Details

analyze505.0ms (8.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
11%	17.1%	71.9%	7
14%	14%	71.9%	8
18%	10.1%	71.9%	9
18.5%	9.5%	71.9%	10
20.7%	7.3%	71.9%	11
22.9%	5.2%	71.9%	12
23.2%	4.9%	71.9%	13
24.3%	3.8%	71.9%	14

Compiler

Compiled 43 to 28 computations (34.9% saved)

sample2.0s (33.8%)

Results

1.1s	6617×	body	128	valid
433.0ms	736×	body	1024	valid
230.0ms	524×	body	512	valid
93.0ms	302×	body	256	valid
68.0ms	77×	body	2048	valid

preprocess29.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

708×	`associate-+l+_binary64`
672×	`associate-+r+_binary64`
656×	`fma-def_binary64`
272×	`distribute-lft-in_binary64`
272×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	172
1	112	156
2	380	148
3	1818	148
0	3	3

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

Inputs
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 beta alpha) (-.f64 alpha beta)) (+.f64 (+.f64 beta alpha) (.f64 2 i))) (+.f64 (+.f64 (+.f64 beta alpha) (*.f64 2 i)) 2)) 1) 2)
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 i beta) (-.f64 beta i)) (+.f64 (+.f64 i beta) (.f64 2 alpha))) (+.f64 (+.f64 (+.f64 i beta) (*.f64 2 alpha)) 2)) 1) 2)
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha i) (-.f64 i alpha)) (+.f64 (+.f64 alpha i) (.f64 2 beta))) (+.f64 (+.f64 (+.f64 alpha i) (*.f64 2 beta)) 2)) 1) 2)

Outputs
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)
(/.f64 (+.f64 (/.f64 (.f64 (-.f64 beta alpha) (+.f64 alpha beta)) (.f64 (+.f64 2 (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 alpha (+.f64 beta (.f64 2 i))))) 1) 2)
(/.f64 (+.f64 (*.f64 (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 2 i 2)))) (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (+.f64 beta (+.f64 2 (fma.f64 2 i alpha)))) (/.f64 (-.f64 beta alpha) (+.f64 beta (fma.f64 2 i alpha))) 1) 2)
(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 2 (+.f64 i 1) beta))) (/.f64 (-.f64 beta alpha) (+.f64 beta (fma.f64 2 i alpha))) 1) 2)
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 beta alpha) (-.f64 alpha beta)) (+.f64 (+.f64 beta alpha) (.f64 2 i))) (+.f64 (+.f64 (+.f64 beta alpha) (*.f64 2 i)) 2)) 1) 2)
(/.f64 (+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 alpha beta)) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 2 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))) 2)
(/.f64 (+.f64 1 (*.f64 (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 2 i 2)))) (/.f64 (-.f64 alpha beta) (fma.f64 2 i (+.f64 alpha beta))))) 2)
(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (+.f64 beta (+.f64 2 (fma.f64 2 i alpha)))) (/.f64 (-.f64 alpha beta) (+.f64 beta (fma.f64 2 i alpha))) 1) 2)
(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (+.f64 alpha (fma.f64 2 (+.f64 i 1) beta))) (/.f64 (-.f64 alpha beta) (+.f64 beta (fma.f64 2 i alpha))) 1) 2)
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 i beta) (-.f64 beta i)) (+.f64 (+.f64 i beta) (.f64 2 alpha))) (+.f64 (+.f64 (+.f64 i beta) (*.f64 2 alpha)) 2)) 1) 2)
(/.f64 (+.f64 1 (/.f64 (/.f64 (+.f64 beta i) (/.f64 (+.f64 (+.f64 beta i) (.f64 alpha 2)) (-.f64 beta i))) (+.f64 2 (+.f64 (+.f64 beta i) (.f64 alpha 2))))) 2)
(/.f64 (+.f64 1 (/.f64 (*.f64 (/.f64 (+.f64 beta i) (fma.f64 alpha 2 (+.f64 beta i))) (-.f64 beta i)) (+.f64 2 (fma.f64 alpha 2 (+.f64 beta i))))) 2)
(/.f64 (fma.f64 (/.f64 (+.f64 beta i) (+.f64 beta (+.f64 (fma.f64 alpha 2 i) 2))) (/.f64 (-.f64 beta i) (+.f64 beta (fma.f64 alpha 2 i))) 1) 2)
(/.f64 (fma.f64 (/.f64 (+.f64 beta i) (+.f64 beta (+.f64 2 (fma.f64 alpha 2 i)))) (/.f64 (-.f64 beta i) (+.f64 beta (fma.f64 alpha 2 i))) 1) 2)
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha i) (-.f64 i alpha)) (+.f64 (+.f64 alpha i) (.f64 2 beta))) (+.f64 (+.f64 (+.f64 alpha i) (*.f64 2 beta)) 2)) 1) 2)
(/.f64 (+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha i) (-.f64 i alpha)) (+.f64 (+.f64 alpha i) (.f64 beta 2))) (+.f64 2 (+.f64 (+.f64 alpha i) (*.f64 beta 2))))) 2)
(/.f64 (+.f64 1 (/.f64 (/.f64 (*.f64 (+.f64 alpha i) (-.f64 i alpha)) (fma.f64 beta 2 (+.f64 alpha i))) (+.f64 alpha (+.f64 i (fma.f64 beta 2 2))))) 2)
(/.f64 (fma.f64 (/.f64 (+.f64 alpha i) (+.f64 (fma.f64 beta 2 i) (+.f64 alpha 2))) (/.f64 (-.f64 i alpha) (+.f64 alpha (fma.f64 beta 2 i))) 1) 2)
(/.f64 (fma.f64 (/.f64 (+.f64 alpha i) (+.f64 alpha (+.f64 2 (fma.f64 beta 2 i)))) (/.f64 (-.f64 i alpha) (+.f64 alpha (fma.f64 beta 2 i))) 1) 2)

