (pow.f64 n 2))) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (+.f64 (fabs.f64 (-.f64 m n)) (*.f64 -1/4 (pow.f64 n 2))) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(*.f64 -1/4 (pow.f64 n 2))
(.f64 (.f64 n n) -1/4)
(.f64 n (.f64 n -1/4))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (fabs.f64 (+.f64 (.f64 -1 n) m))) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (fabs.f64 (+.f64 (.f64 -1 n) m))) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (fabs.f64 (+.f64 (.f64 -1 n) m))) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (fabs.f64 (-.f64 m n)) (*.f64 1/4 (pow.f64 n 2)))
(fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n)))
(fma.f64 (*.f64 n n) -1/4 (fabs.f64 (-.f64 n m)))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(*.f64 -1 l)
(neg.f64 l)
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(*.f64 -1 l)
(neg.f64 l)
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (.f64 1/4 (pow.f64 n 2)))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 n 2))))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 n 2))))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 n 2))))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (.f64 1/4 (pow.f64 n 2))))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fabs.f64 (-.f64 m n))) l)
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l))
(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l))

localize68.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.5b	(-.f64 (.f64 m m) (.f64 n n))
✓	8.6b	(.f64 (-.f64 (.f64 m m) (*.f64 n n)) K)
✓	17.0b	(/.f64 (.f64 (-.f64 (.f64 m m) (*.f64 n n)) K) (-.f64 m n))
✓	34.1b	(cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (*.f64 n n)) K) (-.f64 m n)) 2) M))

Compiler

Compiled 215 to 68 computations (68.4% saved)

series23.0ms (0.2%)

Counts

4 → 144

Calls

36 calls:

Time	Variable		Point	Expression
5.0ms	m	@	inf	(cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (*.f64 n n)) K) (-.f64 m n)) 2) M))
2.0ms	K	@	0	(cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (*.f64 n n)) K) (-.f64 m n)) 2) M))
1.0ms	M	@	0	(cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (*.f64 n n)) K) (-.f64 m n)) 2) M))
1.0ms	K	@	0	(/.f64 (.f64 (-.f64 (.f64 m m) (*.f64 n n)) K) (-.f64 m n))
1.0ms	m	@	0	(cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (*.f64 n n)) K) (-.f64 m n)) 2) M))

rewrite147.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

797×	`fma-def_binary64`
363×	`fma-neg_binary64`
329×	`expm1-udef_binary64`
329×	`log1p-udef_binary64`
192×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	69
1	359	45
2	5478	45

Stop Event

1×	node limit

Counts

4 → 312

Calls

Call 1

Inputs
(cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (*.f64 n n)) K) (-.f64 m n)) 2) M))
(/.f64 (.f64 (-.f64 (.f64 m m) (*.f64 n n)) K) (-.f64 m n))
(.f64 (-.f64 (.f64 m m) (*.f64 n n)) K)
(-.f64 (.f64 m m) (.f64 n n))

Outputs
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n)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 m (pow.f64 (cbrt.f64 m) 2)) (cbrt.f64 m) (fma.f64 n (neg.f64 n) (fma.f64 n (neg.f64 n) (.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 m (pow.f64 (cbrt.f64 m) 2)) (cbrt.f64 m) (neg.f64 (-.f64 (.f64 n n) (fma.f64 n (neg.f64 n) (.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (neg.f64 n) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n) (.f64 m m))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (neg.f64 n) (sqrt.f64 n)) (sqrt.f64 n) (.f64 m m))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 m n) 1) (-.f64 m n) (fma.f64 n (neg.f64 n) (.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 m n) 1) (-.f64 m n) (fma.f64 (.f64 n (neg.f64 n)) 1 (.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 m n) 1) (-.f64 m n) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 (pow.f64 n 4)) (.f64 n n)))))) (#(struct:change #<rule 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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 m n) (cbrt.f64 (pow.f64 (-.f64 m n) 2))) (cbrt.f64 (-.f64 m n)) (+.f64 (fma.f64 n (neg.f64 n) (.f64 n n)) (fma.f64 n (neg.f64 n) (.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 m n) (sqrt.f64 (-.f64 m n))) (sqrt.f64 (-.f64 m n)) (fma.f64 n (neg.f64 n) (.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 m n) (sqrt.f64 (-.f64 m n))) (sqrt.f64 (-.f64 m n)) (fma.f64 (.f64 n (neg.f64 n)) 1 (.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 m n) (sqrt.f64 (-.f64 m n))) (sqrt.f64 (-.f64 m n)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 (pow.f64 n 4)) (.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 m n) (sqrt.f64 (-.f64 m n))) (sqrt.f64 (-.f64 m n)) (.f64 (fma.f64 n (neg.f64 n) (.f64 n n)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 m n) (sqrt.f64 (-.f64 m n))) (sqrt.f64 (-.f64 m n)) (+.f64 (fma.f64 n (neg.f64 n) (.f64 n n)) (fma.f64 n (neg.f64 n) (*.f64 n n))))))))

simplify174.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

797×	`associate-r_binary64`
780×	`associate-l_binary64`
483×	`fma-def_binary64`
432×	`times-frac_binary64`
389×	`div-sub_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	2893
1	367	2769
2	1190	2651
3	7108	2648

Stop Event

1×	node limit

Counts

456 → 369

Calls

Call 1

Inputs
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 -1/2 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (*.f64 K m))))
(+.f64 (.f64 -1/8 (.f64 (pow.f64 K 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (pow.f64 m 2)))) (+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 -1/2 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 K m)))))
(+.f64 (.f64 -1/8 (.f64 (pow.f64 K 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (pow.f64 m 2)))) (+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (+.f64 (.f64 1/48 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 (pow.f64 K 3) (pow.f64 m 3)))) (.f64 -1/2 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (*.f64 K m))))))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 -1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 n (*.f64 -1 m)))) M))
(cos.f64 (-.f64 (.f64 -1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 n (*.f64 -1 m)))) M))
(cos.f64 (-.f64 (.f64 -1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 n (*.f64 -1 m)))) M))
(cos.f64 (-.f64 (.f64 -1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 n (*.f64 -1 m)))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))
(+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)))
(+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))) (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (pow.f64 K 2)))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))
(+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))) (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (pow.f64 K 2)))) (+.f64 (.f64 1/48 (.f64 (pow.f64 n 3) (.f64 (pow.f64 K 3) (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)))))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 (*.f64 -1 n) m))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 (*.f64 -1 n) m))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 (*.f64 -1 n) m))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 (*.f64 -1 n) m))) M))
(cos.f64 (neg.f64 M))
(+.f64 (cos.f64 (neg.f64 M)) (.f64 -1/2 (/.f64 (.f64 K (*.f64 (sin.f64 (neg.f64 M)) (-.f64 (pow.f64 m 2) (pow.f64 n 2)))) (-.f64 m n))))
(+.f64 (cos.f64 (neg.f64 M)) (+.f64 (.f64 -1/2 (/.f64 (.f64 K (.f64 (sin.f64 (neg.f64 M)) (-.f64 (pow.f64 m 2) (pow.f64 n 2)))) (-.f64 m n))) (.f64 -1/8 (/.f64 (.f64 (cos.f64 (neg.f64 M)) (.f64 (pow.f64 K 2) (pow.f64 (-.f64 (pow.f64 m 2) (pow.f64 n 2)) 2))) (pow.f64 (-.f64 m n) 2)))))
(+.f64 (cos.f64 (neg.f64 M)) (+.f64 (.f64 -1/2 (/.f64 (.f64 K (.f64 (sin.f64 (neg.f64 M)) (-.f64 (pow.f64 m 2) (pow.f64 n 2)))) (-.f64 m n))) (+.f64 (.f64 -1/8 (/.f64 (.f64 (cos.f64 (neg.f64 M)) (.f64 (pow.f64 K 2) (pow.f64 (-.f64 (pow.f64 m 2) (pow.f64 n 2)) 2))) (pow.f64 (-.f64 m n) 2))) (.f64 1/48 (/.f64 (.f64 (pow.f64 K 3) (*.f64 (sin.f64 (neg.f64 M)) (pow.f64 (-.f64 (pow.f64 m 2) (pow.f64 n 2)) 3))) (pow.f64 (-.f64 m n) 3))))))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))))
(+.f64 (cos.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n)))) (.f64 (sin.f64 (.f64 1/2 (/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n)))) M))
(+.f64 (cos.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n)))) (+.f64 (.f64 -1/2 (.f64 (cos.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n)))) (pow.f64 M 2))) (.f64 (sin.f64 (.f64 1/2 (/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n)))) M)))
(+.f64 (.f64 -1/6 (.f64 (sin.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n)))) (pow.f64 M 3))) (+.f64 (cos.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n)))) (+.f64 (.f64 -1/2 (.f64 (cos.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n)))) (pow.f64 M 2))) (.f64 (sin.f64 (.f64 1/2 (/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n)))) M))))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) (*.f64 -1 M)))
(cos.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) (*.f64 -1 M)))
(cos.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) (*.f64 -1 M)))
(cos.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) (*.f64 -1 M)))
(*.f64 n K)
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(*.f64 K m)
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(*.f64 K m)
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(*.f64 K m)
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(*.f64 n K)
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(*.f64 n K)
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(+.f64 (.f64 n K) (.f64 K m))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(.f64 -1 (.f64 (pow.f64 n 2) K))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(*.f64 K (pow.f64 m 2))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(*.f64 K (pow.f64 m 2))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(*.f64 K (pow.f64 m 2))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(.f64 -1 (.f64 (pow.f64 n 2) K))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(.f64 -1 (.f64 (pow.f64 n 2) K))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(*.f64 -1 (pow.f64 n 2))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(pow.f64 m 2)
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(pow.f64 m 2)
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(pow.f64 m 2)
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(*.f64 -1 (pow.f64 n 2))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(*.f64 -1 (pow.f64 n 2))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))

Outputs
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (fma.f64 (*.f64 1/2 n) K (neg.f64 M)))
(cos.f64 (fma.f64 n (*.f64 1/2 K) (neg.f64 M)))
(+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 -1/2 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (*.f64 K m))))
(+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 (.f64 -1/2 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (*.f64 K m)))
(fma.f64 -1/2 (.f64 K (.f64 m (sin.f64 (fma.f64 (.f64 1/2 n) K (neg.f64 M))))) (cos.f64 (fma.f64 (.f64 1/2 n) K (neg.f64 M))))
(fma.f64 (sin.f64 (fma.f64 n (.f64 1/2 K) (neg.f64 M))) (.f64 K (.f64 -1/2 m)) (cos.f64 (fma.f64 n (.f64 1/2 K) (neg.f64 M))))
(+.f64 (.f64 -1/8 (.f64 (pow.f64 K 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (pow.f64 m 2)))) (+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 -1/2 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 K m)))))
(fma.f64 -1/8 (.f64 (.f64 K K) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 m m))) (+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 (.f64 -1/2 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (*.f64 K m))))
(fma.f64 -1/8 (.f64 (cos.f64 (fma.f64 (.f64 1/2 n) K (neg.f64 M))) (.f64 (.f64 m m) (.f64 K K))) (fma.f64 -1/2 (.f64 K (.f64 m (sin.f64 (fma.f64 (.f64 1/2 n) K (neg.f64 M))))) (cos.f64 (fma.f64 (*.f64 1/2 n) K (neg.f64 M)))))
(fma.f64 (sin.f64 (fma.f64 n (.f64 1/2 K) (neg.f64 M))) (.f64 K (.f64 -1/2 m)) (.f64 (+.f64 (.f64 (.f64 K -1/8) (.f64 K (.f64 m m))) 1) (cos.f64 (fma.f64 n (*.f64 1/2 K) (neg.f64 M)))))
(+.f64 (.f64 -1/8 (.f64 (pow.f64 K 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (pow.f64 m 2)))) (+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (+.f64 (.f64 1/48 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 (pow.f64 K 3) (pow.f64 m 3)))) (.f64 -1/2 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (*.f64 K m))))))
(fma.f64 -1/8 (.f64 (.f64 K K) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 m m))) (+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (fma.f64 1/48 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 (pow.f64 K 3) (pow.f64 m 3))) (.f64 (.f64 -1/2 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (*.f64 K m)))))
(+.f64 (fma.f64 -1/8 (.f64 (cos.f64 (fma.f64 (.f64 1/2 n) K (neg.f64 M))) (.f64 (.f64 m m) (.f64 K K))) (fma.f64 -1/2 (.f64 K (.f64 m (sin.f64 (fma.f64 (.f64 1/2 n) K (neg.f64 M))))) (cos.f64 (fma.f64 (.f64 1/2 n) K (neg.f64 M))))) (.f64 (sin.f64 (fma.f64 (.f64 1/2 n) K (neg.f64 M))) (.f64 (*.f64 (pow.f64 K 3) (pow.f64 m 3)) 1/48)))
(+.f64 (.f64 (sin.f64 (fma.f64 n (.f64 1/2 K) (neg.f64 M))) (+.f64 (.f64 K (.f64 -1/2 m)) (.f64 (pow.f64 K 3) (.f64 1/48 (pow.f64 m 3))))) (.f64 (+.f64 (.f64 (.f64 K -1/8) (.f64 K (.f64 m m))) 1) (cos.f64 (fma.f64 n (.f64 1/2 K) (neg.f64 M)))))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (fma.f64 1/2 (/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n)))) (neg.f64 M)))
(cos.f64 (-.f64 (/.f64 (.f64 1/2 K) (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (*.f64 n n)))) M))
(cos.f64 (-.f64 (/.f64 1/2 (/.f64 (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))) K)) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (fma.f64 1/2 (/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n)))) (neg.f64 M)))
(cos.f64 (-.f64 (/.f64 (.f64 1/2 K) (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (*.f64 n n)))) M))
(cos.f64 (-.f64 (/.f64 1/2 (/.f64 (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))) K)) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (fma.f64 1/2 (/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n)))) (neg.f64 M)))
(cos.f64 (-.f64 (/.f64 (.f64 1/2 K) (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (*.f64 n n)))) M))
(cos.f64 (-.f64 (/.f64 1/2 (/.f64 (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))) K)) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (fma.f64 1/2 (/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n)))) (neg.f64 M)))
(cos.f64 (-.f64 (/.f64 (.f64 1/2 K) (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (*.f64 n n)))) M))
(cos.f64 (-.f64 (/.f64 1/2 (/.f64 (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))) K)) M))
(cos.f64 (-.f64 (.f64 -1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 n (*.f64 -1 m)))) M))
(cos.f64 (fma.f64 -1/2 (/.f64 (.f64 K (-.f64 (.f64 m m) (*.f64 n n))) (+.f64 n (neg.f64 m))) (neg.f64 M)))
(cos.f64 (fma.f64 -1/2 (.f64 (/.f64 K (-.f64 n m)) (-.f64 (.f64 m m) (*.f64 n n))) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 (/.f64 K (-.f64 n m)) (.f64 -1/2 (-.f64 (.f64 m m) (.f64 n n)))) M))
(cos.f64 (-.f64 (.f64 -1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 n (*.f64 -1 m)))) M))
(cos.f64 (fma.f64 -1/2 (/.f64 (.f64 K (-.f64 (.f64 m m) (*.f64 n n))) (+.f64 n (neg.f64 m))) (neg.f64 M)))
(cos.f64 (fma.f64 -1/2 (.f64 (/.f64 K (-.f64 n m)) (-.f64 (.f64 m m) (*.f64 n n))) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 (/.f64 K (-.f64 n m)) (.f64 -1/2 (-.f64 (.f64 m m) (.f64 n n)))) M))
(cos.f64 (-.f64 (.f64 -1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 n (*.f64 -1 m)))) M))
(cos.f64 (fma.f64 -1/2 (/.f64 (.f64 K (-.f64 (.f64 m m) (*.f64 n n))) (+.f64 n (neg.f64 m))) (neg.f64 M)))
(cos.f64 (fma.f64 -1/2 (.f64 (/.f64 K (-.f64 n m)) (-.f64 (.f64 m m) (*.f64 n n))) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 (/.f64 K (-.f64 n m)) (.f64 -1/2 (-.f64 (.f64 m m) (.f64 n n)))) M))
(cos.f64 (-.f64 (.f64 -1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 n (*.f64 -1 m)))) M))
(cos.f64 (fma.f64 -1/2 (/.f64 (.f64 K (-.f64 (.f64 m m) (*.f64 n n))) (+.f64 n (neg.f64 m))) (neg.f64 M)))
(cos.f64 (fma.f64 -1/2 (.f64 (/.f64 K (-.f64 n m)) (-.f64 (.f64 m m) (*.f64 n n))) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 (/.f64 K (-.f64 n m)) (.f64 -1/2 (-.f64 (.f64 m m) (.f64 n n)))) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))
(cos.f64 (fma.f64 1/2 (*.f64 K m) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 K (.f64 m 1/2)) M))
(cos.f64 (-.f64 (.f64 K (.f64 1/2 m)) M))
(+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)))
(fma.f64 -1/2 (.f64 (.f64 n K) (sin.f64 (fma.f64 1/2 (.f64 K m) (neg.f64 M)))) (cos.f64 (fma.f64 1/2 (.f64 K m) (neg.f64 M))))
(fma.f64 -1/2 (.f64 (.f64 n K) (sin.f64 (-.f64 (.f64 K (.f64 m 1/2)) M))) (cos.f64 (-.f64 (.f64 K (.f64 m 1/2)) M)))
(fma.f64 n (.f64 K (.f64 -1/2 (sin.f64 (-.f64 (.f64 K (.f64 1/2 m)) M)))) (cos.f64 (-.f64 (.f64 K (.f64 1/2 m)) M)))
(+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))) (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (pow.f64 K 2)))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))
(fma.f64 -1/2 (.f64 (.f64 n K) (sin.f64 (fma.f64 1/2 (.f64 K m) (neg.f64 M)))) (fma.f64 -1/8 (.f64 (.f64 (.f64 n n) (cos.f64 (fma.f64 1/2 (.f64 K m) (neg.f64 M)))) (.f64 K K)) (cos.f64 (fma.f64 1/2 (*.f64 K m) (neg.f64 M)))))
(fma.f64 -1/2 (.f64 (.f64 n K) (sin.f64 (-.f64 (.f64 K (.f64 m 1/2)) M))) (fma.f64 -1/8 (.f64 (.f64 K K) (.f64 (.f64 n n) (cos.f64 (-.f64 (.f64 K (.f64 m 1/2)) M)))) (cos.f64 (-.f64 (.f64 K (.f64 m 1/2)) M))))
(fma.f64 n (.f64 K (.f64 -1/2 (sin.f64 (-.f64 (.f64 K (.f64 1/2 m)) M)))) (.f64 (+.f64 (.f64 (.f64 (.f64 -1/8 (.f64 n n)) K) K) 1) (cos.f64 (-.f64 (.f64 K (*.f64 1/2 m)) M))))
(+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))) (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (pow.f64 K 2)))) (+.f64 (.f64 1/48 (.f64 (pow.f64 n 3) (.f64 (pow.f64 K 3) (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)))))
(fma.f64 -1/2 (.f64 (.f64 n K) (sin.f64 (fma.f64 1/2 (.f64 K m) (neg.f64 M)))) (fma.f64 -1/8 (.f64 (.f64 (.f64 n n) (cos.f64 (fma.f64 1/2 (.f64 K m) (neg.f64 M)))) (.f64 K K)) (fma.f64 1/48 (.f64 (pow.f64 n 3) (.f64 (pow.f64 K 3) (sin.f64 (fma.f64 1/2 (.f64 K m) (neg.f64 M))))) (cos.f64 (fma.f64 1/2 (.f64 K m) (neg.f64 M))))))
(fma.f64 -1/2 (.f64 (.f64 n K) (sin.f64 (-.f64 (.f64 K (.f64 m 1/2)) M))) (fma.f64 -1/8 (.f64 (.f64 K K) (.f64 (.f64 n n) (cos.f64 (-.f64 (.f64 K (.f64 m 1/2)) M)))) (fma.f64 1/48 (.f64 (pow.f64 K 3) (.f64 (sin.f64 (-.f64 (.f64 K (.f64 m 1/2)) M)) (pow.f64 n 3))) (cos.f64 (-.f64 (.f64 K (.f64 m 1/2)) M)))))
(fma.f64 n (.f64 K (.f64 -1/2 (sin.f64 (-.f64 (.f64 K (.f64 1/2 m)) M)))) (fma.f64 1/48 (.f64 (pow.f64 K 3) (.f64 (sin.f64 (-.f64 (.f64 K (.f64 1/2 m)) M)) (pow.f64 n 3))) (.f64 (+.f64 (.f64 (.f64 (.f64 -1/8 (.f64 n n)) K) K) 1) (cos.f64 (-.f64 (.f64 K (*.f64 1/2 m)) M)))))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (fma.f64 1/2 (/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n)))) (neg.f64 M)))
(cos.f64 (-.f64 (/.f64 (.f64 1/2 K) (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (*.f64 n n)))) M))
(cos.f64 (-.f64 (/.f64 1/2 (/.f64 (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))) K)) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (fma.f64 1/2 (/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n)))) (neg.f64 M)))
(cos.f64 (-.f64 (/.f64 (.f64 1/2 K) (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (*.f64 n n)))) M))
(cos.f64 (-.f64 (/.f64 1/2 (/.f64 (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))) K)) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (fma.f64 1/2 (/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n)))) (neg.f64 M)))
(cos.f64 (-.f64 (/.f64 (.f64 1/2 K) (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (*.f64 n n)))) M))
(cos.f64 (-.f64 (/.f64 1/2 (/.f64 (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))) K)) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))) M))
(cos.f64 (fma.f64 1/2 (/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n)))) (neg.f64 M)))
(cos.f64 (-.f64 (/.f64 (.f64 1/2 K) (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (*.f64 n n)))) M))
(cos.f64 (-.f64 (/.f64 1/2 (/.f64 (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))) K)) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 (*.f64 -1 n) m))) M))
(cos.f64 (fma.f64 1/2 (/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n)))) (neg.f64 M)))
(cos.f64 (-.f64 (/.f64 (.f64 1/2 K) (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (*.f64 n n)))) M))
(cos.f64 (-.f64 (/.f64 1/2 (/.f64 (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))) K)) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 (*.f64 -1 n) m))) M))
(cos.f64 (fma.f64 1/2 (/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n)))) (neg.f64 M)))
(cos.f64 (-.f64 (/.f64 (.f64 1/2 K) (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (*.f64 n n)))) M))
(cos.f64 (-.f64 (/.f64 1/2 (/.f64 (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))) K)) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 (*.f64 -1 n) m))) M))
(cos.f64 (fma.f64 1/2 (/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n)))) (neg.f64 M)))
(cos.f64 (-.f64 (/.f64 (.f64 1/2 K) (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (*.f64 n n)))) M))
(cos.f64 (-.f64 (/.f64 1/2 (/.f64 (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))) K)) M))
(cos.f64 (-.f64 (.f64 1/2 (/.f64 (.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (+.f64 (*.f64 -1 n) m))) M))
(cos.f64 (fma.f64 1/2 (/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n)))) (neg.f64 M)))
(cos.f64 (-.f64 (/.f64 (.f64 1/2 K) (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (*.f64 n n)))) M))
(cos.f64 (-.f64 (/.f64 1/2 (/.f64 (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))) K)) M))
(cos.f64 (neg.f64 M))
(cos.f64 M)
(+.f64 (cos.f64 (neg.f64 M)) (.f64 -1/2 (/.f64 (.f64 K (*.f64 (sin.f64 (neg.f64 M)) (-.f64 (pow.f64 m 2) (pow.f64 n 2)))) (-.f64 m n))))
(+.f64 (cos.f64 M) (.f64 -1/2 (/.f64 K (/.f64 (-.f64 m n) (.f64 (-.f64 (.f64 m m) (.f64 n n)) (neg.f64 (sin.f64 M)))))))
(fma.f64 -1/2 (.f64 (/.f64 K (-.f64 m n)) (.f64 (-.f64 (.f64 m m) (.f64 n n)) (neg.f64 (sin.f64 M)))) (cos.f64 M))
(fma.f64 -1/2 (.f64 (.f64 (sin.f64 M) (neg.f64 (-.f64 (.f64 m m) (.f64 n n)))) (/.f64 K (-.f64 m n))) (cos.f64 M))
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(+.f64 (.f64 n K) (.f64 K m))
(fma.f64 n K (*.f64 K m))
(*.f64 K (+.f64 m n))
(*.f64 K (+.f64 n m))
(+.f64 (.f64 n K) (.f64 K m))
(fma.f64 n K (*.f64 K m))
(*.f64 K (+.f64 m n))
(*.f64 K (+.f64 n m))
(+.f64 (.f64 n K) (.f64 K m))
(fma.f64 n K (*.f64 K m))
(*.f64 K (+.f64 m n))
(*.f64 K (+.f64 n m))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))))
(.f64 (/.f64 K (-.f64 m n)) (-.f64 (.f64 m m) (*.f64 n n)))
(.f64 (-.f64 (.f64 m m) (*.f64 n n)) (/.f64 K (-.f64 m n)))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))))
(.f64 (/.f64 K (-.f64 m n)) (-.f64 (.f64 m m) (*.f64 n n)))
(.f64 (-.f64 (.f64 m m) (*.f64 n n)) (/.f64 K (-.f64 m n)))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))))
(.f64 (/.f64 K (-.f64 m n)) (-.f64 (.f64 m m) (*.f64 n n)))
(.f64 (-.f64 (.f64 m m) (*.f64 n n)) (/.f64 K (-.f64 m n)))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))))
(.f64 (/.f64 K (-.f64 m n)) (-.f64 (.f64 m m) (*.f64 n n)))
(.f64 (-.f64 (.f64 m m) (*.f64 n n)) (/.f64 K (-.f64 m n)))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))))
(.f64 (/.f64 K (-.f64 m n)) (-.f64 (.f64 m m) (*.f64 n n)))
(.f64 (-.f64 (.f64 m m) (*.f64 n n)) (/.f64 K (-.f64 m n)))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))))
(.f64 (/.f64 K (-.f64 m n)) (-.f64 (.f64 m m) (*.f64 n n)))
(.f64 (-.f64 (.f64 m m) (*.f64 n n)) (/.f64 K (-.f64 m n)))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))))
(.f64 (/.f64 K (-.f64 m n)) (-.f64 (.f64 m m) (*.f64 n n)))
(.f64 (-.f64 (.f64 m m) (*.f64 n n)) (/.f64 K (-.f64 m n)))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))))
(.f64 (/.f64 K (-.f64 m n)) (-.f64 (.f64 m m) (*.f64 n n)))
(.f64 (-.f64 (.f64 m m) (*.f64 n n)) (/.f64 K (-.f64 m n)))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))))
(.f64 (/.f64 K (-.f64 m n)) (-.f64 (.f64 m m) (*.f64 n n)))
(.f64 (-.f64 (.f64 m m) (*.f64 n n)) (/.f64 K (-.f64 m n)))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))))
(.f64 (/.f64 K (-.f64 m n)) (-.f64 (.f64 m m) (*.f64 n n)))
(.f64 (-.f64 (.f64 m m) (*.f64 n n)) (/.f64 K (-.f64 m n)))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))))
(.f64 (/.f64 K (-.f64 m n)) (-.f64 (.f64 m m) (*.f64 n n)))
(.f64 (-.f64 (.f64 m m) (*.f64 n n)) (/.f64 K (-.f64 m n)))
(/.f64 (*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2))) (-.f64 m n))
(/.f64 K (/.f64 (-.f64 m n) (-.f64 (.f64 m m) (.f64 n n))))
(.f64 (/.f64 K (-.f64 m n)) (-.f64 (.f64 m m) (*.f64 n n)))
(.f64 (-.f64 (.f64 m m) (*.f64 n n)) (/.f64 K (-.f64 m n)))
(.f64 -1 (.f64 (pow.f64 n 2) K))
(.f64 (neg.f64 (.f64 n n)) K)
(.f64 K (.f64 n (neg.f64 n)))
(.f64 n (.f64 (neg.f64 n) K))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 K (pow.f64 m 2))
(.f64 K (.f64 m m))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 K (pow.f64 m 2))
(.f64 K (.f64 m m))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 K (pow.f64 m 2))
(.f64 K (.f64 m m))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(.f64 -1 (.f64 (pow.f64 n 2) K))
(.f64 (neg.f64 (.f64 n n)) K)
(.f64 K (.f64 n (neg.f64 n)))
(.f64 n (.f64 (neg.f64 n) K))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(.f64 -1 (.f64 (pow.f64 n 2) K))
(.f64 (neg.f64 (.f64 n n)) K)
(.f64 K (.f64 n (neg.f64 n)))
(.f64 n (.f64 (neg.f64 n) K))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(+.f64 (.f64 K (pow.f64 m 2)) (.f64 -1 (*.f64 (pow.f64 n 2) K)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 K (-.f64 (pow.f64 m 2) (pow.f64 n 2)))
(fma.f64 K (.f64 m m) (.f64 (neg.f64 (*.f64 n n)) K))
(.f64 K (-.f64 (.f64 m m) (*.f64 n n)))
(*.f64 -1 (pow.f64 n 2))
(neg.f64 (*.f64 n n))
(*.f64 n (neg.f64 n))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(pow.f64 m 2)
(*.f64 m m)
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(pow.f64 m 2)
(*.f64 m m)
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(pow.f64 m 2)
(*.f64 m m)
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(*.f64 -1 (pow.f64 n 2))
(neg.f64 (*.f64 n n))
(*.f64 n (neg.f64 n))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(*.f64 -1 (pow.f64 n 2))
(neg.f64 (*.f64 n n))
(*.f64 n (neg.f64 n))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))
(+.f64 (*.f64 -1 (pow.f64 n 2)) (pow.f64 m 2))
(-.f64 (.f64 m m) (.f64 n n))