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify28.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

817×	`distribute-rgt-in_binary64`
748×	`distribute-lft-in_binary64`
245×	`+-commutative_binary64`
193×	`associate-+l+_binary64`
184×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	34	39
2	112	37
3	520	37
4	2735	37
5	4514	37

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)

Outputs
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)
(/.f64 (+.f64 (/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) (-.f64 beta alpha))) (+.f64 (+.f64 alpha beta) (+.f64 (.f64 2 i) 2))) 1) 2)
(/.f64 (+.f64 (/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 alpha (+.f64 beta (fma.f64 2 i 2)))) 1) 2)
(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (+.f64 alpha (+.f64 beta (fma.f64 2 i 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)
(/.f64 (fma.f64 (/.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (fma.f64 2 i beta))) (-.f64 beta alpha) 1) 2)
(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)

eval1.0ms (0%)

Compiler: Compiled 58 to 33 computations (43.1% saved)

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

13.5b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	13.5b	(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)
	25.6b	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)

Status

Error

Program

▶

13.5b

(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)

25.6b

(/.f64 (+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)

Compiler

Compiled 122 to 76 computations (37.7% saved)

localize16.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2)))
✓	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))
✓	2.1b	(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

New

Error

Program

✓

0.0b

(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2)))

✓

0.0b

(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))

✓

2.1b

(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

series43.0ms (0.7%)

Counts

3 → 108

Calls

27 calls:

Time	Variable		Point	Expression
8.0ms	i	@	-inf	(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2)))
4.0ms	beta	@	0	(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)
3.0ms	alpha	@	0	(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)
3.0ms	alpha	@	inf	(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)
3.0ms	alpha	@	-inf	(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

rewrite42.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

185×	`add-sqr-sqrt_binary64`
181×	`*-un-lft-identity_binary64`
181×	`pow1_binary64`
172×	`add-cbrt-cube_binary64`
172×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	65
1	349	65

Stop Event

1×	node limit

Counts

3 → 89

Calls

Call 1

Inputs
(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)
(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))
(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2)))

Inputs

(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))

(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)) 2) (cbrt.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)) (sqrt.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 3) 1) (+.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) (-.f64 1 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) 1) (-.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 beta (+.f64 alpha (fma.f64 2 i beta))) (neg.f64 (/.f64 alpha (+.f64 alpha (fma.f64 2 i beta)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 beta (+.f64 alpha (fma.f64 2 i beta))) (/.f64 alpha (+.f64 alpha (fma.f64 2 i beta))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 beta alpha) (/.f64 1 (+.f64 alpha (fma.f64 2 i beta))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (pow.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 2) (cbrt.f64 (/.f64 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Outputs

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(+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2))))))))))

simplify106.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

590×	`fma-def_binary64`
397×	`distribute-rgt-in_binary64`
392×	`distribute-lft-in_binary64`
384×	`times-frac_binary64`
218×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	624	9038
1	2199	7802

Stop Event

1×	node limit

Counts

197 → 257

Calls

Call 1

Inputs
(+.f64 1 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (*.f64 2 i))))))
(+.f64 1 (+.f64 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i))))) (.f64 (+.f64 (/.f64 (.f64 beta (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 beta (.f64 2 i))) (.f64 -1 (/.f64 (.f64 beta (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2)))) (+.f64 beta (+.f64 2 (*.f64 2 i)))))) alpha)))
(+.f64 1 (+.f64 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i))))) (+.f64 (.f64 (+.f64 (/.f64 (.f64 beta (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 beta (.f64 2 i))) (.f64 -1 (/.f64 (.f64 beta (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2)))) (+.f64 beta (+.f64 2 (.f64 2 i)))))) alpha) (.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2))) (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))))) (+.f64 (/.f64 (.f64 beta (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2)))) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i))))) (/.f64 (.f64 beta (-.f64 (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2)))))
(+.f64 (.f64 (+.f64 (/.f64 (.f64 beta (-.f64 (/.f64 1 (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 3)) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 4)))) (+.f64 beta (.f64 2 i))) (+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2))) (-.f64 (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))))) (+.f64 (/.f64 (.f64 (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2))) (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 beta (.f64 2 i))) (.f64 -1 (/.f64 (.f64 beta (+.f64 (/.f64 1 (pow.f64 (+.f64 beta (.f64 2 i)) 3)) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 4)))) (+.f64 beta (+.f64 2 (.f64 2 i)))))))) (pow.f64 alpha 3)) (+.f64 1 (+.f64 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i))))) (+.f64 (.f64 (+.f64 (/.f64 (.f64 beta (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 beta (.f64 2 i))) (.f64 -1 (/.f64 (.f64 beta (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2)))) (+.f64 beta (+.f64 2 (.f64 2 i)))))) alpha) (.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2))) (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))))) (+.f64 (/.f64 (.f64 beta (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2)))) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i))))) (/.f64 (.f64 beta (-.f64 (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2))))))