eval969.0ms (6.6%)

Compiler: Compiled 53215 to 22190 computations (58.3% saved)

prune270.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	1396	10	1406
Fresh	0	0	0
Picked	1	0	1
Done	4	0	4
Total	1401	10	1411

Error

0.4b

Counts

1411 → 10

Alt Table

Click to see full alt table

Status	Error	Program
	44.1b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (.f64 n n)) K) (-.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (*.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	43.6b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (expm1.f64 (log1p.f64 (.f64 (-.f64 (.f64 m m) (.f64 n n)) K))) (-.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	25.1b	(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 m (*.f64 m 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	37.7b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (.f64 n (.f64 n -1/4))))
▶	25.9b	(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 n (*.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	61.8b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (*.f64 M M)))
▶	47.8b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
▶	22.6b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (+.f64 (-.f64 (.f64 n (.f64 n -1/4)) l) (-.f64 m n))))
▶	28.9b	(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	37.2b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (.f64 m (.f64 m -1/4))))

Compiler

Compiled 510 to 352 computations (31% saved)

localize40.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(-.f64 (.f64 n (.f64 n -1/4)) l)
	33.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 110 to 50 computations (54.5% saved)

series8.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	n	@	0	(-.f64 (.f64 n (.f64 n -1/4)) l)
0.0ms	l	@	0	(-.f64 (.f64 n (.f64 n -1/4)) l)
0.0ms	n	@	inf	(-.f64 (.f64 n (.f64 n -1/4)) l)
0.0ms	n	@	-inf	(-.f64 (.f64 n (.f64 n -1/4)) l)
0.0ms	l	@	-inf	(-.f64 (.f64 n (.f64 n -1/4)) l)

rewrite51.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

800×	`pow1_binary64`
746×	`add-log-exp_binary64`
746×	`log1p-expm1-u_binary64`
746×	`expm1-log1p-u_binary64`
731×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	153	10
2	2016	10

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

Inputs
(-.f64 (.f64 n (.f64 n -1/4)) l)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 n (*.f64 n -1/4)) (neg.f64 l))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 n (*.f64 n -1/4)) (*.f64 (neg.f64 l) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l)) (fma.f64 (neg.f64 l) 1 l))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l)) (fma.f64 (neg.f64 (cbrt.f64 l)) (pow.f64 (cbrt.f64 l) 2) l))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l)) (fma.f64 (neg.f64 (sqrt.f64 l)) (sqrt.f64 l) l))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 l) (*.f64 n (*.f64 n -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l))) (pow.f64 (cbrt.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l))) 2) (cbrt.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l))) (sqrt.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 (*.f64 n n) 3) -1/64) (pow.f64 l 3)) (/.f64 1 (+.f64 (pow.f64 (*.f64 n (*.f64 n -1/4)) 2) (*.f64 l (fma.f64 n (*.f64 n -1/4) l)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 n (*.f64 n -1/4)) 2) (*.f64 l l)) (/.f64 1 (fma.f64 n (*.f64 n -1/4) l)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 n (sqrt.f64 -1/4)) (sqrt.f64 l)) (-.f64 (*.f64 n (sqrt.f64 -1/4)) (sqrt.f64 l)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (*.f64 n (*.f64 n -1/4)) 2) (*.f64 l (fma.f64 n (*.f64 n -1/4) l))) (-.f64 (*.f64 (pow.f64 (*.f64 n n) 3) -1/64) (pow.f64 l 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 n (*.f64 n -1/4) l) (-.f64 (pow.f64 (*.f64 n (*.f64 n -1/4)) 2) (*.f64 l l))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 (*.f64 n n) 3) -1/64) (pow.f64 l 3)) (+.f64 (pow.f64 (*.f64 n (*.f64 n -1/4)) 2) (*.f64 l (fma.f64 n (*.f64 n -1/4) l))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 n (*.f64 n -1/4)) 2) (*.f64 l l)) (fma.f64 n (*.f64 n -1/4) l))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 (*.f64 n n) 3) -1/64) (pow.f64 l 3))) (neg.f64 (+.f64 (pow.f64 (*.f64 n (*.f64 n -1/4)) 2) (*.f64 l (fma.f64 n (*.f64 n -1/4) l)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 n (*.f64 n -1/4)) 2) (*.f64 l l))) (neg.f64 (fma.f64 n (*.f64 n -1/4) l)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 (*.f64 n n) 3) -1/64) (pow.f64 (neg.f64 l) 3)) (+.f64 (pow.f64 (*.f64 n (*.f64 n -1/4)) 2) (-.f64 (*.f64 (neg.f64 l) (neg.f64 l)) (*.f64 (*.f64 n (*.f64 n -1/4)) (neg.f64 l)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 n (*.f64 n -1/4)) 2) (*.f64 (neg.f64 l) (neg.f64 l))) (-.f64 (*.f64 n (*.f64 n -1/4)) (neg.f64 l)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (*.f64 n n) -1/4 (neg.f64 l))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 n (*.f64 n -1/4) (neg.f64 l))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 n -1/4) n (neg.f64 l))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 n (*.f64 n -1/4)) (neg.f64 l))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 n n) -1/4 (neg.f64 l))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 n -1/4))) 2) (cbrt.f64 (*.f64 n (*.f64 n -1/4))) (neg.f64 l))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 n (sqrt.f64 -1/4)) (*.f64 n (sqrt.f64 -1/4)) (neg.f64 l))))))

simplify110.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

636×	`distribute-rgt-neg-in_binary64`
459×	`distribute-lft-neg-in_binary64`
372×	`sub-neg_binary64`
344×	`fma-neg_binary64`
310×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	228
1	20	210
2	36	210
3	66	210
4	165	210
5	548	210
6	1265	210
7	2524	210
8	4200	210
9	5411	210
10	6070	210
11	6594	210
12	7261	210

Stop Event

1×	node limit

Counts

62 → 44

Calls

Call 1

Inputs
(*.f64 -1 l)
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(*.f64 -1/4 (pow.f64 n 2))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(*.f64 -1/4 (pow.f64 n 2))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(*.f64 -1/4 (pow.f64 n 2))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(*.f64 -1 l)
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(*.f64 -1 l)
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))

Outputs
(*.f64 -1 l)
(neg.f64 l)
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(*.f64 -1/4 (pow.f64 n 2))
(.f64 -1/4 (.f64 n n))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(*.f64 -1/4 (pow.f64 n 2))
(.f64 -1/4 (.f64 n n))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(*.f64 -1/4 (pow.f64 n 2))
(.f64 -1/4 (.f64 n n))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(*.f64 -1 l)
(neg.f64 l)
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(*.f64 -1 l)
(neg.f64 l)
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))
(+.f64 (.f64 -1 l) (.f64 -1/4 (pow.f64 n 2)))
(fma.f64 -1 l (.f64 -1/4 (.f64 n n)))
(-.f64 (.f64 -1/4 (.f64 n n)) l)
(fma.f64 -1/4 (*.f64 n n) (neg.f64 l))

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
	33.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 64 to 24 computations (62.5% saved)

series11.0ms (0.1%)

Counts

1 → 60

Calls

15 calls:

Time	Variable		Expression
1.0ms	m	@	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
1.0ms	n	@	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
1.0ms	K	@	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
1.0ms	M	@	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
1.0ms	l	@	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))

rewrite70.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

811×	`log-prod_binary64`
482×	`fma-def_binary64`
301×	`expm1-udef_binary64`
301×	`log1p-udef_binary64`
249×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	340	20
2	4870	20

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

Inputs
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (exp.f64 l)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (cos.f64 M)) (exp.f64 l)) (*.f64 (*.f64 (sin.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (sin.f64 M)) (exp.f64 l)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (exp.f64 l) (*.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (cos.f64 M))) (*.f64 (exp.f64 l) (*.f64 (sin.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (sin.f64 M))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (exp.f64 l)) (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))))) (cbrt.f64 (pow.f64 (exp.f64 (exp.f64 l)) (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (exp.f64 l)) (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (exp.f64 l)) (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M)))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (exp.f64 l)) (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (exp.f64 l)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (exp.f64 l))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (exp.f64 l)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (exp.f64 l)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (exp.f64 l))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (exp.f64 l))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (exp.f64 l)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (exp.f64 l)) (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (exp.f64 l)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (exp.f64 l)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) 3) (pow.f64 (exp.f64 l) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 l) 3) (pow.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (exp.f64 l))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (exp.f64 l))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 l (log.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 l (log.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (exp.f64 l) (*.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (cos.f64 M)) (*.f64 (exp.f64 l) (*.f64 (sin.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (sin.f64 M))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (cos.f64 M)) (exp.f64 l) (*.f64 (*.f64 (sin.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (sin.f64 M)) (exp.f64 l)))))))

simplify77.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

827×	`fma-def_binary64`
815×	`distribute-rgt-neg-out_binary64`
528×	`*-commutative_binary64`
503×	`unswap-sqr_binary64`
212×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	151	2026
1	460	1982
2	1581	1733
3	5151	1731

Stop Event

1×	node limit

Counts

83 → 69

Calls

Call 1

Inputs
(*.f64 (exp.f64 (neg.f64 l)) (cos.f64 (neg.f64 M)))
(+.f64 (.f64 (exp.f64 (neg.f64 l)) (cos.f64 (neg.f64 M))) (.f64 -1/2 (.f64 (exp.f64 (neg.f64 l)) (.f64 K (*.f64 (sin.f64 (neg.f64 M)) (+.f64 n m))))))
(+.f64 (.f64 (exp.f64 (neg.f64 l)) (cos.f64 (neg.f64 M))) (+.f64 (.f64 -1/2 (.f64 (exp.f64 (neg.f64 l)) (.f64 K (.f64 (sin.f64 (neg.f64 M)) (+.f64 n m))))) (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (.f64 (cos.f64 (neg.f64 M)) (*.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2)))))))
(+.f64 (.f64 (exp.f64 (neg.f64 l)) (cos.f64 (neg.f64 M))) (+.f64 (.f64 1/48 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 K 3) (.f64 (sin.f64 (neg.f64 M)) (pow.f64 (+.f64 n m) 3))))) (+.f64 (.f64 -1/2 (.f64 (exp.f64 (neg.f64 l)) (.f64 K (.f64 (sin.f64 (neg.f64 M)) (+.f64 n m))))) (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (.f64 (cos.f64 (neg.f64 M)) (*.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2))))))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (neg.f64 l)) (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 K m)))) (.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M))))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (neg.f64 l)) (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 K m)))) (+.f64 (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 K 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (pow.f64 m 2))))) (.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)))))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (neg.f64 l)) (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 K m)))) (+.f64 (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 K 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (pow.f64 m 2))))) (+.f64 (.f64 1/48 (.f64 (exp.f64 (neg.f64 l)) (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (.f64 (pow.f64 K 3) (pow.f64 m 3))))) (.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M))))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (.f64 -1 m)))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (.f64 -1 m)))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (.f64 -1 m)))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (.f64 -1 m)))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (neg.f64 l)) (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M))))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (neg.f64 l)) (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (+.f64 (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (.f64 (pow.f64 n 2) (pow.f64 K 2))))) (.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)))))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (neg.f64 l)) (.f64 n (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (+.f64 (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (.f64 (pow.f64 n 2) (pow.f64 K 2))))) (+.f64 (.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M))) (.f64 1/48 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 n 3) (.f64 (pow.f64 K 3) (sin.f64 (-.f64 (.f64 1/2 (*.f64 K m)) M)))))))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (.f64 -1 n)))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (.f64 -1 n)))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (.f64 -1 n)))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (.f64 -1 n)))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 K (+.f64 n m)))))
(+.f64 (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (neg.f64 l)) M)) (.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 K (+.f64 n m))))))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (neg.f64 l)) (.f64 (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (pow.f64 M 2)))) (+.f64 (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (neg.f64 l)) M)) (.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))))))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (neg.f64 l)) (.f64 (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (pow.f64 M 2)))) (+.f64 (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (neg.f64 l)) M)) (+.f64 (.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))) (.f64 -1/6 (.f64 (exp.f64 (neg.f64 l)) (.f64 (sin.f64 (.f64 1/2 (*.f64 K (+.f64 n m)))) (pow.f64 M 3)))))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (.f64 -1 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) l)))
(+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (+.f64 (.f64 1/2 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (pow.f64 l 2))) (.f64 -1 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) l))))
(+.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (+.f64 (.f64 1/2 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (pow.f64 l 2))) (+.f64 (.f64 -1/6 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (pow.f64 l 3))) (.f64 -1 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) l)))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (-.f64 (.f64 1/2 (*.f64 K (+.f64 n m))) M)))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1 l)))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1 l)))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1 l)))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1 l)))

Outputs
(*.f64 (exp.f64 (neg.f64 l)) (cos.f64 (neg.f64 M)))
(*.f64 (exp.f64 (neg.f64 l)) (cos.f64 M))
(/.f64 (cos.f64 M) (exp.f64 l))
(+.f64 (.f64 (exp.f64 (neg.f64 l)) (cos.f64 (neg.f64 M))) (.f64 -1/2 (.f64 (exp.f64 (neg.f64 l)) (.f64 K (*.f64 (sin.f64 (neg.f64 M)) (+.f64 n m))))))
(fma.f64 (exp.f64 (neg.f64 l)) (cos.f64 M) (.f64 -1/2 (.f64 (exp.f64 (neg.f64 l)) (.f64 K (.f64 (neg.f64 (sin.f64 M)) (+.f64 n m))))))
(fma.f64 (exp.f64 (neg.f64 l)) (cos.f64 M) (.f64 (.f64 K (*.f64 (neg.f64 (sin.f64 M)) (+.f64 n m))) (/.f64 -1/2 (exp.f64 l))))
(.f64 (exp.f64 (neg.f64 l)) (+.f64 (cos.f64 M) (.f64 -1/2 (.f64 K (.f64 (neg.f64 (sin.f64 M)) (+.f64 n m))))))
(.f64 (exp.f64 (neg.f64 l)) (+.f64 (cos.f64 M) (.f64 -1/2 (.f64 (+.f64 n m) (.f64 K (neg.f64 (sin.f64 M)))))))
(+.f64 (.f64 (exp.f64 (neg.f64 l)) (cos.f64 (neg.f64 M))) (+.f64 (.f64 -1/2 (.f64 (exp.f64 (neg.f64 l)) (.f64 K (.f64 (sin.f64 (neg.f64 M)) (+.f64 n m))))) (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (.f64 (cos.f64 (neg.f64 M)) (*.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2)))))))
(fma.f64 (exp.f64 (neg.f64 l)) (cos.f64 M) (fma.f64 -1/2 (.f64 (exp.f64 (neg.f64 l)) (.f64 K (.f64 (neg.f64 (sin.f64 M)) (+.f64 n m)))) (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (.f64 (cos.f64 M) (.f64 (.f64 K K) (pow.f64 (+.f64 n m) 2)))))))
(fma.f64 (exp.f64 (neg.f64 l)) (cos.f64 M) (fma.f64 (/.f64 -1/8 (exp.f64 l)) (.f64 (pow.f64 (+.f64 n m) 2) (.f64 (cos.f64 M) (.f64 K K))) (.f64 (.f64 K (.f64 (neg.f64 (sin.f64 M)) (+.f64 n m))) (/.f64 -1/2 (exp.f64 l)))))
(fma.f64 (/.f64 (cos.f64 M) (exp.f64 l)) (.f64 -1/8 (.f64 (.f64 K K) (pow.f64 (+.f64 n m) 2))) (.f64 (exp.f64 (neg.f64 l)) (+.f64 (cos.f64 M) (.f64 -1/2 (.f64 K (*.f64 (neg.f64 (sin.f64 M)) (+.f64 n m)))))))
(fma.f64 (.f64 (pow.f64 (+.f64 n m) 2) (.f64 (cos.f64 M) (.f64 K K))) (/.f64 -1/8 (exp.f64 l)) (.f64 (exp.f64 (neg.f64 l)) (+.f64 (cos.f64 M) (.f64 -1/2 (.f64 (+.f64 n m) (*.f64 K (neg.f64 (sin.f64 M))))))))
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localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (.f64 m (.f64 m -1/4))))
	0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
	0.0b	(*.f64 K (+.f64 m n))
	33.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 76 to 36 computations (52.6% saved)

series9.0ms (0.1%)