(/.f64 (-.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) (.f64 -1 (+.f64 beta (*.f64 2 i)))) alpha)
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 beta (.f64 2 i)) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2))) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i)))) (pow.f64 alpha 2))) (+.f64 (.f64 2 (/.f64 i alpha)) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2))) (.f64 2 (/.f64 1 alpha))))))) (.f64 -1 (/.f64 (+.f64 beta (.f64 2 i)) alpha)))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 i alpha)) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i)))) (pow.f64 alpha 2))) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2))) (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (.f64 (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i)))) (+.f64 beta (+.f64 2 (.f64 2 i))))) (pow.f64 alpha 3)) (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)) (pow.f64 alpha 3)) (+.f64 (/.f64 (.f64 (+.f64 beta (.f64 2 i)) (.f64 (+.f64 2 (.f64 2 i)) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i)))))) (pow.f64 alpha 3)) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 beta (.f64 2 i)) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2))) (+.f64 (/.f64 (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 3)) (.f64 2 (/.f64 1 alpha))))))))))) (.f64 -1 (/.f64 (+.f64 beta (*.f64 2 i)) alpha)))
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2
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2
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1
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(+.f64 (.f64 1/4 (/.f64 (.f64 (+.f64 beta alpha) (-.f64 beta alpha)) (pow.f64 i 2))) (+.f64 (.f64 -1/8 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (.f64 (+.f64 beta alpha) (-.f64 beta alpha))) (pow.f64 i 3))) (+.f64 1 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 (+.f64 beta alpha) 3) (-.f64 beta alpha)) (pow.f64 i 4))) (+.f64 (.f64 1/16 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (.f64 (pow.f64 (+.f64 beta alpha) 2) (-.f64 beta alpha))) (pow.f64 i 4))) (+.f64 (.f64 1/16 (/.f64 (.f64 (+.f64 beta alpha) (.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2) (-.f64 beta alpha))) (pow.f64 i 4))) (.f64 -1/8 (/.f64 (*.f64 (pow.f64 (+.f64 beta alpha) 2) (-.f64 beta alpha)) (pow.f64 i 3)))))))))
1
(+.f64 (.f64 1/4 (/.f64 (.f64 (+.f64 beta alpha) (-.f64 beta alpha)) (pow.f64 i 2))) 1)
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(+.f64 (.f64 1/4 (/.f64 (.f64 (+.f64 beta alpha) (-.f64 beta alpha)) (pow.f64 i 2))) (+.f64 1 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 (+.f64 beta alpha) 3) (-.f64 beta alpha)) (pow.f64 i 4))) (+.f64 (.f64 1/16 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (.f64 (pow.f64 (+.f64 beta alpha) 2) (-.f64 beta alpha))) (pow.f64 i 4))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/8 (.f64 (+.f64 beta alpha) (.f64 (+.f64 beta (+.f64 2 alpha)) (-.f64 beta alpha)))) (.f64 1/8 (.f64 (pow.f64 (+.f64 beta alpha) 2) (-.f64 beta alpha)))) (pow.f64 i 3))) (.f64 1/16 (/.f64 (.f64 (+.f64 beta alpha) (.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2) (-.f64 beta alpha))) (pow.f64 i 4))))))))
(.f64 -1 (/.f64 alpha (+.f64 alpha (.f64 2 i))))