Counts

1 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	K	@	0	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (.f64 m (.f64 m -1/4))))
1.0ms	n	@	0	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (.f64 m (.f64 m -1/4))))
1.0ms	m	@	0	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (.f64 m (.f64 m -1/4))))
1.0ms	M	@	inf	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (.f64 m (.f64 m -1/4))))
1.0ms	M	@	0	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (.f64 m (.f64 m -1/4))))

rewrite75.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

906×	`log-prod_binary64`
508×	`fma-def_binary64`
330×	`expm1-udef_binary64`
330×	`log1p-udef_binary64`
273×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	26
1	360	26
2	5023	26

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (.f64 m (.f64 m -1/4))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (pow.f64 (exp.f64 m) (*.f64 m -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (cos.f64 M)) (pow.f64 (exp.f64 m) (*.f64 m -1/4))) (*.f64 (*.f64 (sin.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (sin.f64 M)) (pow.f64 (exp.f64 m) (*.f64 m -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 (exp.f64 m) (*.f64 m -1/4)) (*.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (cos.f64 M))) (*.f64 (pow.f64 (exp.f64 m) (*.f64 m -1/4)) (*.f64 (sin.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (sin.f64 M))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (exp.f64 m) (*.f64 m -1/4))) (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))))) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (exp.f64 m) (*.f64 m -1/4))) (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (exp.f64 m) (*.f64 m -1/4))) (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (exp.f64 m) (*.f64 m -1/4))) (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M)))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (exp.f64 m) (*.f64 m -1/4))) (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (pow.f64 (exp.f64 m) (*.f64 m -1/4))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (pow.f64 (exp.f64 m) (*.f64 m -1/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (pow.f64 (exp.f64 m) (*.f64 m -1/4))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (pow.f64 (exp.f64 m) (*.f64 m -1/4)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (pow.f64 (exp.f64 m) (*.f64 m -1/4)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (pow.f64 (exp.f64 m) (*.f64 m -1/4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (exp.f64 m) (*.f64 m -1/4))) (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (pow.f64 (exp.f64 m) (*.f64 m -1/4))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (pow.f64 (exp.f64 m) (*.f64 m -1/4))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) 3) (pow.f64 (pow.f64 (exp.f64 m) (*.f64 m -1/4)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 m) (*.f64 m -1/4)) 3) (pow.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (pow.f64 (exp.f64 m) (*.f64 m -1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))) (pow.f64 (exp.f64 m) (*.f64 m -1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 m (*.f64 m -1/4) (log.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 m (*.f64 m -1/4) (log.f64 (cos.f64 (fma.f64 (+.f64 m n) (*.f64 K 1/2) (neg.f64 M))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (exp.f64 m) (*.f64 m -1/4)) (*.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (cos.f64 M)) (*.f64 (pow.f64 (exp.f64 m) (*.f64 m -1/4)) (*.f64 (sin.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (sin.f64 M))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (cos.f64 M)) (pow.f64 (exp.f64 m) (*.f64 m -1/4)) (*.f64 (*.f64 (sin.f64 (*.f64 K (*.f64 (+.f64 m n) 1/2))) (sin.f64 M)) (pow.f64 (exp.f64 m) (*.f64 m -1/4))))))))

simplify71.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-def_binary64`
664×	`distribute-rgt-neg-out_binary64`
597×	`distribute-lft-neg-out_binary64`
429×	`*-commutative_binary64`
415×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	1878
1	411	1854
2	1269	1713
3	4105	1705

Stop Event

1×	node limit

Counts

70 → 59

Calls

Call 1

Inputs
(.f64 (cos.f64 (neg.f64 M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(+.f64 (.f64 -1/2 (.f64 K (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (.f64 (sin.f64 (neg.f64 M)) (+.f64 n m))))) (.f64 (cos.f64 (neg.f64 M)) (exp.f64 (*.f64 -1/4 (pow.f64 m 2)))))
(+.f64 (.f64 -1/2 (.f64 K (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (.f64 (sin.f64 (neg.f64 M)) (+.f64 n m))))) (+.f64 (.f64 (cos.f64 (neg.f64 M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2)))) (.f64 -1/8 (.f64 (cos.f64 (neg.f64 M)) (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2)))))))
(+.f64 (.f64 -1/2 (.f64 K (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (.f64 (sin.f64 (neg.f64 M)) (+.f64 n m))))) (+.f64 (.f64 1/48 (.f64 (pow.f64 K 3) (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (.f64 (sin.f64 (neg.f64 M)) (pow.f64 (+.f64 n m) 3))))) (+.f64 (.f64 (cos.f64 (neg.f64 M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2)))) (.f64 -1/8 (.f64 (cos.f64 (neg.f64 M)) (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (*.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2))))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(+.f64 (.f64 -1/2 (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)))
(+.f64 (.f64 (+.f64 (.f64 -1/4 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (.f64 -1/8 (.f64 (pow.f64 K 2) (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))))) (pow.f64 m 2)) (+.f64 (.f64 -1/2 (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m))) (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M))))
(+.f64 (.f64 (+.f64 (.f64 -1/4 (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))) (.f64 -1/8 (.f64 (pow.f64 K 2) (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))))) (pow.f64 m 2)) (+.f64 (.f64 -1/2 (.f64 K (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) m))) (+.f64 (.f64 (+.f64 (.f64 1/48 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) (pow.f64 K 3))) (.f64 1/8 (.f64 (sin.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)) K))) (pow.f64 m 3)) (cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M)))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))) M)))
(.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))) M)))
(.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))) M)))
(.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))) M)))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(+.f64 (.f64 -1/2 (.f64 n (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (exp.f64 (*.f64 -1/4 (pow.f64 m 2)))))
(+.f64 (.f64 -1/2 (.f64 n (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (+.f64 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2)))) (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (.f64 (pow.f64 K 2) (exp.f64 (.f64 -1/4 (pow.f64 m 2)))))))))
(+.f64 (.f64 -1/2 (.f64 n (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (.f64 K (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (+.f64 (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2)))) (+.f64 (.f64 1/48 (.f64 (pow.f64 n 3) (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (.f64 (pow.f64 K 3) (sin.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)))))) (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K m)) M)) (.f64 (pow.f64 K 2) (exp.f64 (*.f64 -1/4 (pow.f64 m 2))))))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))) M)))
(.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))) M)))
(.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))) M)))
(.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (cos.f64 (-.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))) M)))
(.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))))
(+.f64 (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))) (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (*.f64 -1/4 (pow.f64 m 2))) M)))
(+.f64 (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))) (+.f64 (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) M)) (.f64 -1/2 (.f64 (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (*.f64 -1/4 (pow.f64 m 2))) (pow.f64 M 2))))))
(+.f64 (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))) (+.f64 (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) M)) (+.f64 (.f64 -1/6 (.f64 (sin.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (pow.f64 M 3)))) (.f64 -1/2 (.f64 (cos.f64 (.f64 1/2 (.f64 K (+.f64 n m)))) (.f64 (exp.f64 (*.f64 -1/4 (pow.f64 m 2))) (pow.f64 M 2)))))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))) (exp.f64 (*.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))) (exp.f64 (*.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))) (exp.f64 (*.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))) (exp.f64 (*.f64 -1/4 (pow.f64 m 2))))

Outputs
(.f64 (cos.f64 (neg.f64 M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2))))
(.f64 (cos.f64 M) (pow.f64 (exp.f64 -1/4) (.f64 m m)))
(*.f64 (cos.f64 M) (pow.f64 (pow.f64 (exp.f64 m) m) -1/4))
(+.f64 (.f64 -1/2 (.f64 K (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (.f64 (sin.f64 (neg.f64 M)) (+.f64 n m))))) (.f64 (cos.f64 (neg.f64 M)) (exp.f64 (*.f64 -1/4 (pow.f64 m 2)))))
(fma.f64 -1/2 (.f64 (.f64 K (pow.f64 (exp.f64 -1/4) (.f64 m m))) (.f64 (neg.f64 (sin.f64 M)) (+.f64 m n))) (.f64 (cos.f64 M) (pow.f64 (exp.f64 -1/4) (.f64 m m))))
(fma.f64 (cos.f64 M) (pow.f64 (exp.f64 -1/4) (.f64 m m)) (.f64 K (.f64 (.f64 (.f64 (pow.f64 (exp.f64 -1/4) (.f64 m m)) (+.f64 m n)) (sin.f64 (neg.f64 M))) -1/2)))
(.f64 (pow.f64 (exp.f64 -1/4) (.f64 m m)) (+.f64 (.f64 (.f64 (sin.f64 (neg.f64 M)) (+.f64 m n)) (*.f64 -1/2 K)) (cos.f64 M)))
(.f64 (pow.f64 (pow.f64 (exp.f64 m) m) -1/4) (-.f64 (cos.f64 M) (.f64 (.f64 -1/2 K) (.f64 (+.f64 m n) (sin.f64 M)))))
(+.f64 (.f64 -1/2 (.f64 K (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (.f64 (sin.f64 (neg.f64 M)) (+.f64 n m))))) (+.f64 (.f64 (cos.f64 (neg.f64 M)) (exp.f64 (.f64 -1/4 (pow.f64 m 2)))) (.f64 -1/8 (.f64 (cos.f64 (neg.f64 M)) (.f64 (exp.f64 (.f64 -1/4 (pow.f64 m 2))) (.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2)))))))
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(.f64 (pow.f64 (exp.f64 -1/4) (.f64 m m)) (cos.f64 (-.f64 (.f64 K (.f64 (+.f64 m n) 1/2)) M)))
(.f64 (pow.f64 (pow.f64 (exp.f64 m) m) -1/4) (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))) (exp.f64 (*.f64 -1/4 (pow.f64 m 2))))
(.f64 (pow.f64 (exp.f64 -1/4) (.f64 m m)) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (pow.f64 (exp.f64 -1/4) (.f64 m m)) (cos.f64 (-.f64 (.f64 K (.f64 (+.f64 m n) 1/2)) M)))
(.f64 (pow.f64 (pow.f64 (exp.f64 m) m) -1/4) (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))) (exp.f64 (*.f64 -1/4 (pow.f64 m 2))))
(.f64 (pow.f64 (exp.f64 -1/4) (.f64 m m)) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (pow.f64 (exp.f64 -1/4) (.f64 m m)) (cos.f64 (-.f64 (.f64 K (.f64 (+.f64 m n) 1/2)) M)))
(.f64 (pow.f64 (pow.f64 (exp.f64 m) m) -1/4) (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))) (exp.f64 (*.f64 -1/4 (pow.f64 m 2))))
(.f64 (pow.f64 (exp.f64 -1/4) (.f64 m m)) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (pow.f64 (exp.f64 -1/4) (.f64 m m)) (cos.f64 (-.f64 (.f64 K (.f64 (+.f64 m n) 1/2)) M)))
(.f64 (pow.f64 (pow.f64 (exp.f64 m) m) -1/4) (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))))
(.f64 (cos.f64 (+.f64 (.f64 -1 M) (.f64 1/2 (.f64 K (+.f64 n m))))) (exp.f64 (*.f64 -1/4 (pow.f64 m 2))))
(.f64 (pow.f64 (exp.f64 -1/4) (.f64 m m)) (cos.f64 (fma.f64 1/2 (*.f64 K (+.f64 m n)) (neg.f64 M))))
(.f64 (pow.f64 (exp.f64 -1/4) (.f64 m m)) (cos.f64 (-.f64 (.f64 K (.f64 (+.f64 m n) 1/2)) M)))
(.f64 (pow.f64 (pow.f64 (exp.f64 m) m) -1/4) (cos.f64 (fma.f64 K (.f64 (+.f64 m n) 1/2) (neg.f64 M))))

localize22.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (neg.f64 (*.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))

Compiler

Compiled 69 to 14 computations (79.7% saved)

localize29.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (neg.f64 (.f64 n (.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))
✓	0.0b	(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 n (*.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 83 to 37 computations (55.4% saved)

series9.0ms (0.1%)

Counts

1 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	n	@	0	(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 n (*.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
1.0ms	M	@	0	(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 n (*.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
1.0ms	n	@	inf	(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 n (*.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
1.0ms	l	@	0	(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 n (*.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
1.0ms	m	@	0	(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 n (*.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))

rewrite79.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

854×	`log-prod_binary64`
498×	`fma-neg_binary64`
300×	`expm1-udef_binary64`
300×	`log1p-udef_binary64`
238×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	360	23
2	5339	23

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

Inputs
(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 n (*.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l)))) (cos.f64 M))) (cbrt.f64 (pow.f64 (exp.f64 (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l)))) (cos.f64 M))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l)))) (cos.f64 M)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l)))) (cos.f64 M)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l)))) (cos.f64 M)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) n) n) (cos.f64 M)) (exp.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 M) (pow.f64 (pow.f64 (exp.f64 1/4) n) n)) (exp.f64 (-.f64 l (-.f64 m n))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l)))) (cos.f64 M)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 M) 3) (pow.f64 (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l))) 3) (pow.f64 (cos.f64 M) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l)) (log.f64 (cos.f64 M))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 (+.f64 (-.f64 m n) (-.f64 (*.f64 n (*.f64 n 1/4)) l)) (log.f64 (cos.f64 M))) 1))))))

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

530×	`times-frac_binary64`
516×	`fma-def_binary64`
433×	`associate-l_binary64`
423×	`associate-/l*_binary64`
412×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	1638
1	265	1406
2	797	1279
3	3662	1221

Stop Event

1×	node limit

Counts

68 → 49

Calls

Call 1

Inputs
(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2)))))
(+.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 -1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (pow.f64 M 2))))
(+.f64 (.f64 1/24 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (pow.f64 M 4))) (+.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 -1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (pow.f64 M 2)))))
(+.f64 (.f64 1/24 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (pow.f64 M 4))) (+.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (+.f64 (.f64 -1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (pow.f64 M 2))) (.f64 -1/720 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (pow.f64 M 6))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(*.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 M))
(+.f64 (.f64 -1/4 (.f64 (pow.f64 n 2) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 M)))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 M)))
(+.f64 (.f64 -1/4 (.f64 (pow.f64 n 2) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 M)))) (+.f64 (.f64 1/32 (.f64 (pow.f64 n 4) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 M)))) (*.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 M))))
(+.f64 (.f64 -1/4 (.f64 (pow.f64 n 2) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 M)))) (+.f64 (.f64 1/32 (.f64 (pow.f64 n 4) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 M)))) (+.f64 (.f64 -1/384 (.f64 (pow.f64 n 6) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 M)))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) l)) (cos.f64 M)))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (+.f64 (.f64 -1 n) m)) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2)))))
(+.f64 (.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))) (.f64 -1 (.f64 l (.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))))))
(+.f64 (.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))) (+.f64 (.f64 -1 (.f64 l (.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))))) (.f64 1/2 (.f64 (pow.f64 l 2) (.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2)))))))))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 l 3) (.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))))) (+.f64 (.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))) (+.f64 (.f64 -1 (.f64 l (.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))))) (.f64 1/2 (.f64 (pow.f64 l 2) (.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (*.f64 1/4 (pow.f64 n 2)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (*.f64 1/4 (pow.f64 n 2)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (*.f64 1/4 (pow.f64 n 2)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (*.f64 1/4 (pow.f64 n 2)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))

Outputs
(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (*.f64 1/4 (pow.f64 n 2)))))
(exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (.f64 n n))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (*.f64 n n) l)))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (*.f64 n 1/4) l)))
(+.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (.f64 -1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (pow.f64 M 2))))
(+.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (.f64 n n)))) (.f64 -1/2 (.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (.f64 n n)))) (*.f64 M M))))
(fma.f64 -1/2 (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (.f64 M M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))))
(.f64 (+.f64 (.f64 -1/2 (.f64 M M)) 1) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))))
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(.f64 (.f64 (cos.f64 M) (exp.f64 (fma.f64 (.f64 n n) -1/4 (fabs.f64 (-.f64 n m))))) (+.f64 (fma.f64 l -1 1) (.f64 1/2 (*.f64 l l))))
(.f64 (.f64 (cos.f64 M) (exp.f64 (fma.f64 (.f64 n n) -1/4 (fabs.f64 (-.f64 n m))))) (+.f64 (-.f64 1 l) (.f64 1/2 (*.f64 l l))))
(+.f64 (.f64 -1/6 (.f64 (pow.f64 l 3) (.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))))) (+.f64 (.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))) (+.f64 (.f64 -1 (.f64 l (.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))))) (.f64 1/2 (.f64 (pow.f64 l 2) (.f64 (cos.f64 M) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 1/4 (pow.f64 n 2))))))))))
(fma.f64 -1/6 (.f64 (.f64 (pow.f64 l 3) (cos.f64 M)) (exp.f64 (+.f64 (fabs.f64 (-.f64 m n)) (.f64 -1/4 (.f64 n n))))) (fma.f64 (cos.f64 M) (exp.f64 (+.f64 (fabs.f64 (-.f64 m n)) (.f64 -1/4 (.f64 n n)))) (fma.f64 -1 (.f64 (.f64 l (cos.f64 M)) (exp.f64 (+.f64 (fabs.f64 (-.f64 m n)) (.f64 -1/4 (.f64 n n))))) (.f64 1/2 (.f64 (.f64 (.f64 l l) (cos.f64 M)) (exp.f64 (+.f64 (fabs.f64 (-.f64 m n)) (.f64 -1/4 (.f64 n n)))))))))
(+.f64 (.f64 (.f64 (cos.f64 M) (exp.f64 (+.f64 (fabs.f64 (-.f64 n m)) (.f64 (.f64 n n) -1/4)))) (+.f64 (neg.f64 l) (.f64 1/2 (.f64 l l)))) (.f64 (+.f64 (.f64 -1/6 (pow.f64 l 3)) 1) (.f64 (cos.f64 M) (exp.f64 (+.f64 (fabs.f64 (-.f64 n m)) (.f64 (*.f64 n n) -1/4))))))
(fma.f64 (cos.f64 M) (exp.f64 (fma.f64 (.f64 n n) -1/4 (fabs.f64 (-.f64 n m)))) (.f64 (.f64 (cos.f64 M) (exp.f64 (fma.f64 (.f64 n n) -1/4 (fabs.f64 (-.f64 n m))))) (+.f64 (fma.f64 1/2 (.f64 l l) (neg.f64 l)) (.f64 -1/6 (pow.f64 l 3)))))
(.f64 (.f64 (cos.f64 M) (exp.f64 (fma.f64 (.f64 n n) -1/4 (fabs.f64 (-.f64 n m))))) (+.f64 (-.f64 1 l) (.f64 (.f64 l l) (+.f64 1/2 (.f64 l -1/6)))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (*.f64 1/4 (pow.f64 n 2)))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (*.f64 1/4 (pow.f64 n 2)))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (*.f64 1/4 (pow.f64 n 2)))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (fabs.f64 (-.f64 m n))) (*.f64 1/4 (pow.f64 n 2)))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 l (.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (neg.f64 (+.f64 n (.f64 -1 m)))) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (+.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (.f64 -1/4 (*.f64 n n)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 1/4 (.f64 n n) l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 n (.f64 n 1/4) l))) (cos.f64 M))

eval559.0ms (3.8%)

Compiler: Compiled 33815 to 15904 computations (53% saved)

prune476.0ms (3.2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	1220	19	1239
Fresh	4	1	5
Picked	1	0	1
Done	4	0	4
Total	1229	20	1249

Error

0.4b

Counts

1249 → 20

Alt Table

Click to see full alt table

Status	Error	Program
	35.1b	(.f64 (cos.f64 (.f64 K (.f64 m 1/2))) (exp.f64 (.f64 m (*.f64 m -1/4))))
	47.8b	(/.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 l))
	44.0b	(*.f64 (cos.f64 M) (exp.f64 (neg.f64 l)))
▶	46.0b	(.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 (neg.f64 l)))
	60.9b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
	15.9b	(.f64 (cos.f64 (.f64 K (.f64 m 1/2))) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
	27.0b	(.f64 (cos.f64 M) (exp.f64 (.f64 m (*.f64 m -1/4))))
▶	60.8b	(cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))
	27.3b	(.f64 (cos.f64 M) (exp.f64 (.f64 n (*.f64 n -1/4))))
	26.7b	(.f64 (cos.f64 M) (exp.f64 (.f64 -1 (pow.f64 M 2))))
	44.0b	(/.f64 (cos.f64 M) (exp.f64 l))
▶	61.6b	(.f64 (cos.f64 M) (exp.f64 (.f64 M M)))
	22.6b	(.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
	47.8b	(.f64 (cos.f64 (-.f64 (/.f64 (+.f64 (.f64 n K) (*.f64 K m)) 2) M)) (exp.f64 (neg.f64 l)))
	46.5b	(.f64 (cos.f64 (.f64 K (*.f64 m 1/2))) (exp.f64 (neg.f64 l)))
▶	7.9b	(.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
	43.6b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (expm1.f64 (log1p.f64 (.f64 (-.f64 (.f64 m m) (.f64 n n)) K))) (-.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	31.0b	(.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 (.f64 m (*.f64 m -1/4))))
▶	37.2b	(.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 (.f64 m (*.f64 m -1/4))))
	54.1b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (.f64 n n)) K) (-.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))