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(+.f64 (.f64 beta (-.f64 (/.f64 1 (+.f64 alpha (.f64 2 i))) (.f64 -1 (/.f64 alpha (pow.f64 (+.f64 alpha (.f64 2 i)) 2))))) (+.f64 (.f64 -1 (/.f64 alpha (+.f64 alpha (.f64 2 i)))) (.f64 (-.f64 (.f64 -1 (/.f64 alpha (pow.f64 (+.f64 alpha (.f64 2 i)) 3))) (/.f64 1 (pow.f64 (+.f64 alpha (.f64 2 i)) 2))) (pow.f64 beta 2))))
(+.f64 (.f64 beta (-.f64 (/.f64 1 (+.f64 alpha (.f64 2 i))) (.f64 -1 (/.f64 alpha (pow.f64 (+.f64 alpha (.f64 2 i)) 2))))) (+.f64 (.f64 -1 (/.f64 alpha (+.f64 alpha (.f64 2 i)))) (+.f64 (.f64 (pow.f64 beta 3) (-.f64 (/.f64 1 (pow.f64 (+.f64 alpha (.f64 2 i)) 3)) (.f64 -1 (/.f64 alpha (pow.f64 (+.f64 alpha (.f64 2 i)) 4))))) (.f64 (-.f64 (.f64 -1 (/.f64 alpha (pow.f64 (+.f64 alpha (.f64 2 i)) 3))) (/.f64 1 (pow.f64 (+.f64 alpha (.f64 2 i)) 2))) (pow.f64 beta 2)))))
1
(-.f64 (+.f64 (.f64 -1 (/.f64 alpha beta)) 1) (+.f64 (/.f64 alpha beta) (.f64 2 (/.f64 i beta))))
(-.f64 (+.f64 (.f64 -1 (/.f64 alpha beta)) (+.f64 1 (.f64 -1 (/.f64 (.f64 (+.f64 alpha (.f64 2 i)) (-.f64 (.f64 -1 alpha) (+.f64 alpha (.f64 2 i)))) (pow.f64 beta 2))))) (+.f64 (/.f64 alpha beta) (*.f64 2 (/.f64 i beta))))
(-.f64 (+.f64 (/.f64 (.f64 (pow.f64 (+.f64 alpha (.f64 2 i)) 2) (-.f64 (.f64 -1 alpha) (+.f64 alpha (.f64 2 i)))) (pow.f64 beta 3)) (+.f64 (.f64 -1 (/.f64 alpha beta)) (+.f64 1 (.f64 -1 (/.f64 (.f64 (+.f64 alpha (.f64 2 i)) (-.f64 (.f64 -1 alpha) (+.f64 alpha (.f64 2 i)))) (pow.f64 beta 2)))))) (+.f64 (/.f64 alpha beta) (*.f64 2 (/.f64 i beta))))
1
(-.f64 (+.f64 (.f64 -1 (/.f64 alpha beta)) 1) (+.f64 (/.f64 alpha beta) (.f64 2 (/.f64 i beta))))
(-.f64 (+.f64 (.f64 -1 (/.f64 alpha beta)) (+.f64 1 (.f64 -1 (/.f64 (.f64 (+.f64 alpha (.f64 2 i)) (-.f64 (.f64 -1 alpha) (+.f64 alpha (.f64 2 i)))) (pow.f64 beta 2))))) (+.f64 (/.f64 alpha beta) (*.f64 2 (/.f64 i beta))))
(-.f64 (+.f64 (/.f64 (.f64 (pow.f64 (+.f64 alpha (.f64 2 i)) 2) (-.f64 (.f64 -1 alpha) (+.f64 alpha (.f64 2 i)))) (pow.f64 beta 3)) (+.f64 (.f64 -1 (/.f64 alpha beta)) (+.f64 1 (.f64 -1 (/.f64 (.f64 (+.f64 alpha (.f64 2 i)) (-.f64 (.f64 -1 alpha) (+.f64 alpha (.f64 2 i)))) (pow.f64 beta 2)))))) (+.f64 (/.f64 alpha beta) (*.f64 2 (/.f64 i beta))))
(/.f64 beta (+.f64 beta (*.f64 2 i)))
(+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2))) alpha)) (/.f64 beta (+.f64 beta (*.f64 2 i))))
(+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2))) alpha)) (+.f64 (/.f64 (.f64 (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2))) (pow.f64 alpha 2)) (+.f64 beta (.f64 2 i))) (/.f64 beta (+.f64 beta (*.f64 2 i)))))
(+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2))) alpha)) (+.f64 (/.f64 (.f64 (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2))) (pow.f64 alpha 2)) (+.f64 beta (.f64 2 i))) (+.f64 (/.f64 beta (+.f64 beta (.f64 2 i))) (.f64 -1 (.f64 (+.f64 (/.f64 1 (pow.f64 (+.f64 beta (.f64 2 i)) 3)) (/.f64 beta (pow.f64 (+.f64 beta (*.f64 2 i)) 4))) (pow.f64 alpha 3))))))
-1
(-.f64 (/.f64 beta alpha) (+.f64 1 (.f64 -1 (/.f64 (+.f64 beta (.f64 2 i)) alpha))))
(-.f64 (+.f64 (/.f64 beta alpha) (.f64 -1 (/.f64 (.f64 (+.f64 beta (.f64 2 i)) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2)))) (+.f64 1 (.f64 -1 (/.f64 (+.f64 beta (*.f64 2 i)) alpha))))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 beta (.f64 2 i)) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2))) (/.f64 (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 3)))) (+.f64 1 (.f64 -1 (/.f64 (+.f64 beta (*.f64 2 i)) alpha))))
-1
(-.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 beta) (+.f64 beta (*.f64 2 i))) alpha)) 1)