Compiler

Compiled 734 to 542 computations (26.2% saved)

localize55.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
✓	0.0b	(+.f64 (-.f64 (.f64 n (.f64 n -1/4)) l) (-.f64 m n))
	0.0b	(-.f64 (.f64 n (.f64 n -1/4)) l)

Compiler

Compiled 68 to 35 computations (48.5% saved)

series13.0ms (0.1%)

Counts

2 → 84

Calls

21 calls:

Time	Variable		Point	Expression
2.0ms	n	@	0	(.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
1.0ms	l	@	0	(.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
1.0ms	M	@	0	(.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
1.0ms	M	@	inf	(.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
1.0ms	m	@	0	(.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))

rewrite88.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

823×	`fma-def_binary64`
799×	`log-prod_binary64`
465×	`fma-neg_binary64`
291×	`expm1-udef_binary64`
291×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	39
1	312	39
2	4554	37

Stop Event

1×	node limit

Counts

2 → 145

Calls

Call 1

Inputs
(+.f64 (-.f64 (.f64 n (.f64 n -1/4)) l) (-.f64 m n))
(.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (*.f64 n -1/4)) (-.f64 l (-.f64 m n)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 m (-.f64 n (-.f64 (*.f64 n (*.f64 n -1/4)) l)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (-.f64 (*.f64 n (*.f64 n -1/4)) l) 2) (+.f64 (-.f64 (-.f64 (*.f64 n (*.f64 n -1/4)) l) m) n)) (/.f64 (pow.f64 (-.f64 m n) 2) (+.f64 (-.f64 (-.f64 (*.f64 n (*.f64 n -1/4)) l) m) n)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (-.f64 m n) (*.f64 n (*.f64 n -1/4))) l)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n))))) (#(struct:change #<rule 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(fma.f64 -1 l (-.f64 m n)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 M)) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n)))) (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 M)) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 M)) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 M)) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 M)) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 M)) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 M) 3) (pow.f64 (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n)) 3) (pow.f64 (cos.f64 M) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 M) (exp.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n) (log.f64 (cos.f64 M))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 (-.f64 (fma.f64 n (*.f64 n -1/4) (fma.f64 -1 l m)) n) (log.f64 (cos.f64 M))) 1))))))

simplify90.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-neg_binary64`
656×	`fma-def_binary64`
652×	`times-frac_binary64`
572×	`associate-l_binary64`
557×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	1895
1	373	1858
2	1140	1690
3	5570	1682

Stop Event

1×	node limit

Counts

229 → 201

Calls

Call 1

Inputs
(-.f64 m l)
(-.f64 (+.f64 (*.f64 -1 n) m) l)
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 (.f64 -1 n) m)) l)
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 (.f64 -1 n) m)) l)
(*.f64 -1/4 (pow.f64 n 2))
(+.f64 (.f64 -1/4 (pow.f64 n 2)) (.f64 -1 n))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 (.f64 -1 n) m)) l)
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 (.f64 -1 n) m)) l)
(*.f64 -1/4 (pow.f64 n 2))
(+.f64 (.f64 -1/4 (pow.f64 n 2)) (.f64 -1 n))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 (.f64 -1 n) m)) l)
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 (.f64 -1 n) m)) l)
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) n)
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(*.f64 -1 l)
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(*.f64 -1 l)
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (*.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
m
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
m
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(exp.f64 (-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l)))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (pow.f64 M 2))) (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (pow.f64 M 2))) (+.f64 (.f64 1/24 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (pow.f64 M 4))) (exp.f64 (-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l)))))
(+.f64 (.f64 -1/720 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (pow.f64 M 6))) (+.f64 (.f64 -1/2 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (pow.f64 M 2))) (+.f64 (.f64 1/24 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (pow.f64 M 4))) (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))))))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(*.f64 (exp.f64 (-.f64 m l)) (cos.f64 M))
(+.f64 (.f64 -1 (.f64 (exp.f64 (-.f64 m l)) (.f64 n (cos.f64 M)))) (.f64 (exp.f64 (-.f64 m l)) (cos.f64 M)))
(+.f64 (.f64 -1 (.f64 (exp.f64 (-.f64 m l)) (.f64 n (cos.f64 M)))) (+.f64 (.f64 (exp.f64 (-.f64 m l)) (cos.f64 M)) (.f64 1/4 (.f64 (exp.f64 (-.f64 m l)) (*.f64 (pow.f64 n 2) (cos.f64 M))))))
(+.f64 (.f64 -1 (.f64 (exp.f64 (-.f64 m l)) (.f64 n (cos.f64 M)))) (+.f64 (.f64 (exp.f64 (-.f64 m l)) (cos.f64 M)) (+.f64 (.f64 1/12 (.f64 (exp.f64 (-.f64 m l)) (.f64 (pow.f64 n 3) (cos.f64 M)))) (.f64 1/4 (.f64 (exp.f64 (-.f64 m l)) (.f64 (pow.f64 n 2) (cos.f64 M)))))))
(.f64 (exp.f64 (-.f64 m (+.f64 n (+.f64 l (.f64 1/4 (pow.f64 n 2)))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 m (+.f64 n (+.f64 l (.f64 1/4 (pow.f64 n 2)))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 m (+.f64 n (+.f64 l (.f64 1/4 (pow.f64 n 2)))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 m (+.f64 n (+.f64 l (.f64 1/4 (pow.f64 n 2)))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 n) m) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 n) m) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 n) m) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 n) m) (+.f64 l (*.f64 1/4 (pow.f64 n 2))))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) n)) (cos.f64 M))
(+.f64 (.f64 -1 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) n)) (.f64 l (cos.f64 M)))) (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) n)) (cos.f64 M)))
(+.f64 (.f64 -1 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) n)) (.f64 l (cos.f64 M)))) (+.f64 (.f64 1/2 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) n)) (.f64 (pow.f64 l 2) (cos.f64 M)))) (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) n)) (cos.f64 M))))
(+.f64 (.f64 -1/6 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) n)) (.f64 (pow.f64 l 3) (cos.f64 M)))) (+.f64 (.f64 -1 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) n)) (.f64 l (cos.f64 M)))) (+.f64 (.f64 1/2 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) n)) (.f64 (pow.f64 l 2) (cos.f64 M)))) (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) n)) (cos.f64 M)))))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m)) n)) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m)) n)) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m)) n)) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m)) n)) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (cos.f64 M))
(+.f64 (.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (.f64 m (cos.f64 M))) (.f64 (exp.f64 (-.f64 (*.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (cos.f64 M)))
(+.f64 (.f64 1/2 (.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (.f64 (pow.f64 m 2) (cos.f64 M)))) (+.f64 (.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (.f64 m (cos.f64 M))) (.f64 (exp.f64 (-.f64 (*.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (cos.f64 M))))
(+.f64 (.f64 1/6 (.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (.f64 (pow.f64 m 3) (cos.f64 M)))) (+.f64 (.f64 1/2 (.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (.f64 (pow.f64 m 2) (cos.f64 M)))) (+.f64 (.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (.f64 m (cos.f64 M))) (.f64 (exp.f64 (-.f64 (*.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (cos.f64 M)))))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n (+.f64 (*.f64 -1 m) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n (+.f64 (*.f64 -1 m) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n (+.f64 (*.f64 -1 m) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n (+.f64 (*.f64 -1 m) l)))) (cos.f64 M))

Outputs
(-.f64 m l)
(-.f64 (+.f64 (*.f64 -1 n) m) l)
(-.f64 (fma.f64 -1 n m) l)
(-.f64 m (+.f64 l n))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 (.f64 -1 n) m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 (.f64 -1 n) m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(*.f64 -1/4 (pow.f64 n 2))
(.f64 -1/4 (.f64 n n))
(.f64 n (.f64 n -1/4))
(+.f64 (.f64 -1/4 (pow.f64 n 2)) (.f64 -1 n))
(fma.f64 -1/4 (*.f64 n n) (neg.f64 n))
(neg.f64 (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 (.f64 -1 n) m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 (.f64 -1 n) m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(*.f64 -1/4 (pow.f64 n 2))
(.f64 -1/4 (.f64 n n))
(.f64 n (.f64 n -1/4))
(+.f64 (.f64 -1/4 (pow.f64 n 2)) (.f64 -1 n))
(fma.f64 -1/4 (*.f64 n n) (neg.f64 n))
(neg.f64 (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 (.f64 -1 n) m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 (.f64 -1 n) m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) n)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) n)
(-.f64 m (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(*.f64 -1 l)
(neg.f64 l)
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(*.f64 -1 l)
(neg.f64 l)
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (.f64 -1 l) (+.f64 (.f64 -1/4 (pow.f64 n 2)) m)) n)
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (*.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))
(fma.f64 -1/4 (*.f64 n n) (neg.f64 (+.f64 l n)))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (neg.f64 n)) l)
(-.f64 (neg.f64 n) (fma.f64 n (*.f64 n 1/4) l))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
m
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
m
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))
(-.f64 (fma.f64 -1/4 (*.f64 n n) (fma.f64 -1 n m)) l)
(-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n))
(-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l)))
(-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n))
(exp.f64 (-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l)))
(exp.f64 (-.f64 (fma.f64 -1/4 (*.f64 n n) m) (+.f64 l n)))
(exp.f64 (-.f64 m (+.f64 n (fma.f64 n (*.f64 n 1/4) l))))
(exp.f64 (-.f64 (-.f64 m l) (fma.f64 n (*.f64 n 1/4) n)))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (pow.f64 M 2))) (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))))
(fma.f64 -1/2 (.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (.f64 M M)) (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))))
(.f64 (+.f64 (.f64 -1/2 (.f64 M M)) 1) (exp.f64 (-.f64 m (+.f64 n (fma.f64 n (.f64 n 1/4) l)))))
(.f64 (+.f64 (.f64 -1/2 (.f64 M M)) 1) (exp.f64 (-.f64 (-.f64 m l) (fma.f64 n (.f64 n 1/4) n))))
(+.f64 (.f64 -1/2 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (pow.f64 M 2))) (+.f64 (.f64 1/24 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (pow.f64 M 4))) (exp.f64 (-.f64 (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l)))))
(fma.f64 -1/2 (.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (.f64 M M)) (fma.f64 1/24 (.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (pow.f64 M 4)) (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n)))))
(+.f64 (exp.f64 (-.f64 m (+.f64 n (fma.f64 n (.f64 n 1/4) l)))) (.f64 (exp.f64 (-.f64 m (+.f64 n (fma.f64 n (.f64 n 1/4) l)))) (+.f64 (.f64 -1/2 (.f64 M M)) (.f64 1/24 (pow.f64 M 4)))))
(+.f64 (exp.f64 (-.f64 (-.f64 m l) (fma.f64 n (.f64 n 1/4) n))) (.f64 (exp.f64 (-.f64 (-.f64 m l) (fma.f64 n (.f64 n 1/4) n))) (+.f64 (.f64 -1/2 (.f64 M M)) (.f64 1/24 (pow.f64 M 4)))))
(+.f64 (.f64 -1/720 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (pow.f64 M 6))) (+.f64 (.f64 -1/2 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (pow.f64 M 2))) (+.f64 (.f64 1/24 (.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (pow.f64 M 4))) (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))))))
(fma.f64 -1/720 (.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (pow.f64 M 6)) (fma.f64 -1/2 (.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (.f64 M M)) (fma.f64 1/24 (.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (pow.f64 M 4)) (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))))))
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(.f64 (exp.f64 (-.f64 m (+.f64 n (fma.f64 n (.f64 n 1/4) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (-.f64 m l) (fma.f64 n (.f64 n 1/4) n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m)) n)) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 m (+.f64 n (fma.f64 n (.f64 n 1/4) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (-.f64 m l) (fma.f64 n (.f64 n 1/4) n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1 l) (+.f64 (*.f64 -1/4 (pow.f64 n 2)) m)) n)) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 m (+.f64 n (fma.f64 n (.f64 n 1/4) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (-.f64 m l) (fma.f64 n (.f64 n 1/4) n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (cos.f64 M))
(.f64 (cos.f64 M) (exp.f64 (fma.f64 -1/4 (.f64 n n) (neg.f64 (+.f64 l n)))))
(.f64 (cos.f64 M) (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) (neg.f64 n)) l)))
(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 n) (fma.f64 n (.f64 n 1/4) l))))
(/.f64 (cos.f64 M) (exp.f64 (+.f64 l (fma.f64 n (*.f64 n 1/4) n))))
(+.f64 (.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (.f64 m (cos.f64 M))) (.f64 (exp.f64 (-.f64 (*.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (cos.f64 M)))
(.f64 (exp.f64 (fma.f64 -1/4 (.f64 n n) (neg.f64 (+.f64 l n)))) (+.f64 (*.f64 m (cos.f64 M)) (cos.f64 M)))
(.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) (neg.f64 n)) l)) (fma.f64 m (cos.f64 M) (cos.f64 M)))
(.f64 (cos.f64 M) (.f64 (+.f64 m 1) (exp.f64 (-.f64 (neg.f64 n) (fma.f64 n (*.f64 n 1/4) l)))))
(.f64 (+.f64 m 1) (/.f64 (cos.f64 M) (exp.f64 (+.f64 l (fma.f64 n (.f64 n 1/4) n)))))
(+.f64 (.f64 1/2 (.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (.f64 (pow.f64 m 2) (cos.f64 M)))) (+.f64 (.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (.f64 m (cos.f64 M))) (.f64 (exp.f64 (-.f64 (*.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (cos.f64 M))))
(fma.f64 1/2 (.f64 (exp.f64 (fma.f64 -1/4 (.f64 n n) (neg.f64 (+.f64 l n)))) (.f64 (cos.f64 M) (.f64 m m))) (.f64 (exp.f64 (fma.f64 -1/4 (.f64 n n) (neg.f64 (+.f64 l n)))) (+.f64 (*.f64 m (cos.f64 M)) (cos.f64 M))))
(fma.f64 1/2 (.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) (neg.f64 n)) l)) (.f64 m (.f64 m (cos.f64 M)))) (.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) (neg.f64 n)) l)) (fma.f64 m (cos.f64 M) (cos.f64 M))))
(.f64 (exp.f64 (-.f64 (neg.f64 n) (fma.f64 n (.f64 n 1/4) l))) (+.f64 (.f64 (cos.f64 M) (+.f64 m 1)) (.f64 (cos.f64 M) (.f64 (.f64 m m) 1/2))))
(.f64 (exp.f64 (-.f64 (neg.f64 n) (fma.f64 n (.f64 n 1/4) l))) (+.f64 (.f64 (cos.f64 M) (+.f64 m 1)) (.f64 m (.f64 (.f64 m (cos.f64 M)) 1/2))))
(+.f64 (.f64 1/6 (.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (.f64 (pow.f64 m 3) (cos.f64 M)))) (+.f64 (.f64 1/2 (.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (.f64 (pow.f64 m 2) (cos.f64 M)))) (+.f64 (.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (.f64 m (cos.f64 M))) (.f64 (exp.f64 (-.f64 (*.f64 -1/4 (pow.f64 n 2)) (+.f64 n l))) (cos.f64 M)))))
(fma.f64 1/6 (.f64 (exp.f64 (fma.f64 -1/4 (.f64 n n) (neg.f64 (+.f64 l n)))) (.f64 (cos.f64 M) (pow.f64 m 3))) (fma.f64 1/2 (.f64 (exp.f64 (fma.f64 -1/4 (.f64 n n) (neg.f64 (+.f64 l n)))) (.f64 (cos.f64 M) (.f64 m m))) (.f64 (exp.f64 (fma.f64 -1/4 (.f64 n n) (neg.f64 (+.f64 l n)))) (+.f64 (.f64 m (cos.f64 M)) (cos.f64 M)))))
(fma.f64 1/6 (.f64 (cos.f64 M) (.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) (neg.f64 n)) l)) (pow.f64 m 3))) (fma.f64 1/2 (.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) (neg.f64 n)) l)) (.f64 m (.f64 m (cos.f64 M)))) (.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (*.f64 n n) (neg.f64 n)) l)) (fma.f64 m (cos.f64 M) (cos.f64 M)))))
(fma.f64 (cos.f64 M) (.f64 (+.f64 m 1) (exp.f64 (-.f64 (neg.f64 n) (fma.f64 n (.f64 n 1/4) l)))) (.f64 (exp.f64 (-.f64 (neg.f64 n) (fma.f64 n (.f64 n 1/4) l))) (+.f64 (.f64 (cos.f64 M) (.f64 (pow.f64 m 3) 1/6)) (.f64 (cos.f64 M) (.f64 (*.f64 m m) 1/2)))))
(fma.f64 1/2 (.f64 m (/.f64 (.f64 m (cos.f64 M)) (exp.f64 (+.f64 l (fma.f64 n (.f64 n 1/4) n))))) (.f64 (exp.f64 (-.f64 (neg.f64 n) (fma.f64 n (.f64 n 1/4) l))) (+.f64 (.f64 (pow.f64 m 3) (.f64 (cos.f64 M) 1/6)) (.f64 (cos.f64 M) (+.f64 m 1)))))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 m (+.f64 n (fma.f64 n (.f64 n 1/4) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (-.f64 m l) (fma.f64 n (.f64 n 1/4) n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 m (+.f64 n (fma.f64 n (.f64 n 1/4) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (-.f64 m l) (fma.f64 n (.f64 n 1/4) n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 m (+.f64 n (fma.f64 n (.f64 n 1/4) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (-.f64 m l) (fma.f64 n (.f64 n 1/4) n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 n 2)) m) (+.f64 n l))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 m (+.f64 n (fma.f64 n (.f64 n 1/4) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (-.f64 m l) (fma.f64 n (.f64 n 1/4) n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n (+.f64 (*.f64 -1 m) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 m (+.f64 n (fma.f64 n (.f64 n 1/4) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (-.f64 m l) (fma.f64 n (.f64 n 1/4) n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n (+.f64 (*.f64 -1 m) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 m (+.f64 n (fma.f64 n (.f64 n 1/4) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (-.f64 m l) (fma.f64 n (.f64 n 1/4) n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n (+.f64 (*.f64 -1 m) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 m (+.f64 n (fma.f64 n (.f64 n 1/4) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (-.f64 m l) (fma.f64 n (.f64 n 1/4) n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (.f64 -1/4 (pow.f64 n 2)) (+.f64 n (+.f64 (*.f64 -1 m) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (fma.f64 -1/4 (.f64 n n) m) (+.f64 l n))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 m (+.f64 n (fma.f64 n (.f64 n 1/4) l)))) (cos.f64 M))
(.f64 (exp.f64 (-.f64 (-.f64 m l) (fma.f64 n (.f64 n 1/4) n))) (cos.f64 M))

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 K (.f64 n 1/2)) M)
✓	24.3b	(cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))

Compiler

Compiled 32 to 20 computations (37.5% saved)

series9.0ms (0.1%)

Counts

2 → 72

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	K	@	0	(cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))
1.0ms	M	@	0	(cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))
1.0ms	n	@	0	(cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))
0.0ms	n	@	inf	(-.f64 (.f64 K (.f64 n 1/2)) M)
0.0ms	K	@	inf	(-.f64 (.f64 K (.f64 n 1/2)) M)

rewrite83.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

834×	`prod-diff_binary64`
502×	`log-prod_binary64`
315×	`pow-prod-down_binary64`
300×	`fma-def_binary64`
275×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	199	22
2	2649	22