(-.f64 (+.f64 (/.f64 (.f64 (-.f64 (.f64 -1 beta) (+.f64 beta (.f64 2 i))) (+.f64 beta (.f64 2 i))) (pow.f64 alpha 2)) (.f64 -1 (/.f64 (-.f64 (.f64 -1 beta) (+.f64 beta (*.f64 2 i))) alpha))) 1)
(-.f64 (+.f64 (.f64 -1 (/.f64 (.f64 (-.f64 (.f64 -1 beta) (+.f64 beta (.f64 2 i))) (pow.f64 (+.f64 beta (.f64 2 i)) 2)) (pow.f64 alpha 3))) (+.f64 (/.f64 (.f64 (+.f64 beta (.f64 2 i)) (-.f64 (.f64 -1 beta) (+.f64 beta (.f64 2 i)))) (pow.f64 alpha 2)) (.f64 -1 (/.f64 (-.f64 (.f64 -1 beta) (+.f64 beta (.f64 2 i))) alpha)))) 1)
(/.f64 (-.f64 beta alpha) (+.f64 beta alpha))
(-.f64 (+.f64 (/.f64 beta (+.f64 beta alpha)) (.f64 -2 (/.f64 (.f64 i (-.f64 beta alpha)) (pow.f64 (+.f64 beta alpha) 2)))) (/.f64 alpha (+.f64 beta alpha)))
(-.f64 (+.f64 (/.f64 beta (+.f64 beta alpha)) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 i 2) (-.f64 beta alpha)) (pow.f64 (+.f64 beta alpha) 3))) (.f64 -2 (/.f64 (.f64 i (-.f64 beta alpha)) (pow.f64 (+.f64 beta alpha) 2))))) (/.f64 alpha (+.f64 beta alpha)))
(-.f64 (+.f64 (/.f64 beta (+.f64 beta alpha)) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 i 2) (-.f64 beta alpha)) (pow.f64 (+.f64 beta alpha) 3))) (+.f64 (.f64 -8 (/.f64 (.f64 (pow.f64 i 3) (-.f64 beta alpha)) (pow.f64 (+.f64 beta alpha) 4))) (.f64 -2 (/.f64 (.f64 i (-.f64 beta alpha)) (pow.f64 (+.f64 beta alpha) 2)))))) (/.f64 alpha (+.f64 beta alpha)))
(*.f64 1/2 (/.f64 (-.f64 beta alpha) i))
(+.f64 (.f64 1/2 (/.f64 (-.f64 beta alpha) i)) (.f64 -1/4 (/.f64 (*.f64 (+.f64 beta alpha) (-.f64 beta alpha)) (pow.f64 i 2))))
(+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 (+.f64 beta alpha) 2) (-.f64 beta alpha)) (pow.f64 i 3))) (+.f64 (.f64 1/2 (/.f64 (-.f64 beta alpha) i)) (.f64 -1/4 (/.f64 (*.f64 (+.f64 beta alpha) (-.f64 beta alpha)) (pow.f64 i 2)))))
(+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 (+.f64 beta alpha) 2) (-.f64 beta alpha)) (pow.f64 i 3))) (+.f64 (.f64 1/2 (/.f64 (-.f64 beta alpha) i)) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta alpha) (-.f64 beta alpha)) (pow.f64 i 2))) (.f64 -1/16 (/.f64 (*.f64 (pow.f64 (+.f64 beta alpha) 3) (-.f64 beta alpha)) (pow.f64 i 4))))))
(*.f64 1/2 (/.f64 (-.f64 beta alpha) i))
(+.f64 (.f64 1/2 (/.f64 (-.f64 beta alpha) i)) (.f64 -1/4 (/.f64 (*.f64 (+.f64 beta alpha) (-.f64 beta alpha)) (pow.f64 i 2))))
(+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 (+.f64 beta alpha) 2) (-.f64 beta alpha)) (pow.f64 i 3))) (+.f64 (.f64 1/2 (/.f64 (-.f64 beta alpha) i)) (.f64 -1/4 (/.f64 (*.f64 (+.f64 beta alpha) (-.f64 beta alpha)) (pow.f64 i 2)))))
(+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 (+.f64 beta alpha) 2) (-.f64 beta alpha)) (pow.f64 i 3))) (+.f64 (.f64 1/2 (/.f64 (-.f64 beta alpha) i)) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta alpha) (-.f64 beta alpha)) (pow.f64 i 2))) (.f64 -1/16 (/.f64 (*.f64 (pow.f64 (+.f64 beta alpha) 3) (-.f64 beta alpha)) (pow.f64 i 4))))))
(/.f64 beta (+.f64 beta (+.f64 2 (*.f64 2 i))))
(+.f64 (.f64 alpha (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (/.f64 beta (+.f64 beta (+.f64 2 (.f64 2 i)))))
(+.f64 (.f64 alpha (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 (.f64 (-.f64 (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))) (pow.f64 alpha 2)) (/.f64 beta (+.f64 beta (+.f64 2 (*.f64 2 i))))))
(+.f64 (.f64 alpha (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 (.f64 (-.f64 (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))) (pow.f64 alpha 2)) (+.f64 (/.f64 beta (+.f64 beta (+.f64 2 (.f64 2 i)))) (.f64 (-.f64 (/.f64 1 (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 3)) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 4))) (pow.f64 alpha 3)))))