Stop Event

1×	node limit

Counts

2 → 170

Calls

Call 1

Inputs
(cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))
(-.f64 (.f64 K (.f64 n 1/2)) M)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (cos.f64 M)) (*.f64 (sin.f64 (*.f64 K (*.f64 n 1/2))) (sin.f64 M)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sin.f64 (*.f64 K (*.f64 n 1/2))) (sin.f64 M)) (*.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (cos.f64 M)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cos.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (cos.f64 M)) 1) (*.f64 (*.f64 (sin.f64 (*.f64 K (*.f64 n 1/2))) (sin.f64 M)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (cos.f64 M) (neg.f64 (*.f64 (neg.f64 (sin.f64 M)) (sin.f64 (*.f64 K (*.f64 n 1/2)))))) (fma.f64 (neg.f64 (neg.f64 (sin.f64 M))) (sin.f64 (*.f64 K (*.f64 n 1/2))) (*.f64 (neg.f64 (sin.f64 M)) (sin.f64 (*.f64 K (*.f64 n 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (cos.f64 (exp.f64 (log1p.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)))) (cos.f64 1)) (*.f64 (sin.f64 (exp.f64 (log1p.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)))) (sin.f64 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (cos.f64 (/.f64 (*.f64 (pow.f64 (*.f64 K n) 3) 1/8) (fma.f64 M (fma.f64 K (*.f64 n 1/2) M) (*.f64 (pow.f64 (*.f64 K n) 2) 1/4)))) (cos.f64 (/.f64 (pow.f64 M 3) (fma.f64 M (fma.f64 K (*.f64 n 1/2) M) (*.f64 (pow.f64 (*.f64 K n) 2) 1/4))))) (*.f64 (sin.f64 (/.f64 (*.f64 (pow.f64 (*.f64 K n) 3) 1/8) (fma.f64 M (fma.f64 K (*.f64 n 1/2) M) (*.f64 (pow.f64 (*.f64 K n) 2) 1/4)))) (sin.f64 (/.f64 (pow.f64 M 3) (fma.f64 M (fma.f64 K (*.f64 n 1/2) M) (*.f64 (pow.f64 (*.f64 K n) 2) 1/4))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (cos.f64 (/.f64 (*.f64 (pow.f64 (*.f64 K n) 2) 1/4) (fma.f64 K (*.f64 n 1/2) M))) (cos.f64 (/.f64 (*.f64 M M) (fma.f64 K (*.f64 n 1/2) M)))) (*.f64 (sin.f64 (/.f64 (*.f64 (pow.f64 (*.f64 K n) 2) 1/4) (fma.f64 K (*.f64 n 1/2) M))) (sin.f64 (/.f64 (*.f64 M M) (fma.f64 K (*.f64 n 1/2) M)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M))))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (cos.f64 M)) (*.f64 (sin.f64 (*.f64 K (*.f64 n 1/2))) (neg.f64 (sin.f64 M))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (cos.f64 M)) (*.f64 (neg.f64 (sin.f64 M)) (sin.f64 (*.f64 K (*.f64 n 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (cos.f64 (*.f64 (neg.f64 M) 1))) (*.f64 (sin.f64 (*.f64 K (*.f64 n 1/2))) (sin.f64 (*.f64 (neg.f64 M) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)) (cos.f64 (fma.f64 (neg.f64 M) 1 M))) (*.f64 (sin.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)) (sin.f64 (fma.f64 (neg.f64 M) 1 M))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (cbrt.f64 (*.f64 M M)) M))) (*.f64 (sin.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 M)) (cbrt.f64 (*.f64 M M)) M))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)) (cos.f64 (+.f64 (neg.f64 M) M))) (*.f64 (sin.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)) (sin.f64 (+.f64 (neg.f64 M) M))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cos.f64 (-.f64 (*.f64 K 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(pow.f64 (cbrt.f64 K) 2) (*.f64 (cbrt.f64 K) (*.f64 n 1/2)) (*.f64 (neg.f64 M) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 K (*.f64 n 1/2))) (pow.f64 (cbrt.f64 (*.f64 K (*.f64 n 1/2))) 2) (neg.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 K (*.f64 n 1/2))) (pow.f64 (cbrt.f64 (*.f64 K (*.f64 n 1/2))) 2) (*.f64 (neg.f64 M) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 K (*.f64 n 1/2))) 2) (cbrt.f64 (*.f64 K (*.f64 n 1/2))) (neg.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 K (*.f64 n 1/2))) 2) (cbrt.f64 (*.f64 K (*.f64 n 1/2))) (*.f64 (neg.f64 M) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 M M)) (neg.f64 (cbrt.f64 M)) (*.f64 K (*.f64 n 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)) (sqrt.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)) (fma.f64 (neg.f64 M) 1 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)) (sqrt.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)) (fma.f64 (neg.f64 (cbrt.f64 M)) (cbrt.f64 (*.f64 M M)) M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)) (sqrt.f64 (-.f64 (*.f64 K (*.f64 n 1/2)) M)) (+.f64 (neg.f64 M) M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 n 1/2)) (*.f64 (sqrt.f64 (*.f64 n 1/2)) K) (neg.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 n 1/2)) (*.f64 (sqrt.f64 (*.f64 n 1/2)) K) (*.f64 (neg.f64 M) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 K) (*.f64 (sqrt.f64 K) (*.f64 n 1/2)) (neg.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 K) (*.f64 (sqrt.f64 K) (*.f64 n 1/2)) (*.f64 (neg.f64 M) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 K (*.f64 n 1/2))) (sqrt.f64 (*.f64 K (*.f64 n 1/2))) (neg.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 K (*.f64 n 1/2))) (sqrt.f64 (*.f64 K (*.f64 n 1/2))) (*.f64 (neg.f64 M) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 M) (neg.f64 (sqrt.f64 M)) (*.f64 K (*.f64 n 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (*.f64 (pow.f64 (*.f64 K n) 3) 1/8) (pow.f64 M 3)) (/.f64 1 (fma.f64 M (fma.f64 K (*.f64 n 1/2) M) (*.f64 (pow.f64 (*.f64 K n) 2) 1/4))) (fma.f64 (neg.f64 M) 1 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (*.f64 (pow.f64 (*.f64 K n) 3) 1/8) (pow.f64 M 3)) (/.f64 1 (fma.f64 M (fma.f64 K (*.f64 n 1/2) M) (*.f64 (pow.f64 (*.f64 K n) 2) 1/4))) (fma.f64 (neg.f64 (cbrt.f64 M)) (cbrt.f64 (*.f64 M M)) M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (*.f64 (pow.f64 (*.f64 K n) 3) 1/8) (pow.f64 M 3)) (/.f64 1 (fma.f64 M (fma.f64 K (*.f64 n 1/2) M) (*.f64 (pow.f64 (*.f64 K n) 2) 1/4))) (+.f64 (neg.f64 M) M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (pow.f64 (*.f64 K n) 2) 1/4 (neg.f64 (*.f64 M M))) (/.f64 1 (fma.f64 K (*.f64 n 1/2) M)) (fma.f64 (neg.f64 M) 1 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (pow.f64 (*.f64 K n) 2) 1/4 (neg.f64 (*.f64 M M))) (/.f64 1 (fma.f64 K (*.f64 n 1/2) M)) (fma.f64 (neg.f64 (cbrt.f64 M)) (cbrt.f64 (*.f64 M M)) M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (pow.f64 (*.f64 K n) 2) 1/4 (neg.f64 (*.f64 M M))) (/.f64 1 (fma.f64 K (*.f64 n 1/2) M)) (+.f64 (neg.f64 M) M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 K n) 1/2 (neg.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 K n) 1/2 (*.f64 (neg.f64 M) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (neg.f64 M)) 2) (cbrt.f64 (neg.f64 M)) (*.f64 K (*.f64 n 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (neg.f64 M)) (sqrt.f64 (neg.f64 M)) (*.f64 K (*.f64 n 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sqrt.f64 M)) (sqrt.f64 M) (*.f64 K (*.f64 n 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 M (*.f64 K (*.f64 n 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (sqrt.f64 (*.f64 K n)) (sqrt.f64 1/2) (sqrt.f64 M)) (-.f64 (sqrt.f64 (*.f64 K (*.f64 n 1/2))) (sqrt.f64 M)) (fma.f64 (neg.f64 M) 1 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (sqrt.f64 (*.f64 K n)) (sqrt.f64 1/2) (sqrt.f64 M)) (-.f64 (sqrt.f64 (*.f64 K (*.f64 n 1/2))) (sqrt.f64 M)) (fma.f64 (neg.f64 (cbrt.f64 M)) (cbrt.f64 (*.f64 M M)) M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (sqrt.f64 (*.f64 K n)) (sqrt.f64 1/2) (sqrt.f64 M)) (-.f64 (sqrt.f64 (*.f64 K (*.f64 n 1/2))) (sqrt.f64 M)) (+.f64 (neg.f64 M) M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (*.f64 M M))) (cbrt.f64 M) (*.f64 K (*.f64 n 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 K 1/2) n (neg.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 K 1/2) n (*.f64 (neg.f64 M) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 K (cbrt.f64 (*.f64 (*.f64 n n) 1/4))) (cbrt.f64 (*.f64 n 1/2)) (neg.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 K (cbrt.f64 (*.f64 (*.f64 n n) 1/4))) (cbrt.f64 (*.f64 n 1/2)) (*.f64 (neg.f64 M) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 K (sqrt.f64 (*.f64 n 1/2))) (sqrt.f64 (*.f64 n 1/2)) (neg.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 K (sqrt.f64 (*.f64 n 1/2))) (sqrt.f64 (*.f64 n 1/2)) (*.f64 (neg.f64 M) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 n 1/2) (pow.f64 (cbrt.f64 K) 2)) (cbrt.f64 K) (neg.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 n 1/2) (pow.f64 (cbrt.f64 K) 2)) (cbrt.f64 K) (*.f64 (neg.f64 M) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 n 1/2) (sqrt.f64 K)) (sqrt.f64 K) (neg.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 n 1/2) (sqrt.f64 K)) (sqrt.f64 K) (*.f64 (neg.f64 M) 1))))))

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

730×	`distribute-lft-neg-out_binary64`
681×	`distribute-rgt-neg-out_binary64`
588×	`unswap-sqr_binary64`
470×	`neg-sub0_binary64`
465×	`neg-mul-1_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	965
1	176	955
2	514	926
3	2125	908
4	4034	908

Stop Event

1×	node limit

Counts

242 → 197

Calls

Call 1

Inputs
(cos.f64 (neg.f64 M))
(+.f64 (cos.f64 (neg.f64 M)) (.f64 -1/2 (.f64 n (*.f64 K (sin.f64 (neg.f64 M))))))
(+.f64 (.f64 -1/8 (.f64 (cos.f64 (neg.f64 M)) (.f64 (pow.f64 n 2) (pow.f64 K 2)))) (+.f64 (cos.f64 (neg.f64 M)) (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (neg.f64 M)))))))
(+.f64 (.f64 -1/8 (.f64 (cos.f64 (neg.f64 M)) (.f64 (pow.f64 n 2) (pow.f64 K 2)))) (+.f64 (cos.f64 (neg.f64 M)) (+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (neg.f64 M))))) (.f64 1/48 (.f64 (pow.f64 n 3) (*.f64 (pow.f64 K 3) (sin.f64 (neg.f64 M))))))))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (neg.f64 M))
(+.f64 (cos.f64 (neg.f64 M)) (.f64 -1/2 (.f64 n (*.f64 K (sin.f64 (neg.f64 M))))))
(+.f64 (cos.f64 (neg.f64 M)) (+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (neg.f64 M))))) (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (cos.f64 (neg.f64 M)) (pow.f64 K 2))))))
(+.f64 (cos.f64 (neg.f64 M)) (+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (neg.f64 M))))) (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (cos.f64 (neg.f64 M)) (pow.f64 K 2)))) (.f64 1/48 (.f64 (pow.f64 n 3) (*.f64 (pow.f64 K 3) (sin.f64 (neg.f64 M))))))))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (.f64 1/2 (.f64 n K)))
(+.f64 (.f64 (sin.f64 (.f64 1/2 (.f64 n K))) M) (cos.f64 (.f64 1/2 (*.f64 n K))))
(+.f64 (.f64 -1/2 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (pow.f64 M 2))) (+.f64 (.f64 (sin.f64 (.f64 1/2 (.f64 n K))) M) (cos.f64 (.f64 1/2 (*.f64 n K)))))
(+.f64 (.f64 -1/2 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (pow.f64 M 2))) (+.f64 (.f64 (sin.f64 (.f64 1/2 (.f64 n K))) M) (+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (.f64 -1/6 (.f64 (sin.f64 (.f64 1/2 (*.f64 n K))) (pow.f64 M 3))))))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M)))
(cos.f64 (+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M)))
(cos.f64 (+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M)))
(cos.f64 (+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M)))
(*.f64 -1 M)
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(.f64 1/2 (.f64 n K))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(.f64 1/2 (.f64 n K))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(*.f64 -1 M)
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(.f64 1/2 (.f64 n K))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(.f64 1/2 (.f64 n K))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(.f64 1/2 (.f64 n K))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(*.f64 -1 M)
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(*.f64 -1 M)
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))

Outputs
(cos.f64 (neg.f64 M))
(cos.f64 M)
(+.f64 (cos.f64 (neg.f64 M)) (.f64 -1/2 (.f64 n (*.f64 K (sin.f64 (neg.f64 M))))))
(+.f64 (cos.f64 M) (.f64 -1/2 (.f64 n (*.f64 K (neg.f64 (sin.f64 M))))))
(fma.f64 -1/2 (.f64 (neg.f64 (sin.f64 M)) (.f64 n K)) (cos.f64 M))
(fma.f64 n (.f64 K (.f64 (sin.f64 M) 1/2)) (cos.f64 M))
(+.f64 (.f64 -1/8 (.f64 (cos.f64 (neg.f64 M)) (.f64 (pow.f64 n 2) (pow.f64 K 2)))) (+.f64 (cos.f64 (neg.f64 M)) (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (neg.f64 M)))))))
(fma.f64 -1/8 (.f64 (cos.f64 M) (.f64 (.f64 n n) (.f64 K K))) (+.f64 (cos.f64 M) (.f64 -1/2 (.f64 n (*.f64 K (neg.f64 (sin.f64 M)))))))
(fma.f64 (.f64 (cos.f64 M) -1/8) (.f64 n (.f64 n (.f64 K K))) (fma.f64 -1/2 (.f64 (neg.f64 (sin.f64 M)) (.f64 n K)) (cos.f64 M)))
(fma.f64 (cos.f64 M) (.f64 -1/8 (.f64 n (.f64 K (.f64 n K)))) (fma.f64 -1/2 (.f64 (neg.f64 (sin.f64 M)) (.f64 n K)) (cos.f64 M)))
(+.f64 (cos.f64 M) (.f64 (.f64 n K) (+.f64 (.f64 (sin.f64 M) 1/2) (.f64 (.f64 (cos.f64 M) -1/8) (.f64 n K)))))
(+.f64 (.f64 -1/8 (.f64 (cos.f64 (neg.f64 M)) (.f64 (pow.f64 n 2) (pow.f64 K 2)))) (+.f64 (cos.f64 (neg.f64 M)) (+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (neg.f64 M))))) (.f64 1/48 (.f64 (pow.f64 n 3) (*.f64 (pow.f64 K 3) (sin.f64 (neg.f64 M))))))))
(fma.f64 -1/8 (.f64 (cos.f64 M) (.f64 (.f64 n n) (.f64 K K))) (+.f64 (cos.f64 M) (fma.f64 -1/2 (.f64 n (.f64 K (neg.f64 (sin.f64 M)))) (.f64 1/48 (.f64 (pow.f64 n 3) (*.f64 (neg.f64 (sin.f64 M)) (pow.f64 K 3)))))))
(+.f64 (fma.f64 -1/2 (.f64 (neg.f64 (sin.f64 M)) (.f64 n K)) (cos.f64 M)) (fma.f64 -1/8 (.f64 (cos.f64 M) (.f64 n (.f64 n (.f64 K K)))) (.f64 (.f64 (pow.f64 n 3) (pow.f64 K 3)) (*.f64 (neg.f64 (sin.f64 M)) 1/48))))
(+.f64 (cos.f64 M) (fma.f64 (cos.f64 M) (.f64 -1/8 (.f64 n (.f64 K (.f64 n K)))) (.f64 (neg.f64 (sin.f64 M)) (+.f64 (.f64 -1/2 (.f64 n K)) (.f64 1/48 (*.f64 (pow.f64 n 3) (pow.f64 K 3)))))))
(+.f64 (.f64 (.f64 n K) (+.f64 (.f64 (sin.f64 M) 1/2) (.f64 (.f64 (cos.f64 M) -1/8) (.f64 n K)))) (fma.f64 (pow.f64 n 3) (.f64 (pow.f64 K 3) (.f64 (sin.f64 M) -1/48)) (cos.f64 M)))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (fma.f64 1/2 (*.f64 n K) (neg.f64 M)))
(cos.f64 (fma.f64 K (*.f64 n 1/2) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 n (.f64 K 1/2)) M))
(cos.f64 (fma.f64 n (*.f64 K 1/2) (neg.f64 M)))
(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))
(cos.f64 (fma.f64 1/2 (*.f64 n K) (neg.f64 M)))
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(fma.f64 n (*.f64 K 1/2) (neg.f64 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(-.f64 (.f64 1/2 (.f64 n K)) M)
(fma.f64 1/2 (*.f64 n K) (neg.f64 M))
(fma.f64 K (*.f64 n 1/2) (neg.f64 M))
(-.f64 (.f64 n (.f64 K 1/2)) M)
(fma.f64 n (*.f64 K 1/2) (neg.f64 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(-.f64 (.f64 1/2 (.f64 n K)) M)
(fma.f64 1/2 (*.f64 n K) (neg.f64 M))
(fma.f64 K (*.f64 n 1/2) (neg.f64 M))
(-.f64 (.f64 n (.f64 K 1/2)) M)
(fma.f64 n (*.f64 K 1/2) (neg.f64 M))
(.f64 1/2 (.f64 n K))
(.f64 n (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(-.f64 (.f64 1/2 (.f64 n K)) M)
(fma.f64 1/2 (*.f64 n K) (neg.f64 M))
(fma.f64 K (*.f64 n 1/2) (neg.f64 M))
(-.f64 (.f64 n (.f64 K 1/2)) M)
(fma.f64 n (*.f64 K 1/2) (neg.f64 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(-.f64 (.f64 1/2 (.f64 n K)) M)
(fma.f64 1/2 (*.f64 n K) (neg.f64 M))
(fma.f64 K (*.f64 n 1/2) (neg.f64 M))
(-.f64 (.f64 n (.f64 K 1/2)) M)
(fma.f64 n (*.f64 K 1/2) (neg.f64 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(-.f64 (.f64 1/2 (.f64 n K)) M)
(fma.f64 1/2 (*.f64 n K) (neg.f64 M))
(fma.f64 K (*.f64 n 1/2) (neg.f64 M))
(-.f64 (.f64 n (.f64 K 1/2)) M)
(fma.f64 n (*.f64 K 1/2) (neg.f64 M))
(*.f64 -1 M)
(neg.f64 M)
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(-.f64 (.f64 1/2 (.f64 n K)) M)
(fma.f64 1/2 (*.f64 n K) (neg.f64 M))
(fma.f64 K (*.f64 n 1/2) (neg.f64 M))
(-.f64 (.f64 n (.f64 K 1/2)) M)
(fma.f64 n (*.f64 K 1/2) (neg.f64 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(-.f64 (.f64 1/2 (.f64 n K)) M)
(fma.f64 1/2 (*.f64 n K) (neg.f64 M))
(fma.f64 K (*.f64 n 1/2) (neg.f64 M))
(-.f64 (.f64 n (.f64 K 1/2)) M)
(fma.f64 n (*.f64 K 1/2) (neg.f64 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(-.f64 (.f64 1/2 (.f64 n K)) M)
(fma.f64 1/2 (*.f64 n K) (neg.f64 M))
(fma.f64 K (*.f64 n 1/2) (neg.f64 M))
(-.f64 (.f64 n (.f64 K 1/2)) M)
(fma.f64 n (*.f64 K 1/2) (neg.f64 M))
(*.f64 -1 M)
(neg.f64 M)
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(-.f64 (.f64 1/2 (.f64 n K)) M)
(fma.f64 1/2 (*.f64 n K) (neg.f64 M))
(fma.f64 K (*.f64 n 1/2) (neg.f64 M))
(-.f64 (.f64 n (.f64 K 1/2)) M)
(fma.f64 n (*.f64 K 1/2) (neg.f64 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(-.f64 (.f64 1/2 (.f64 n K)) M)
(fma.f64 1/2 (*.f64 n K) (neg.f64 M))
(fma.f64 K (*.f64 n 1/2) (neg.f64 M))
(-.f64 (.f64 n (.f64 K 1/2)) M)
(fma.f64 n (*.f64 K 1/2) (neg.f64 M))
(+.f64 (.f64 1/2 (.f64 n K)) (*.f64 -1 M))
(-.f64 (.f64 1/2 (.f64 n K)) M)
(fma.f64 1/2 (*.f64 n K) (neg.f64 M))
(fma.f64 K (*.f64 n 1/2) (neg.f64 M))
(-.f64 (.f64 n (.f64 K 1/2)) M)
(fma.f64 n (*.f64 K 1/2) (neg.f64 M))

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (*.f64 M M))

Compiler

Compiled 22 to 9 computations (59.1% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	M	@	0	(exp.f64 (*.f64 M M))
0.0ms	M	@	inf	(exp.f64 (*.f64 M M))
0.0ms	M	@	-inf	(exp.f64 (*.f64 M M))

rewrite49.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

321×	`pow1_binary64`
314×	`associate-l_binary64`
308×	`add-sqr-sqrt_binary64`
302×	`*-un-lft-identity_binary64`
296×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	76	6
2	874	6

Stop Event

1×	node limit

Counts

1 → 66

Calls

Call 1

Inputs
(exp.f64 (*.f64 M M))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (expm1.f64 (*.f64 M M)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (pow.f64 (exp.f64 M) M)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (exp.f64 M) M))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 M) M))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (exp.f64 M) M)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (exp.f64 M) M)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (exp.f64 M) M)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (exp.f64 M) M)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 M) M) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (exp.f64 M) M))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M)) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M)) (*.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M)) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M)) 2) (cbrt.f64 (pow.f64 (exp.f64 M) M)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (exp.f64 M) M)) (sqrt.f64 (pow.f64 (exp.f64 M) M)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M))) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (exp.f64 M) M) 1/6) (*.f64 (pow.f64 (pow.f64 (exp.f64 M) M) 1/6) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M)) 4)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M))) 2) (cbrt.f64 (pow.f64 (exp.f64 M) M))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (exp.f64 M) M) 1/4) (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 M) M) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (exp.f64 M) M) 1/4) (*.f64 (pow.f64 (pow.f64 (exp.f64 M) M) 1/4) (sqrt.f64 (pow.f64 (exp.f64 M) M))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 (exp.f64 M) M) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M)) 5))) (cbrt.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 M) M) 5/2)) (pow.f64 (pow.f64 (exp.f64 M) M) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 M) M) 3/2)) (pow.f64 (pow.f64 (exp.f64 M) M) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M)) 5)) (pow.f64 (pow.f64 (exp.f64 M) M) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (pow.f64 (exp.f64 M) M))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 M) (pow.f64 (exp.f64 M) M))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 M) 2)) M) (pow.f64 (cbrt.f64 (exp.f64 M)) M))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (exp.f64 M)) M) (pow.f64 (sqrt.f64 (exp.f64 M)) M))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (exp.f64 M) M) (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M)) 5)) 1/3) (cbrt.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 M) M) 5/2) 1/3) (pow.f64 (pow.f64 (exp.f64 M) M) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (E.f64) (*.f64 1/2 (*.f64 M M))) (pow.f64 (E.f64) (*.f64 1/2 (*.f64 M M))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (E.f64) (*.f64 2 (*.f64 1/3 (*.f64 M M)))) (pow.f64 (E.f64) (*.f64 1/3 (*.f64 M M))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (exp.f64 (+.f64 1 (*.f64 M M))) (E.f64))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (exp.f64 M) (+.f64 1 M)) (exp.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (E.f64) (+.f64 1 (*.f64 M M))) (E.f64))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 M) M)) 3) 1) (+.f64 (*.f64 (+.f64 1 (pow.f64 (exp.f64 M) M)) (+.f64 1 (pow.f64 (exp.f64 M) M))) (+.f64 1 (*.f64 (+.f64 1 (pow.f64 (exp.f64 M) M)) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (expm1.f64 (*.f64 M M)) 3)) (+.f64 1 (-.f64 (pow.f64 (expm1.f64 (*.f64 M M)) 2) (expm1.f64 (*.f64 M M)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 (pow.f64 (exp.f64 M) M)) (+.f64 1 (pow.f64 (exp.f64 M) M))) 1) (+.f64 (+.f64 1 (pow.f64 (exp.f64 M) M)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (expm1.f64 (*.f64 M M)) 2)) (-.f64 1 (expm1.f64 (*.f64 M M))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 M) M) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 M) M)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 M) (*.f64 (*.f64 M 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 M) (+.f64 (*.f64 M 1/2) (*.f64 M 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 M) (/.f64 (+.f64 M M) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 M) (*.f64 2 (*.f64 M 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (exp.f64 M) M) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 M) (*.f64 M 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (exp.f64 M) M)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 (exp.f64 M) M)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (*.f64 M M))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 M)) (pow.f64 M 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 M) 2)) (*.f64 M (cbrt.f64 M)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (*.f64 M (cbrt.f64 M))) (pow.f64 (cbrt.f64 M) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 M) 2) (*.f64 M 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 M) 5)) (cbrt.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 M 3/2)) (sqrt.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 M) (cbrt.f64 M)) (pow.f64 (cbrt.f64 M) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (*.f64 M (cbrt.f64 M))) (cbrt.f64 M)) (cbrt.f64 M))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (*.f64 M (cbrt.f64 M))) (cbrt.f64 (*.f64 M (cbrt.f64 M)))) (pow.f64 (cbrt.f64 (cbrt.f64 M)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 M) 5)) (pow.f64 (cbrt.f64 (cbrt.f64 M)) 2)) (cbrt.f64 (cbrt.f64 M)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 M) 5)) (pow.f64 M 1/6)) (pow.f64 M 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 M 3/2)) (cbrt.f64 M)) (pow.f64 M 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (pow.f64 M 3/2)) (pow.f64 M 1/4)) (pow.f64 M 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (exp.f64 M) M) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (exp.f64 M) M))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (exp.f64 M) M)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 M) (*.f64 M 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (exp.f64 M) M)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (exp.f64 M) M)))))))

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

823×	`associate-/l/_binary64`
682×	`fma-def_binary64`
679×	`associate-/r/_binary64`
582×	`associate-/l*_binary64`
375×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	93
1	46	89
2	102	87
3	275	85
4	1050	85
5	2890	85
6	3723	85
7	4664	85

Stop Event

1×	node limit

Counts

78 → 74

Calls

Call 1

Inputs
1
(+.f64 1 (pow.f64 M 2))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 M 4)) (pow.f64 M 2)))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 M 4)) (+.f64 (pow.f64 M 2) (.f64 1/6 (pow.f64 M 6)))))
(exp.f64 (pow.f64 M 2))
(exp.f64 (pow.f64 M 2))
(exp.f64 (pow.f64 M 2))
(exp.f64 (pow.f64 M 2))
(exp.f64 (pow.f64 M 2))
(exp.f64 (pow.f64 M 2))
(exp.f64 (pow.f64 M 2))
(exp.f64 (pow.f64 M 2))

Outputs
1
(+.f64 1 (pow.f64 M 2))
(+.f64 1 (*.f64 M M))
(fma.f64 M M 1)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 M 4)) (pow.f64 M 2)))
(+.f64 1 (fma.f64 1/2 (pow.f64 M 4) (*.f64 M M)))
(+.f64 1 (fma.f64 M M (*.f64 1/2 (pow.f64 M 4))))
(fma.f64 M M (fma.f64 1/2 (pow.f64 M 4) 1))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 M 4)) (+.f64 (pow.f64 M 2) (.f64 1/6 (pow.f64 M 6)))))
(+.f64 1 (+.f64 (fma.f64 1/2 (pow.f64 M 4) (.f64 M M)) (.f64 1/6 (pow.f64 M 6))))
(+.f64 1 (fma.f64 1/2 (pow.f64 M 4) (fma.f64 M M (*.f64 1/6 (pow.f64 M 6)))))
(fma.f64 M M (fma.f64 1/2 (pow.f64 M 4) (fma.f64 1/6 (pow.f64 M 6) 1)))
(fma.f64 M (fma.f64 1/2 (pow.f64 M 3) M) (fma.f64 1/6 (pow.f64 M 6) 1))
(exp.f64 (pow.f64 M 2))
(exp.f64 (*.f64 M M))
(pow.f64 (exp.f64 M) M)
(exp.f64 (pow.f64 M 2))
(exp.f64 (*.f64 M M))
(pow.f64 (exp.f64 M) M)
(exp.f64 (pow.f64 M 2))
(exp.f64 (*.f64 M M))
(pow.f64 (exp.f64 M) M)
(exp.f64 (pow.f64 M 2))
(exp.f64 (*.f64 M M))
(pow.f64 (exp.f64 M) M)
(exp.f64 (pow.f64 M 2))
(exp.f64 (*.f64 M M))
(pow.f64 (exp.f64 M) M)
(exp.f64 (pow.f64 M 2))
(exp.f64 (*.f64 M M))
(pow.f64 (exp.f64 M) M)
(exp.f64 (pow.f64 M 2))
(exp.f64 (*.f64 M M))
(pow.f64 (exp.f64 M) M)
(exp.f64 (pow.f64 M 2))
(exp.f64 (*.f64 M M))
(pow.f64 (exp.f64 M) M)

localize18.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 (neg.f64 l)))
✓	28.9b	(cos.f64 (.f64 K (.f64 n 1/2)))

Compiler

Compiled 38 to 22 computations (42.1% saved)

series9.0ms (0.1%)

Counts

2 → 60

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	l	@	inf	(.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 (neg.f64 l)))
1.0ms	K	@	0	(cos.f64 (.f64 K (.f64 n 1/2)))
1.0ms	l	@	0	(.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 (neg.f64 l)))
1.0ms	K	@	0	(.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 (neg.f64 l)))
1.0ms	n	@	-inf	(.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 (neg.f64 l)))

rewrite69.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

942×	`pow1_binary64`
863×	`add-log-exp_binary64`
862×	`log1p-expm1-u_binary64`
862×	`expm1-log1p-u_binary64`
844×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	219	23
2	2618	23

Stop Event

1×	node limit

Counts

2 → 30

Calls

Call 1

Inputs
(cos.f64 (.f64 K (.f64 n 1/2)))
(.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 (neg.f64 l)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cos.f64 (*.f64 K (*.f64 n 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cos.f64 (*.f64 K (*.f64 n 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cos.f64 (*.f64 K (*.f64 n 1/2)))) (pow.f64 (cbrt.f64 (cos.f64 (*.f64 K (*.f64 n 1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 (*.f64 K (*.f64 n 1/2)))) 2) (cbrt.f64 (cos.f64 (*.f64 K (*.f64 n 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 (*.f64 K (*.f64 n 1/2)))) (sqrt.f64 (cos.f64 (*.f64 K (*.f64 n 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cos.f64 (*.f64 K (*.f64 n 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (cos.f64 (*.f64 K (*.f64 n 1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cos.f64 (*.f64 K (*.f64 n 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cos.f64 (*.f64 K (*.f64 n 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cos.f64 (*.f64 K (*.f64 n 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cos.f64 (*.f64 K (*.f64 n 1/2)))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (exp.f64 l))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (exp.f64 l))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (exp.f64 l)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (exp.f64 l)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (exp.f64 l))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (exp.f64 l))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (exp.f64 l)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (exp.f64 l)) (cos.f64 (*.f64 K (*.f64 n 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (exp.f64 l)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) 3) (pow.f64 (exp.f64 l) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 l) 3) (pow.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (exp.f64 l))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))) (exp.f64 l))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 l (log.f64 (cos.f64 (*.f64 K (*.f64 n 1/2))))))))))

simplify74.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

574×	`unswap-sqr_binary64`
491×	`associate-/r/_binary64`
428×	`distribute-lft-out_binary64`
384×	`fma-def_binary64`
352×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	68	1136
1	189	1100
2	553	994
3	2404	960
4	5043	938

Stop Event

1×	node limit

Counts

90 → 54

Calls

Call 1

Inputs
1
(+.f64 1 (.f64 -1/8 (.f64 (pow.f64 n 2) (pow.f64 K 2))))
(+.f64 1 (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (pow.f64 K 2))) (.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)))))
(+.f64 1 (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (pow.f64 K 2))) (+.f64 (.f64 -1/46080 (.f64 (pow.f64 n 6) (pow.f64 K 6))) (.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4))))))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 1/2 (.f64 n K)))
1
(+.f64 1 (.f64 -1/8 (.f64 (pow.f64 n 2) (pow.f64 K 2))))
(+.f64 1 (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (pow.f64 K 2))) (.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)))))
(+.f64 1 (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (pow.f64 K 2))) (+.f64 (.f64 -1/46080 (.f64 (pow.f64 n 6) (pow.f64 K 6))) (.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4))))))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(exp.f64 (neg.f64 l))
(+.f64 (exp.f64 (neg.f64 l)) (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (*.f64 (pow.f64 n 2) (pow.f64 K 2)))))
(+.f64 (exp.f64 (neg.f64 l)) (+.f64 (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 n 2) (pow.f64 K 2)))) (.f64 1/384 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 n 4) (pow.f64 K 4))))))
(+.f64 (exp.f64 (neg.f64 l)) (+.f64 (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 n 2) (pow.f64 K 2)))) (+.f64 (.f64 -1/46080 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 n 6) (pow.f64 K 6)))) (.f64 1/384 (.f64 (exp.f64 (neg.f64 l)) (*.f64 (pow.f64 n 4) (pow.f64 K 4)))))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(exp.f64 (neg.f64 l))
(+.f64 (exp.f64 (neg.f64 l)) (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (*.f64 (pow.f64 n 2) (pow.f64 K 2)))))
(+.f64 (exp.f64 (neg.f64 l)) (+.f64 (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 n 2) (pow.f64 K 2)))) (.f64 1/384 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 n 4) (pow.f64 K 4))))))
(+.f64 (exp.f64 (neg.f64 l)) (+.f64 (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 n 2) (pow.f64 K 2)))) (+.f64 (.f64 -1/46080 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 n 6) (pow.f64 K 6)))) (.f64 1/384 (.f64 (exp.f64 (neg.f64 l)) (*.f64 (pow.f64 n 4) (pow.f64 K 4)))))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(cos.f64 (.f64 1/2 (.f64 n K)))
(+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (.f64 -1 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) l)))
(+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (+.f64 (.f64 -1 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) l)) (.f64 1/2 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (pow.f64 l 2)))))
(+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (+.f64 (.f64 -1 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) l)) (+.f64 (.f64 -1/6 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (pow.f64 l 3))) (.f64 1/2 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (pow.f64 l 2))))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (exp.f64 (.f64 -1 l)))
(.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (exp.f64 (.f64 -1 l)))
(.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (exp.f64 (.f64 -1 l)))
(.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (exp.f64 (.f64 -1 l)))

Outputs
1
(+.f64 1 (.f64 -1/8 (.f64 (pow.f64 n 2) (pow.f64 K 2))))
(+.f64 1 (.f64 -1/8 (.f64 (.f64 n n) (.f64 K K))))
(fma.f64 -1/8 (.f64 n (.f64 n (*.f64 K K))) 1)
(fma.f64 -1/8 (.f64 (.f64 n n) (*.f64 K K)) 1)
(fma.f64 -1/8 (.f64 (.f64 n K) (*.f64 n K)) 1)
(+.f64 1 (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (pow.f64 K 2))) (.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)))))
(+.f64 1 (fma.f64 -1/8 (.f64 (.f64 n n) (.f64 K K)) (.f64 1/384 (*.f64 (pow.f64 n 4) (pow.f64 K 4)))))
(+.f64 (fma.f64 -1/8 (.f64 n (.f64 n (.f64 K K))) 1) (.f64 1/384 (*.f64 (pow.f64 n 4) (pow.f64 K 4))))
(fma.f64 -1/8 (.f64 (.f64 n n) (.f64 K K)) (fma.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)) 1))
(fma.f64 -1/8 (.f64 (.f64 n K) (.f64 n K)) (fma.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)) 1))
(+.f64 1 (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (pow.f64 K 2))) (+.f64 (.f64 -1/46080 (.f64 (pow.f64 n 6) (pow.f64 K 6))) (.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4))))))
(+.f64 1 (fma.f64 -1/8 (.f64 (.f64 n n) (.f64 K K)) (fma.f64 -1/46080 (.f64 (pow.f64 n 6) (pow.f64 K 6)) (.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4))))))
(+.f64 (fma.f64 -1/8 (.f64 n (.f64 n (.f64 K K))) 1) (fma.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)) (.f64 -1/46080 (.f64 (pow.f64 n 6) (pow.f64 K 6)))))
(+.f64 (fma.f64 -1/46080 (.f64 (pow.f64 n 6) (pow.f64 K 6)) (.f64 (.f64 K K) (.f64 -1/8 (.f64 n n)))) (fma.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)) 1))
(+.f64 (fma.f64 -1/46080 (.f64 (pow.f64 n 6) (pow.f64 K 6)) (.f64 -1/8 (.f64 (.f64 n K) (.f64 n K)))) (fma.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)) 1))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
1
(+.f64 1 (.f64 -1/8 (.f64 (pow.f64 n 2) (pow.f64 K 2))))
(+.f64 1 (.f64 -1/8 (.f64 (.f64 n n) (.f64 K K))))
(fma.f64 -1/8 (.f64 n (.f64 n (*.f64 K K))) 1)
(fma.f64 -1/8 (.f64 (.f64 n n) (*.f64 K K)) 1)
(fma.f64 -1/8 (.f64 (.f64 n K) (*.f64 n K)) 1)
(+.f64 1 (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (pow.f64 K 2))) (.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)))))
(+.f64 1 (fma.f64 -1/8 (.f64 (.f64 n n) (.f64 K K)) (.f64 1/384 (*.f64 (pow.f64 n 4) (pow.f64 K 4)))))
(+.f64 (fma.f64 -1/8 (.f64 n (.f64 n (.f64 K K))) 1) (.f64 1/384 (*.f64 (pow.f64 n 4) (pow.f64 K 4))))
(fma.f64 -1/8 (.f64 (.f64 n n) (.f64 K K)) (fma.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)) 1))
(fma.f64 -1/8 (.f64 (.f64 n K) (.f64 n K)) (fma.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)) 1))
(+.f64 1 (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (pow.f64 K 2))) (+.f64 (.f64 -1/46080 (.f64 (pow.f64 n 6) (pow.f64 K 6))) (.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4))))))
(+.f64 1 (fma.f64 -1/8 (.f64 (.f64 n n) (.f64 K K)) (fma.f64 -1/46080 (.f64 (pow.f64 n 6) (pow.f64 K 6)) (.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4))))))
(+.f64 (fma.f64 -1/8 (.f64 n (.f64 n (.f64 K K))) 1) (fma.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)) (.f64 -1/46080 (.f64 (pow.f64 n 6) (pow.f64 K 6)))))
(+.f64 (fma.f64 -1/46080 (.f64 (pow.f64 n 6) (pow.f64 K 6)) (.f64 (.f64 K K) (.f64 -1/8 (.f64 n n)))) (fma.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)) 1))
(+.f64 (fma.f64 -1/46080 (.f64 (pow.f64 n 6) (pow.f64 K 6)) (.f64 -1/8 (.f64 (.f64 n K) (.f64 n K)))) (fma.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)) 1))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(exp.f64 (neg.f64 l))
(+.f64 (exp.f64 (neg.f64 l)) (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (*.f64 (pow.f64 n 2) (pow.f64 K 2)))))
(+.f64 (exp.f64 (neg.f64 l)) (.f64 -1/8 (.f64 (.f64 (.f64 n n) (*.f64 K K)) (exp.f64 (neg.f64 l)))))
(fma.f64 (/.f64 -1/8 (exp.f64 l)) (.f64 n (.f64 n (*.f64 K K))) (exp.f64 (neg.f64 l)))
(.f64 (fma.f64 -1/8 (.f64 (.f64 n n) (.f64 K K)) 1) (exp.f64 (neg.f64 l)))
(.f64 (fma.f64 -1/8 (.f64 (.f64 n K) (.f64 n K)) 1) (exp.f64 (neg.f64 l)))
(/.f64 (fma.f64 -1/8 (.f64 (.f64 n K) (*.f64 n K)) 1) (exp.f64 l))
(+.f64 (exp.f64 (neg.f64 l)) (+.f64 (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 n 2) (pow.f64 K 2)))) (.f64 1/384 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 n 4) (pow.f64 K 4))))))
(+.f64 (exp.f64 (neg.f64 l)) (fma.f64 -1/8 (.f64 (.f64 (.f64 n n) (.f64 K K)) (exp.f64 (neg.f64 l))) (.f64 1/384 (.f64 (*.f64 (pow.f64 n 4) (pow.f64 K 4)) (exp.f64 (neg.f64 l))))))
(+.f64 (exp.f64 (neg.f64 l)) (fma.f64 (/.f64 1/384 (exp.f64 l)) (.f64 (pow.f64 n 4) (pow.f64 K 4)) (.f64 (.f64 n (.f64 n (*.f64 K K))) (/.f64 -1/8 (exp.f64 l)))))
(fma.f64 -1/8 (.f64 K (/.f64 (.f64 (.f64 n n) K) (exp.f64 l))) (.f64 (fma.f64 1/384 (*.f64 (pow.f64 n 4) (pow.f64 K 4)) 1) (exp.f64 (neg.f64 l))))
(.f64 (exp.f64 (neg.f64 l)) (fma.f64 -1/8 (.f64 (.f64 n K) (.f64 n K)) (fma.f64 1/384 (*.f64 (pow.f64 n 4) (pow.f64 K 4)) 1)))
(+.f64 (exp.f64 (neg.f64 l)) (+.f64 (.f64 -1/8 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 n 2) (pow.f64 K 2)))) (+.f64 (.f64 -1/46080 (.f64 (exp.f64 (neg.f64 l)) (.f64 (pow.f64 n 6) (pow.f64 K 6)))) (.f64 1/384 (.f64 (exp.f64 (neg.f64 l)) (*.f64 (pow.f64 n 4) (pow.f64 K 4)))))))
(+.f64 (exp.f64 (neg.f64 l)) (fma.f64 -1/8 (.f64 (.f64 (.f64 n n) (.f64 K K)) (exp.f64 (neg.f64 l))) (fma.f64 -1/46080 (.f64 (.f64 (pow.f64 n 6) (pow.f64 K 6)) (exp.f64 (neg.f64 l))) (.f64 1/384 (.f64 (*.f64 (pow.f64 n 4) (pow.f64 K 4)) (exp.f64 (neg.f64 l)))))))
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(.f64 (exp.f64 (neg.f64 l)) (+.f64 (fma.f64 -1/46080 (.f64 (pow.f64 n 6) (pow.f64 K 6)) (.f64 -1/8 (.f64 (.f64 n K) (.f64 n K)))) (fma.f64 1/384 (*.f64 (pow.f64 n 4) (pow.f64 K 4)) 1)))
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(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
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(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
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(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
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(fma.f64 (/.f64 -1/8 (exp.f64 l)) (.f64 n (.f64 n (*.f64 K K))) (exp.f64 (neg.f64 l)))
(.f64 (fma.f64 -1/8 (.f64 (.f64 n n) (.f64 K K)) 1) (exp.f64 (neg.f64 l)))
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(fma.f64 -1/8 (.f64 K (/.f64 (.f64 (.f64 n n) K) (exp.f64 l))) (.f64 (fma.f64 1/384 (*.f64 (pow.f64 n 4) (pow.f64 K 4)) 1) (exp.f64 (neg.f64 l))))
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(+.f64 (exp.f64 (neg.f64 l)) (fma.f64 -1/8 (.f64 (.f64 (.f64 n n) (.f64 K K)) (exp.f64 (neg.f64 l))) (fma.f64 -1/46080 (.f64 (.f64 (pow.f64 n 6) (pow.f64 K 6)) (exp.f64 (neg.f64 l))) (.f64 1/384 (.f64 (*.f64 (pow.f64 n 4) (pow.f64 K 4)) (exp.f64 (neg.f64 l)))))))
(+.f64 (fma.f64 (/.f64 -1/8 (exp.f64 l)) (.f64 n (.f64 n (.f64 K K))) (exp.f64 (neg.f64 l))) (fma.f64 (/.f64 1/384 (exp.f64 l)) (.f64 (pow.f64 n 4) (pow.f64 K 4)) (.f64 (.f64 (pow.f64 n 6) (pow.f64 K 6)) (/.f64 -1/46080 (exp.f64 l)))))
(+.f64 (.f64 (fma.f64 -1/8 (.f64 (.f64 n n) (.f64 K K)) 1) (exp.f64 (neg.f64 l))) (.f64 (exp.f64 (neg.f64 l)) (fma.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)) (.f64 -1/46080 (.f64 (pow.f64 n 6) (pow.f64 K 6))))))
(+.f64 (exp.f64 (neg.f64 l)) (.f64 (exp.f64 (neg.f64 l)) (fma.f64 -1/8 (.f64 (.f64 n K) (.f64 n K)) (fma.f64 1/384 (.f64 (pow.f64 n 4) (pow.f64 K 4)) (.f64 -1/46080 (*.f64 (pow.f64 n 6) (pow.f64 K 6)))))))
(.f64 (exp.f64 (neg.f64 l)) (+.f64 (fma.f64 -1/46080 (.f64 (pow.f64 n 6) (pow.f64 K 6)) (.f64 -1/8 (.f64 (.f64 n K) (.f64 n K)))) (fma.f64 1/384 (*.f64 (pow.f64 n 4) (pow.f64 K 4)) 1)))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(cos.f64 (.f64 K (.f64 n 1/2)))
(+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (.f64 -1 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) l)))
(+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (neg.f64 (.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) l)))
(-.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) l))
(.f64 (+.f64 (neg.f64 l) 1) (cos.f64 (.f64 n (*.f64 K 1/2))))
(.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (-.f64 1 l))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (-.f64 1 l))
(+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (+.f64 (.f64 -1 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) l)) (.f64 1/2 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (pow.f64 l 2)))))
(+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (fma.f64 -1 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) l) (.f64 1/2 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (.f64 l l)))))
(+.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (-.f64 (.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (.f64 (.f64 l l) 1/2)) (.f64 (cos.f64 (.f64 n (.f64 K 1/2))) l)))
(+.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (-.f64 (.f64 l (*.f64 l 1/2)) l)))
(.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (+.f64 1 (-.f64 (.f64 1/2 (*.f64 l l)) l)))
(.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (+.f64 1 (.f64 l (fma.f64 1/2 l -1))))
(+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (+.f64 (.f64 -1 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) l)) (+.f64 (.f64 -1/6 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (pow.f64 l 3))) (.f64 1/2 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (pow.f64 l 2))))))
(+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (fma.f64 -1 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) l) (fma.f64 -1/6 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (pow.f64 l 3)) (.f64 1/2 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (*.f64 l l))))))
(+.f64 (-.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (.f64 (cos.f64 (.f64 n (.f64 K 1/2))) l)) (fma.f64 1/2 (.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (.f64 l l)) (.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (*.f64 (pow.f64 l 3) -1/6))))
(+.f64 (.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (+.f64 (neg.f64 l) (.f64 -1/6 (pow.f64 l 3)))) (.f64 (+.f64 (.f64 l (.f64 l 1/2)) 1) (cos.f64 (.f64 n (*.f64 K 1/2)))))
(+.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (-.f64 (.f64 (.f64 l l) (+.f64 (.f64 -1/6 l) 1/2)) l)))
(.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (-.f64 1 (-.f64 l (.f64 (.f64 l l) (+.f64 (.f64 -1/6 l) 1/2)))))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
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(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
(.f64 (exp.f64 (neg.f64 l)) (cos.f64 (.f64 1/2 (*.f64 n K))))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
(.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (exp.f64 (.f64 -1 l)))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
(.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (exp.f64 (.f64 -1 l)))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
(.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (exp.f64 (.f64 -1 l)))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))
(.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (exp.f64 (.f64 -1 l)))
(.f64 (cos.f64 (.f64 1/2 (*.f64 n K))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 n (.f64 K 1/2))) (exp.f64 l))
(/.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))

localize28.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 K (.f64 (+.f64 n m) 1/2))
✓	38.9b	(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))

Compiler

Compiled 62 to 35 computations (43.5% saved)

series7.0ms (0%)

Counts

2 → 72

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	K	@	0	(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
1.0ms	n	@	0	(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
1.0ms	m	@	0	(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
0.0ms	K	@	0	(.f64 K (.f64 (+.f64 n m) 1/2))
0.0ms	m	@	-inf	(.f64 K (.f64 (+.f64 n m) 1/2))

rewrite66.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

816×	`prod-diff_binary64`
466×	`log-prod_binary64`
316×	`pow-prod-down_binary64`
254×	`pow2_binary64`
207×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	190	22
2	2487	22

Stop Event

1×	node limit

Counts

2 → 48

Calls

Call 1

Inputs
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(.f64 K (.f64 (+.f64 n m) 1/2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (cos.f64 (exp.f64 (log1p.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))))) (cos.f64 1)) (*.f64 (sin.f64 (exp.f64 (log1p.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))))) (sin.f64 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))) (pow.f64 (cbrt.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))) 2) (cbrt.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))) (sqrt.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (cos.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 K (*.f64 (+.f64 n m) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (+.f64 n m))) K)) 2)) (log.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (+.f64 n m))) K))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (+.f64 n m))) K))) (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (+.f64 n m))) K))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 K (+.f64 n m)) 2) 1/4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 K (+.f64 n m)) 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (sqrt.f64 (exp.f64 (+.f64 n m))) K))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 K (*.f64 (+.f64 n m) 1/2))) 1) 1))))))

simplify93.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

757×	`associate-l_binary64`
746×	`associate-r_binary64`
656×	`distribute-rgt-neg-out_binary64`
563×	`distribute-lft-neg-out_binary64`
412×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	87	1066
1	254	1058
2	778	1018
3	4319	1018

Stop Event

1×	node limit

Counts

120 → 82

Calls

Call 1

Inputs
1
(+.f64 1 (.f64 -1/8 (.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2))))
(+.f64 1 (+.f64 (.f64 1/384 (.f64 (pow.f64 K 4) (pow.f64 (+.f64 n m) 4))) (.f64 -1/8 (.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2)))))
(+.f64 1 (+.f64 (.f64 1/384 (.f64 (pow.f64 K 4) (pow.f64 (+.f64 n m) 4))) (+.f64 (.f64 -1/8 (.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2))) (.f64 -1/46080 (.f64 (pow.f64 K 6) (pow.f64 (+.f64 n m) 6))))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K m)))
(+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (.f64 1/2 (.f64 K m)))))) (cos.f64 (.f64 1/2 (*.f64 K m))))
(+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (.f64 1/2 (.f64 K m)))))) (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (pow.f64 K 2) (cos.f64 (.f64 1/2 (.f64 K m)))))) (cos.f64 (.f64 1/2 (.f64 K m)))))
(+.f64 (.f64 1/48 (.f64 (pow.f64 n 3) (.f64 (pow.f64 K 3) (sin.f64 (.f64 1/2 (.f64 K m)))))) (+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (.f64 1/2 (.f64 K m)))))) (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (pow.f64 K 2) (cos.f64 (.f64 1/2 (.f64 K m)))))) (cos.f64 (.f64 1/2 (*.f64 K m))))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))))
(cos.f64 (.f64 1/2 (.f64 n K)))
(+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (.f64 -1/2 (.f64 (sin.f64 (.f64 1/2 (.f64 n K))) (*.f64 K m))))
(+.f64 (.f64 -1/8 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (.f64 (pow.f64 K 2) (pow.f64 m 2)))) (+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (.f64 -1/2 (.f64 (sin.f64 (.f64 1/2 (.f64 n K))) (.f64 K m)))))
(+.f64 (.f64 -1/8 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (.f64 (pow.f64 K 2) (pow.f64 m 2)))) (+.f64 (.f64 1/48 (.f64 (sin.f64 (.f64 1/2 (.f64 n K))) (.f64 (pow.f64 K 3) (pow.f64 m 3)))) (+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (.f64 -1/2 (.f64 (sin.f64 (.f64 1/2 (.f64 n K))) (*.f64 K m))))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 1/2 (.f64 K m))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 n K))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 n K))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 n K))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K m))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K m))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))

Outputs
1
(+.f64 1 (.f64 -1/8 (.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2))))
(+.f64 1 (.f64 -1/8 (.f64 (*.f64 K K) (pow.f64 (+.f64 n m) 2))))
(fma.f64 -1/8 (.f64 K (.f64 K (pow.f64 (+.f64 n m) 2))) 1)
(fma.f64 -1/8 (.f64 (.f64 K K) (pow.f64 (+.f64 n m) 2)) 1)
(+.f64 1 (+.f64 (.f64 1/384 (.f64 (pow.f64 K 4) (pow.f64 (+.f64 n m) 4))) (.f64 -1/8 (.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2)))))
(+.f64 1 (fma.f64 1/384 (.f64 (pow.f64 K 4) (pow.f64 (+.f64 n m) 4)) (.f64 -1/8 (.f64 (.f64 K K) (pow.f64 (+.f64 n m) 2)))))
(+.f64 1 (fma.f64 -1/8 (.f64 K (.f64 K (pow.f64 (+.f64 n m) 2))) (.f64 1/384 (.f64 (pow.f64 K 4) (pow.f64 (+.f64 n m) 4)))))
(fma.f64 -1/8 (.f64 (.f64 K K) (pow.f64 (+.f64 n m) 2)) (fma.f64 1/384 (*.f64 (pow.f64 K 4) (pow.f64 (+.f64 n m) 4)) 1))
(+.f64 1 (+.f64 (.f64 1/384 (.f64 (pow.f64 K 4) (pow.f64 (+.f64 n m) 4))) (+.f64 (.f64 -1/8 (.f64 (pow.f64 K 2) (pow.f64 (+.f64 n m) 2))) (.f64 -1/46080 (.f64 (pow.f64 K 6) (pow.f64 (+.f64 n m) 6))))))
(+.f64 1 (fma.f64 1/384 (.f64 (pow.f64 K 4) (pow.f64 (+.f64 n m) 4)) (fma.f64 -1/8 (.f64 (.f64 K K) (pow.f64 (+.f64 n m) 2)) (.f64 -1/46080 (*.f64 (pow.f64 K 6) (pow.f64 (+.f64 n m) 6))))))
(+.f64 1 (fma.f64 1/384 (.f64 (pow.f64 K 4) (pow.f64 (+.f64 n m) 4)) (fma.f64 -1/8 (.f64 K (.f64 K (pow.f64 (+.f64 n m) 2))) (.f64 -1/46080 (*.f64 (pow.f64 K 6) (pow.f64 (+.f64 n m) 6))))))
(+.f64 1 (fma.f64 -1/8 (.f64 (.f64 K K) (pow.f64 (+.f64 n m) 2)) (fma.f64 1/384 (.f64 (pow.f64 K 4) (pow.f64 (+.f64 n m) 4)) (.f64 -1/46080 (*.f64 (pow.f64 K 6) (pow.f64 (+.f64 n m) 6))))))
(+.f64 1 (fma.f64 (pow.f64 (+.f64 n m) 2) (.f64 -1/8 (.f64 K K)) (fma.f64 1/384 (.f64 (pow.f64 K 4) (pow.f64 (+.f64 n m) 4)) (.f64 (pow.f64 (+.f64 n m) 6) (*.f64 -1/46080 (pow.f64 K 6))))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K m)))
(cos.f64 (.f64 K (.f64 m 1/2)))
(+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (.f64 1/2 (.f64 K m)))))) (cos.f64 (.f64 1/2 (*.f64 K m))))
(fma.f64 -1/2 (.f64 (.f64 K n) (sin.f64 (.f64 1/2 (.f64 K m)))) (cos.f64 (.f64 1/2 (.f64 K m))))
(fma.f64 -1/2 (.f64 K (.f64 (sin.f64 (.f64 K (.f64 m 1/2))) n)) (cos.f64 (.f64 K (.f64 m 1/2))))
(fma.f64 (.f64 K (.f64 n -1/2)) (sin.f64 (.f64 K (.f64 m 1/2))) (cos.f64 (.f64 K (.f64 m 1/2))))
(fma.f64 -1/2 (.f64 K (.f64 n (sin.f64 (.f64 K (.f64 m 1/2))))) (cos.f64 (.f64 K (.f64 m 1/2))))
(+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (.f64 1/2 (.f64 K m)))))) (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (pow.f64 K 2) (cos.f64 (.f64 1/2 (.f64 K m)))))) (cos.f64 (.f64 1/2 (.f64 K m)))))
(fma.f64 -1/2 (.f64 (.f64 K n) (sin.f64 (.f64 1/2 (.f64 K m)))) (fma.f64 -1/8 (.f64 (.f64 (.f64 n n) (.f64 K K)) (cos.f64 (.f64 1/2 (.f64 K m)))) (cos.f64 (.f64 1/2 (.f64 K m)))))
(fma.f64 -1/2 (.f64 K (.f64 (sin.f64 (.f64 K (.f64 m 1/2))) n)) (fma.f64 -1/8 (.f64 n (.f64 n (.f64 (.f64 K K) (cos.f64 (.f64 K (.f64 m 1/2)))))) (cos.f64 (.f64 K (.f64 m 1/2)))))
(fma.f64 (.f64 K (.f64 n -1/2)) (sin.f64 (.f64 K (.f64 m 1/2))) (.f64 (+.f64 (.f64 (.f64 -1/8 (.f64 K n)) (.f64 K n)) 1) (cos.f64 (.f64 K (*.f64 m 1/2)))))
(fma.f64 -1/2 (.f64 K (.f64 n (sin.f64 (.f64 K (.f64 m 1/2))))) (.f64 (+.f64 (.f64 (.f64 n n) (.f64 -1/8 (.f64 K K))) 1) (cos.f64 (.f64 K (*.f64 m 1/2)))))
(+.f64 (.f64 1/48 (.f64 (pow.f64 n 3) (.f64 (pow.f64 K 3) (sin.f64 (.f64 1/2 (.f64 K m)))))) (+.f64 (.f64 -1/2 (.f64 n (.f64 K (sin.f64 (.f64 1/2 (.f64 K m)))))) (+.f64 (.f64 -1/8 (.f64 (pow.f64 n 2) (.f64 (pow.f64 K 2) (cos.f64 (.f64 1/2 (.f64 K m)))))) (cos.f64 (.f64 1/2 (*.f64 K m))))))
(fma.f64 1/48 (.f64 (.f64 (pow.f64 n 3) (pow.f64 K 3)) (sin.f64 (.f64 1/2 (.f64 K m)))) (fma.f64 -1/2 (.f64 (.f64 K n) (sin.f64 (.f64 1/2 (.f64 K m)))) (fma.f64 -1/8 (.f64 (.f64 (.f64 n n) (.f64 K K)) (cos.f64 (.f64 1/2 (.f64 K m)))) (cos.f64 (.f64 1/2 (.f64 K m))))))
(fma.f64 1/48 (.f64 (sin.f64 (.f64 K (.f64 m 1/2))) (.f64 (pow.f64 n 3) (pow.f64 K 3))) (fma.f64 -1/2 (.f64 K (.f64 (sin.f64 (.f64 K (.f64 m 1/2))) n)) (fma.f64 -1/8 (.f64 n (.f64 n (.f64 (.f64 K K) (cos.f64 (.f64 K (.f64 m 1/2)))))) (cos.f64 (.f64 K (.f64 m 1/2))))))
(+.f64 (.f64 (+.f64 (.f64 (.f64 -1/8 (.f64 K n)) (.f64 K n)) 1) (cos.f64 (.f64 K (.f64 m 1/2)))) (.f64 (sin.f64 (.f64 K (.f64 m 1/2))) (+.f64 (.f64 1/48 (.f64 (pow.f64 n 3) (pow.f64 K 3))) (.f64 K (.f64 n -1/2)))))
(+.f64 (.f64 (+.f64 (.f64 (.f64 n n) (.f64 -1/8 (.f64 K K))) 1) (cos.f64 (.f64 K (.f64 m 1/2)))) (.f64 (sin.f64 (.f64 K (.f64 m 1/2))) (+.f64 (.f64 1/48 (.f64 (pow.f64 n 3) (pow.f64 K 3))) (.f64 K (.f64 n -1/2)))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 m (*.f64 -1 n)))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 n K)))
(cos.f64 (.f64 (.f64 1/2 n) K))
(cos.f64 (.f64 K (.f64 n 1/2)))
(cos.f64 (.f64 n (.f64 K 1/2)))
(+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (.f64 -1/2 (.f64 (sin.f64 (.f64 1/2 (.f64 n K))) (*.f64 K m))))
(+.f64 (cos.f64 (.f64 (.f64 1/2 n) K)) (.f64 -1/2 (.f64 (.f64 K m) (sin.f64 (.f64 (*.f64 1/2 n) K)))))
(fma.f64 -1/2 (.f64 (.f64 K m) (sin.f64 (.f64 K (.f64 n 1/2)))) (cos.f64 (.f64 K (.f64 n 1/2))))
(fma.f64 (.f64 K m) (.f64 -1/2 (sin.f64 (.f64 n (.f64 K 1/2)))) (cos.f64 (.f64 n (.f64 K 1/2))))
(+.f64 (.f64 -1/8 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (.f64 (pow.f64 K 2) (pow.f64 m 2)))) (+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (.f64 -1/2 (.f64 (sin.f64 (.f64 1/2 (.f64 n K))) (.f64 K m)))))
(fma.f64 -1/8 (.f64 (cos.f64 (.f64 (.f64 1/2 n) K)) (.f64 (.f64 K K) (.f64 m m))) (+.f64 (cos.f64 (.f64 (.f64 1/2 n) K)) (.f64 -1/2 (.f64 (.f64 K m) (sin.f64 (.f64 (*.f64 1/2 n) K))))))
(fma.f64 -1/8 (.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (.f64 K (.f64 K (.f64 m m)))) (fma.f64 -1/2 (.f64 (.f64 K m) (sin.f64 (.f64 K (.f64 n 1/2)))) (cos.f64 (.f64 K (.f64 n 1/2)))))
(fma.f64 (.f64 K m) (.f64 -1/2 (sin.f64 (.f64 n (.f64 K 1/2)))) (.f64 (+.f64 (.f64 m (.f64 (.f64 K (.f64 K m)) -1/8)) 1) (cos.f64 (.f64 n (*.f64 K 1/2)))))
(fma.f64 (.f64 K m) (.f64 -1/2 (sin.f64 (.f64 n (.f64 K 1/2)))) (.f64 (+.f64 (.f64 (.f64 K K) (.f64 m (.f64 m -1/8))) 1) (cos.f64 (.f64 n (*.f64 K 1/2)))))
(+.f64 (.f64 -1/8 (.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (.f64 (pow.f64 K 2) (pow.f64 m 2)))) (+.f64 (.f64 1/48 (.f64 (sin.f64 (.f64 1/2 (.f64 n K))) (.f64 (pow.f64 K 3) (pow.f64 m 3)))) (+.f64 (cos.f64 (.f64 1/2 (.f64 n K))) (.f64 -1/2 (.f64 (sin.f64 (.f64 1/2 (.f64 n K))) (*.f64 K m))))))
(fma.f64 -1/8 (.f64 (cos.f64 (.f64 (.f64 1/2 n) K)) (.f64 (.f64 K K) (.f64 m m))) (fma.f64 1/48 (.f64 (sin.f64 (.f64 (.f64 1/2 n) K)) (.f64 (pow.f64 K 3) (pow.f64 m 3))) (+.f64 (cos.f64 (.f64 (.f64 1/2 n) K)) (.f64 -1/2 (.f64 (.f64 K m) (sin.f64 (.f64 (*.f64 1/2 n) K)))))))
(fma.f64 -1/8 (.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (.f64 K (.f64 K (.f64 m m)))) (fma.f64 1/48 (.f64 (pow.f64 K 3) (.f64 (pow.f64 m 3) (sin.f64 (.f64 K (.f64 n 1/2))))) (fma.f64 -1/2 (.f64 (.f64 K m) (sin.f64 (.f64 K (.f64 n 1/2)))) (cos.f64 (.f64 K (.f64 n 1/2))))))
(+.f64 (.f64 (+.f64 (.f64 m (.f64 (.f64 K (.f64 K m)) -1/8)) 1) (cos.f64 (.f64 n (.f64 K 1/2)))) (.f64 (sin.f64 (.f64 n (.f64 K 1/2))) (+.f64 (.f64 (pow.f64 K 3) (.f64 1/48 (pow.f64 m 3))) (.f64 K (.f64 m -1/2)))))
(+.f64 (.f64 (+.f64 (.f64 (.f64 K K) (.f64 m (.f64 m -1/8))) 1) (cos.f64 (.f64 n (.f64 K 1/2)))) (.f64 (sin.f64 (.f64 n (.f64 K 1/2))) (+.f64 (.f64 1/48 (.f64 (pow.f64 K 3) (pow.f64 m 3))) (.f64 K (.f64 m -1/2)))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(cos.f64 (.f64 1/2 (.f64 K (-.f64 n (*.f64 -1 m)))))
(cos.f64 (.f64 1/2 (.f64 K (+.f64 n m))))
(cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2)))
(cos.f64 (.f64 (+.f64 n m) (.f64 K 1/2)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 K m))
(.f64 K (.f64 m 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 n K))
(.f64 (.f64 1/2 n) K)
(.f64 K (.f64 n 1/2))
(.f64 n (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 n K))
(.f64 (.f64 1/2 n) K)
(.f64 K (.f64 n 1/2))
(.f64 n (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 n K))
(.f64 (.f64 1/2 n) K)
(.f64 K (.f64 n 1/2))
(.f64 n (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 K m))
(.f64 K (.f64 m 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(.f64 1/2 (.f64 K m))
(.f64 K (.f64 m 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))
(+.f64 (.f64 1/2 (.f64 K m)) (.f64 1/2 (.f64 n K)))
(.f64 1/2 (.f64 K (+.f64 n m)))
(.f64 K (.f64 (+.f64 n m) 1/2))
(.f64 (+.f64 n m) (.f64 K 1/2))

eval372.0ms (2.5%)

Compiler: Compiled 13164 to 7346 computations (44.2% saved)

prune145.0ms (1%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	644	8	652
Fresh	4	11	15
Picked	0	1	1
Done	4	0	4
Total	652	20	672

Error

0.4b

Counts

672 → 20

Alt Table

Click to see full alt table

Status	Error	Program
	47.8b	(/.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 l))
	30.8b	(*.f64 (cos.f64 M) (exp.f64 m))
	50.1b	(-.f64 (+.f64 1 (.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 l))) 1)
	44.0b	(exp.f64 (neg.f64 l))
	43.6b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (expm1.f64 (log1p.f64 (.f64 (-.f64 (.f64 m m) (.f64 n n)) K))) (-.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
✓	37.2b	(.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 (.f64 m (*.f64 m -1/4))))
	27.1b	(.f64 1 (exp.f64 (.f64 m (*.f64 m -1/4))))
	60.9b	(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (-.f64 1 l))
	60.9b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
	15.9b	(.f64 (cos.f64 (.f64 K (.f64 m 1/2))) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
	27.3b	(.f64 (cos.f64 M) (exp.f64 (.f64 n (*.f64 n -1/4))))
	26.7b	(.f64 (cos.f64 M) (exp.f64 (.f64 -1 (pow.f64 M 2))))
	44.0b	(/.f64 (cos.f64 M) (exp.f64 l))
	47.8b	(.f64 (cos.f64 (-.f64 (/.f64 (+.f64 (.f64 n K) (*.f64 K m)) 2) M)) (exp.f64 (neg.f64 l)))
	22.6b	(.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
	60.5b	(cos.f64 M)
	46.5b	(.f64 (cos.f64 (.f64 K (*.f64 m 1/2))) (exp.f64 (neg.f64 l)))
	60.8b	(cos.f64 (.f64 n (.f64 K 1/2)))
	54.1b	(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (.f64 n n)) K) (-.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
	60.8b	(cos.f64 (fma.f64 (*.f64 n 1/2) K (neg.f64 M)))

Compiler

Compiled 341 to 256 computations (24.9% saved)

regimes172.0ms (1.2%)

Counts

43 → 1

Calls

Call 1

Inputs
(cos.f64 M)
(exp.f64 (neg.f64 l))
(cos.f64 (.f64 n (.f64 K 1/2)))
(.f64 1 (exp.f64 (.f64 m (*.f64 m -1/4))))
(cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (-.f64 1 l))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(*.f64 (cos.f64 M) (exp.f64 m))
(/.f64 (cos.f64 M) (exp.f64 l))
(*.f64 (cos.f64 M) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 M) (exp.f64 (.f64 M M)))
(cos.f64 (fma.f64 (*.f64 n 1/2) K (neg.f64 M)))
(.f64 (cos.f64 M) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 M) (exp.f64 (.f64 n (*.f64 n -1/4))))
(.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 K (*.f64 m 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 l))
(-.f64 (+.f64 1 (.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 l))) 1)
(.f64 (cos.f64 (.f64 K (.f64 m 1/2))) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
(.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (*.f64 M M)))
(.f64 (cos.f64 (-.f64 (/.f64 (+.f64 (.f64 n K) (*.f64 K m)) 2) M)) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (.f64 n (.f64 n -1/4))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (.f64 m (.f64 m -1/4))))
(.f64 (cos.f64 (.f64 K (.f64 m 1/2))) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
(.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (.f64 n n)) K) (-.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (+.f64 (-.f64 (.f64 n (.f64 n -1/4)) l) (-.f64 m n))))
(.f64 (cos.f64 M) (exp.f64 (.f64 -1 (pow.f64 M 2))))
(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 m (*.f64 m 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 n (*.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (*.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 n (.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 m (.f64 m 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (.f64 n n)) K) (-.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (*.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (.f64 n n)) K) (-.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (expm1.f64 (log1p.f64 (.f64 (-.f64 (.f64 m m) (.f64 n n)) K))) (-.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Outputs
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Calls

6 calls:

54.0ms	M
26.0ms	l
23.0ms	K
22.0ms	m
22.0ms	n

Results

Error	Segments	Branch
0.4b	1	`K`
0.4b	1	`m`
0.4b	1	`n`
0.4b	1	`M`
0.4b	1	`l`
0.4b	1	`(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))`

Compiler

Compiled 717 to 356 computations (50.3% saved)

regimes505.0ms (3.4%)

Counts

39 → 3

Calls

Call 1

Inputs
(cos.f64 M)
(exp.f64 (neg.f64 l))
(cos.f64 (.f64 n (.f64 K 1/2)))
(.f64 1 (exp.f64 (.f64 m (*.f64 m -1/4))))
(cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (-.f64 1 l))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(*.f64 (cos.f64 M) (exp.f64 m))
(/.f64 (cos.f64 M) (exp.f64 l))
(*.f64 (cos.f64 M) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 M) (exp.f64 (.f64 M M)))
(cos.f64 (fma.f64 (*.f64 n 1/2) K (neg.f64 M)))
(.f64 (cos.f64 M) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 M) (exp.f64 (.f64 n (*.f64 n -1/4))))
(.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 K (*.f64 m 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 l))
(-.f64 (+.f64 1 (.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 l))) 1)
(.f64 (cos.f64 (.f64 K (.f64 m 1/2))) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
(.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (*.f64 M M)))
(.f64 (cos.f64 (-.f64 (/.f64 (+.f64 (.f64 n K) (*.f64 K m)) 2) M)) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (.f64 n (.f64 n -1/4))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (.f64 m (.f64 m -1/4))))
(.f64 (cos.f64 (.f64 K (.f64 m 1/2))) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
(.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (.f64 n n)) K) (-.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (+.f64 (-.f64 (.f64 n (.f64 n -1/4)) l) (-.f64 m n))))
(.f64 (cos.f64 M) (exp.f64 (.f64 -1 (pow.f64 M 2))))
(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 m (*.f64 m 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (.f64 n (*.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (*.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 n (.f64 n 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (.f64 m (.f64 m 1/4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (.f64 n n)) K) (-.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (*.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Outputs
(.f64 (cos.f64 M) (exp.f64 (.f64 -1 (pow.f64 M 2))))
(.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
(.f64 (cos.f64 M) (exp.f64 (.f64 -1 (pow.f64 M 2))))

Calls

5 calls:

248.0ms	m
73.0ms	n
68.0ms	M
64.0ms	l
34.0ms	K

Results

Error	Segments	Branch
7.9b	1	`K`
4.2b	8	`m`
4.9b	3	`n`
1.3b	3	`M`
5.4b	2	`l`

Compiler

Compiled 557 to 282 computations (49.4% saved)

bsearch194.0ms (1.3%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
106.0ms	7.0507269020970345	11301106829.095045
87.0ms	-7599445881238.19	-861339521277.0963

Compiler

Compiled 42 to 30 computations (28.6% saved)

regimes438.0ms (3%)

Counts

31 → 2

Calls

Call 1

Inputs
(cos.f64 M)
(exp.f64 (neg.f64 l))
(cos.f64 (.f64 n (.f64 K 1/2)))
(.f64 1 (exp.f64 (.f64 m (*.f64 m -1/4))))
(cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (-.f64 1 l))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(*.f64 (cos.f64 M) (exp.f64 m))
(/.f64 (cos.f64 M) (exp.f64 l))
(*.f64 (cos.f64 M) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 M) (exp.f64 (.f64 M M)))
(cos.f64 (fma.f64 (*.f64 n 1/2) K (neg.f64 M)))
(.f64 (cos.f64 M) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 M) (exp.f64 (.f64 n (*.f64 n -1/4))))
(.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 K (*.f64 m 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 l))
(-.f64 (+.f64 1 (.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 l))) 1)
(.f64 (cos.f64 (.f64 K (.f64 m 1/2))) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
(.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (*.f64 M M)))
(.f64 (cos.f64 (-.f64 (/.f64 (+.f64 (.f64 n K) (*.f64 K m)) 2) M)) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (.f64 n (.f64 n -1/4))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (.f64 m (.f64 m -1/4))))
(.f64 (cos.f64 (.f64 K (.f64 m 1/2))) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
(.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))
(.f64 (cos.f64 (-.f64 (/.f64 (/.f64 (.f64 (-.f64 (.f64 m m) (.f64 n n)) K) (-.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (+.f64 (-.f64 (.f64 n (.f64 n -1/4)) l) (-.f64 m n))))

Outputs
(-.f64 (+.f64 1 (.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 l))) 1)
(.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (*.f64 n -1/4)) l) (-.f64 m n))))

Calls

5 calls:

148.0ms	m
113.0ms	l
64.0ms	K
62.0ms	n
30.0ms	M

Results

Error	Segments	Branch
7.9b	1	`K`
6.9b	3	`m`
7.9b	1	`n`
7.9b	1	`M`
5.4b	2	`l`

Compiler

Compiled 395 to 224 computations (43.3% saved)

bsearch229.0ms (1.6%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
228.0ms	-5.723102923924859e+144	-5.088265253094056e+143

Compiler

Compiled 282 to 216 computations (23.4% saved)

regimes454.0ms (3.1%)

Counts

21 → 4

Calls

Call 1

Inputs
(cos.f64 M)
(exp.f64 (neg.f64 l))
(cos.f64 (.f64 n (.f64 K 1/2)))
(.f64 1 (exp.f64 (.f64 m (*.f64 m -1/4))))
(cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (-.f64 1 l))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(*.f64 (cos.f64 M) (exp.f64 m))
(/.f64 (cos.f64 M) (exp.f64 l))
(*.f64 (cos.f64 M) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 M) (exp.f64 (.f64 M M)))
(cos.f64 (fma.f64 (*.f64 n 1/2) K (neg.f64 M)))
(.f64 (cos.f64 M) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 M) (exp.f64 (.f64 n (*.f64 n -1/4))))
(.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 (.f64 K (*.f64 m 1/2))) (exp.f64 (neg.f64 l)))
(/.f64 (cos.f64 (.f64 K (.f64 (+.f64 n m) 1/2))) (exp.f64 l))
(-.f64 (+.f64 1 (.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 l))) 1)
(.f64 (cos.f64 (.f64 K (.f64 m 1/2))) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (neg.f64 l)))

Outputs
(*.f64 (cos.f64 M) (exp.f64 m))
(.f64 (cos.f64 M) (exp.f64 (.f64 n (*.f64 n -1/4))))
(.f64 (cos.f64 (.f64 K (*.f64 m 1/2))) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 M) (exp.f64 (.f64 n (*.f64 n -1/4))))

Calls

5 calls:

130.0ms	K
106.0ms	M
101.0ms	m
53.0ms	l
24.0ms	n

Results

Error	Segments	Branch
19.8b	9	`K`
9.6b	4	`m`
11.1b	2	`n`
23.4b	2	`M`
12.0b	5	`l`

Compiler

Compiled 215 to 133 computations (38.1% saved)

bsearch339.0ms (2.3%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
118.0ms	-4.348512960935783e-181	-3.748176916662608e-186
120.0ms	-6.779532853565901e-115	-1.74499931418211e-116
100.0ms	-0.007492285880615575	-3.718215911661265e-5

Compiler

Compiled 42 to 30 computations (28.6% saved)

regimes463.0ms (3.2%)

Counts

15 → 4

Calls

Call 1

Inputs
(cos.f64 M)
(exp.f64 (neg.f64 l))
(cos.f64 (.f64 n (.f64 K 1/2)))
(.f64 1 (exp.f64 (.f64 m (*.f64 m -1/4))))
(cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (-.f64 1 l))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(*.f64 (cos.f64 M) (exp.f64 m))
(/.f64 (cos.f64 M) (exp.f64 l))
(*.f64 (cos.f64 M) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 M) (exp.f64 (.f64 M M)))
(cos.f64 (fma.f64 (*.f64 n 1/2) K (neg.f64 M)))
(.f64 (cos.f64 M) (exp.f64 (.f64 m (*.f64 m -1/4))))
(.f64 (cos.f64 M) (exp.f64 (.f64 n (*.f64 n -1/4))))
(.f64 (cos.f64 (.f64 K (*.f64 n 1/2))) (exp.f64 (neg.f64 l)))

Outputs
(*.f64 (cos.f64 M) (exp.f64 m))
(.f64 (cos.f64 M) (exp.f64 (.f64 n (*.f64 n -1/4))))
(/.f64 (cos.f64 M) (exp.f64 l))
(.f64 (cos.f64 M) (exp.f64 (.f64 n (*.f64 n -1/4))))

Calls

5 calls:

136.0ms	K
109.0ms	l
107.0ms	m
63.0ms	n
40.0ms	M

Results

Error	Segments	Branch
19.8b	9	`K`
9.6b	4	`m`
11.1b	2	`n`
23.4b	2	`M`
15.1b	5	`l`

Compiler

Compiled 141 to 89 computations (36.9% saved)

bsearch171.0ms (1.2%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
48.0ms	-4.348512960935783e-181	-3.748176916662608e-186
50.0ms	-6.779532853565901e-115	-1.74499931418211e-116
72.0ms	-0.007492285880615575	-3.718215911661265e-5

Compiler

Compiled 42 to 30 computations (28.6% saved)

regimes95.0ms (0.6%)

Counts

13 → 2

Calls

Call 1

Inputs
(cos.f64 M)
(exp.f64 (neg.f64 l))
(cos.f64 (.f64 n (.f64 K 1/2)))
(.f64 1 (exp.f64 (.f64 m (*.f64 m -1/4))))
(cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (-.f64 1 l))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(*.f64 (cos.f64 M) (exp.f64 m))
(/.f64 (cos.f64 M) (exp.f64 l))
(*.f64 (cos.f64 M) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 M) (exp.f64 (.f64 M M)))
(cos.f64 (fma.f64 (*.f64 n 1/2) K (neg.f64 M)))
(.f64 (cos.f64 M) (exp.f64 (.f64 m (*.f64 m -1/4))))

Outputs
(.f64 (cos.f64 M) (exp.f64 (.f64 m (*.f64 m -1/4))))
(*.f64 (cos.f64 M) (exp.f64 (neg.f64 l)))

Calls

5 calls:

23.0ms	m
21.0ms	K
18.0ms	l
10.0ms	n
8.0ms	M

Results

Error	Segments	Branch
27.0b	1	`K`
19.0b	3	`m`
27.0b	1	`n`
27.0b	1	`M`
18.9b	2	`l`

Compiler

Compiled 122 to 79 computations (35.2% saved)

bsearch50.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
50.0ms	2.976733590249039e-15	9.350955154486548e-12

Compiler

Compiled 42 to 30 computations (28.6% saved)

regimes69.0ms (0.5%)

Counts

12 → 2

Calls

Call 1

Inputs
(cos.f64 M)
(exp.f64 (neg.f64 l))
(cos.f64 (.f64 n (.f64 K 1/2)))
(.f64 1 (exp.f64 (.f64 m (*.f64 m -1/4))))
(cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (-.f64 1 l))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(*.f64 (cos.f64 M) (exp.f64 m))
(/.f64 (cos.f64 M) (exp.f64 l))
(*.f64 (cos.f64 M) (exp.f64 (neg.f64 l)))
(.f64 (cos.f64 M) (exp.f64 (.f64 M M)))
(cos.f64 (fma.f64 (*.f64 n 1/2) K (neg.f64 M)))

Outputs
(.f64 1 (exp.f64 (.f64 m (*.f64 m -1/4))))
(*.f64 (cos.f64 M) (exp.f64 (neg.f64 l)))

Calls

5 calls:

26.0ms	m
15.0ms	l
8.0ms	M
8.0ms	n
8.0ms	K

Results

Error	Segments	Branch
27.1b	1	`K`
19.0b	3	`m`
27.1b	1	`n`
27.1b	1	`M`
18.9b	2	`l`

Compiler

Compiled 113 to 74 computations (34.5% saved)

bsearch46.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
46.0ms	2.976733590249039e-15	9.350955154486548e-12

Compiler

Compiled 42 to 30 computations (28.6% saved)

regimes95.0ms (0.6%)

Counts

9 → 2

Calls

Call 1

Inputs
(cos.f64 M)
(exp.f64 (neg.f64 l))
(cos.f64 (.f64 n (.f64 K 1/2)))
(.f64 1 (exp.f64 (.f64 m (*.f64 m -1/4))))
(cos.f64 (-.f64 (.f64 K (.f64 n 1/2)) M))
(.f64 (cos.f64 (.f64 n (*.f64 K 1/2))) (-.f64 1 l))
(cos.f64 (-.f64 (.f64 1/2 (.f64 K (+.f64 n m))) M))
(*.f64 (cos.f64 M) (exp.f64 m))
(/.f64 (cos.f64 M) (exp.f64 l))

Outputs
(.f64 1 (exp.f64 (.f64 m (*.f64 m -1/4))))
(exp.f64 (neg.f64 l))

Calls

5 calls:

54.0ms	l
17.0ms	m
8.0ms	n
7.0ms	M
6.0ms	K

Results

Error	Segments	Branch
27.1b	1	`K`
19.0b	3	`m`
27.1b	1	`n`
27.1b	1	`M`
18.9b	2	`l`

Compiler

Compiled 92 to 65 computations (29.3% saved)

bsearch114.0ms (0.8%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
114.0ms	2.976733590249039e-15	9.350955154486548e-12

Compiler

Compiled 42 to 30 computations (28.6% saved)

regimes23.0ms (0.2%)

Accuracy

Total -17.1b remaining (-38.9%)

Threshold costs -17.1b (-38.9%)

Counts

3 → 1

Calls

Call 1

Inputs
(cos.f64 M)
(exp.f64 (neg.f64 l))
(cos.f64 (.f64 n (.f64 K 1/2)))

Outputs
(exp.f64 (neg.f64 l))

Calls

5 calls:

5.0ms	M
4.0ms	m
4.0ms	K
4.0ms	l
4.0ms	n

Results

Error	Segments	Branch
44.0b	1	`K`
44.0b	1	`m`
44.0b	1	`n`
44.0b	1	`M`
44.0b	1	`l`

Compiler

Compiled 46 to 37 computations (19.6% saved)

simplify23.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

27×	`*-commutative_binary64`
20×	`+-commutative_binary64`
17×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	358
1	128	358
2	153	358
3	179	356
4	200	356
5	207	356

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(if (<=.f64 M -7781832582387907/1024) (.f64 (cos.f64 M) (exp.f64 (.f64 -1 (pow.f64 M 2)))) (if (<=.f64 M 3969206381121917/562949953421312) (.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (.f64 n -1/4)) l) (-.f64 m n)))) (.f64 (cos.f64 M) (exp.f64 (*.f64 -1 (pow.f64 M 2))))))
(if (<=.f64 l -519999999999999977689253649988389041122324820682368444530738351910816273730855940052686019102043024947579827647852134142022437830798194556010496) (-.f64 (+.f64 1 (.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))) 1) (.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (.f64 n -1/4)) l) (-.f64 m n)))))
(if (<=.f64 m -1079752188802993/144115188075855872) (.f64 (cos.f64 M) (exp.f64 m)) (if (<=.f64 m -7518962113351433/11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296) (.f64 (cos.f64 M) (exp.f64 (.f64 n (.f64 n -1/4)))) (if (<=.f64 m -4063197626210299/9343878384890255807777119448474196633381331982845050737826186276657715542443371287564109437577976626746659450006721346172290467269376897020421450382791094657540085093089822617769726345721044533248) (.f64 (cos.f64 (.f64 K (.f64 m 1/2))) (exp.f64 (neg.f64 l))) (.f64 (cos.f64 M) (exp.f64 (.f64 n (.f64 n -1/4)))))))
(if (<=.f64 m -1079752188802993/144115188075855872) (.f64 (cos.f64 M) (exp.f64 m)) (if (<=.f64 m -7518962113351433/11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296) (.f64 (cos.f64 M) (exp.f64 (.f64 n (.f64 n -1/4)))) (if (<=.f64 m -4063197626210299/9343878384890255807777119448474196633381331982845050737826186276657715542443371287564109437577976626746659450006721346172290467269376897020421450382791094657540085093089822617769726345721044533248) (/.f64 (cos.f64 M) (exp.f64 l)) (.f64 (cos.f64 M) (exp.f64 (.f64 n (*.f64 n -1/4)))))))
(if (<=.f64 l 7546916244797453/2535301200456458802993406410752) (.f64 (cos.f64 M) (exp.f64 (.f64 m (.f64 m -1/4)))) (.f64 (cos.f64 M) (exp.f64 (neg.f64 l))))
(if (<=.f64 l 7546916244797453/2535301200456458802993406410752) (.f64 1 (exp.f64 (.f64 m (.f64 m -1/4)))) (.f64 (cos.f64 M) (exp.f64 (neg.f64 l))))
(if (<=.f64 l 7546916244797453/2535301200456458802993406410752) (.f64 1 (exp.f64 (.f64 m (*.f64 m -1/4)))) (exp.f64 (neg.f64 l)))
(exp.f64 (neg.f64 l))
(cos.f64 M)

Outputs
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
(*.f64 (cos.f64 M) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2))))
(if (<=.f64 M -7781832582387907/1024) (.f64 (cos.f64 M) (exp.f64 (.f64 -1 (pow.f64 M 2)))) (if (<=.f64 M 3969206381121917/562949953421312) (.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (.f64 n -1/4)) l) (-.f64 m n)))) (.f64 (cos.f64 M) (exp.f64 (*.f64 -1 (pow.f64 M 2))))))
(if (<=.f64 M -7781832582387907/1024) (.f64 (cos.f64 M) (exp.f64 (neg.f64 (pow.f64 M 2)))) (if (<=.f64 M 3969206381121917/562949953421312) (.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 n (.f64 n -1/4)) l)))) (*.f64 (cos.f64 M) (exp.f64 (neg.f64 (pow.f64 M 2))))))
(if (<=.f64 l -519999999999999977689253649988389041122324820682368444530738351910816273730855940052686019102043024947579827647852134142022437830798194556010496) (-.f64 (+.f64 1 (.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))) 1) (.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 (.f64 n (.f64 n -1/4)) l) (-.f64 m n)))))
(if (<=.f64 l -519999999999999977689253649988389041122324820682368444530738351910816273730855940052686019102043024947579827647852134142022437830798194556010496) (+.f64 (+.f64 1 (.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l))) -1) (.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 n (.f64 n -1/4)) l)))))
(if (<=.f64 l -519999999999999977689253649988389041122324820682368444530738351910816273730855940052686019102043024947579827647852134142022437830798194556010496) (+.f64 -1 (+.f64 1 (.f64 (cos.f64 (.f64 K (.f64 n 1/2))) (exp.f64 l)))) (.f64 (cos.f64 M) (exp.f64 (+.f64 (-.f64 m n) (-.f64 (.f64 n (.f64 n -1/4)) l)))))
(if (<=.f64 m -1079752188802993/144115188075855872) (.f64 (cos.f64 M) (exp.f64 m)) (if (<=.f64 m -7518962113351433/11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296) (.f64 (cos.f64 M) (exp.f64 (.f64 n (.f64 n -1/4)))) (if (<=.f64 m -4063197626210299/9343878384890255807777119448474196633381331982845050737826186276657715542443371287564109437577976626746659450006721346172290467269376897020421450382791094657540085093089822617769726345721044533248) (.f64 (cos.f64 (.f64 K (.f64 m 1/2))) (exp.f64 (neg.f64 l))) (.f64 (cos.f64 M) (exp.f64 (.f64 n (.f64 n -1/4)))))))
(if (<=.f64 m -1079752188802993/144115188075855872) (.f64 (cos.f64 M) (exp.f64 m)) (if (<=.f64 m -7518962113351433/11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296) (.f64 (cos.f64 M) (exp.f64 (.f64 n (.f64 n -1/4)))) (if (<=.f64 m -4063197626210299/9343878384890255807777119448474196633381331982845050737826186276657715542443371287564109437577976626746659450006721346172290467269376897020421450382791094657540085093089822617769726345721044533248) (/.f64 (cos.f64 M) (exp.f64 l)) (.f64 (cos.f64 M) (exp.f64 (.f64 n (*.f64 n -1/4)))))))
(if (<=.f64 l 7546916244797453/2535301200456458802993406410752) (.f64 (cos.f64 M) (exp.f64 (.f64 m (.f64 m -1/4)))) (.f64 (cos.f64 M) (exp.f64 (neg.f64 l))))
(if (<=.f64 l 7546916244797453/2535301200456458802993406410752) (.f64 1 (exp.f64 (.f64 m (.f64 m -1/4)))) (.f64 (cos.f64 M) (exp.f64 (neg.f64 l))))
(if (<=.f64 l 7546916244797453/2535301200456458802993406410752) (exp.f64 (.f64 m (.f64 m -1/4))) (*.f64 (cos.f64 M) (exp.f64 (neg.f64 l))))
(if (<=.f64 l 7546916244797453/2535301200456458802993406410752) (.f64 1 (exp.f64 (.f64 m (*.f64 m -1/4)))) (exp.f64 (neg.f64 l)))
(if (<=.f64 l 7546916244797453/2535301200456458802993406410752) (exp.f64 (.f64 m (.f64 m -1/4))) (exp.f64 (neg.f64 l)))
(exp.f64 (neg.f64 l))
(cos.f64 M)

Compiler

Compiled 279 to 198 computations (29% saved)

soundness77.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-def_binary64`
652×	`distribute-rgt-neg-out_binary64`
586×	`distribute-lft-neg-out_binary64`
382×	`*-commutative_binary64`
343×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	2669
1	417	2628
2	1279	2506
3	4078	2506

Stop Event

1×	node limit

Compiler

Compiled 15 to 13 computations (13.3% saved)

end155.0ms (1.1%)

Remove: (sort m n)
Compiler: Compiled 284 to 168 computations (40.8% saved)