1
(+.f64 1 (.f64 -1 (/.f64 (+.f64 2 (.f64 2 i)) alpha)))
(+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i)))) (pow.f64 alpha 2)) (+.f64 1 (.f64 -1 (/.f64 (+.f64 2 (*.f64 2 i)) alpha))))
(+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i)))) (pow.f64 alpha 2)) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)) (pow.f64 alpha 3))) (.f64 -1 (/.f64 (+.f64 2 (*.f64 2 i)) alpha)))))
1
(+.f64 1 (.f64 -1 (/.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (.f64 2 i))))) alpha)))
(+.f64 (/.f64 (.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (.f64 2 i))))) (+.f64 beta (+.f64 2 (.f64 2 i)))) (pow.f64 alpha 2)) (+.f64 1 (.f64 -1 (/.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (*.f64 2 i))))) alpha))))
(+.f64 (/.f64 (.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (.f64 2 i))))) (+.f64 beta (+.f64 2 (.f64 2 i)))) (pow.f64 alpha 2)) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (.f64 2 i))))) alpha)) (.f64 -1 (/.f64 (.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (.f64 2 i))))) (pow.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) 2)) (pow.f64 alpha 3))))))
(/.f64 alpha (+.f64 2 (+.f64 alpha (*.f64 2 i))))
(+.f64 (/.f64 alpha (+.f64 2 (+.f64 alpha (.f64 2 i)))) (.f64 beta (-.f64 (/.f64 1 (+.f64 2 (+.f64 alpha (.f64 2 i)))) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)))))
(+.f64 (.f64 (pow.f64 beta 2) (-.f64 (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)))) (+.f64 (/.f64 alpha (+.f64 2 (+.f64 alpha (.f64 2 i)))) (.f64 beta (-.f64 (/.f64 1 (+.f64 2 (+.f64 alpha (.f64 2 i)))) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (*.f64 2 i))) 2))))))
(+.f64 (.f64 (-.f64 (/.f64 1 (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 3)) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 4))) (pow.f64 beta 3)) (+.f64 (.f64 (pow.f64 beta 2) (-.f64 (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)))) (+.f64 (/.f64 alpha (+.f64 2 (+.f64 alpha (.f64 2 i)))) (.f64 beta (-.f64 (/.f64 1 (+.f64 2 (+.f64 alpha (.f64 2 i)))) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)))))))
1
(+.f64 1 (.f64 -1 (/.f64 (+.f64 2 (.f64 2 i)) beta)))
(+.f64 1 (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 2 (+.f64 alpha (.f64 2 i)))) (pow.f64 beta 2)) (.f64 -1 (/.f64 (+.f64 2 (*.f64 2 i)) beta))))
(+.f64 1 (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 2 (+.f64 alpha (.f64 2 i)))) (pow.f64 beta 2)) (+.f64 (.f64 -1 (/.f64 (+.f64 2 (.f64 2 i)) beta)) (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (pow.f64 (+.f64 2 (+.f64 alpha (*.f64 2 i))) 2)) (pow.f64 beta 3))))))
1
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) beta)) 1)
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) beta)) (+.f64 1 (/.f64 (.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) (+.f64 2 (+.f64 alpha (*.f64 2 i)))) (pow.f64 beta 2))))
(+.f64 (.f64 -1 (/.f64 (.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)) (pow.f64 beta 3))) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) beta)) (+.f64 1 (/.f64 (.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) (+.f64 2 (+.f64 alpha (*.f64 2 i)))) (pow.f64 beta 2)))))
(/.f64 (+.f64 beta alpha) (+.f64 beta (+.f64 2 alpha)))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (+.f64 (.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (+.f64 (.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 i 2) (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3))) (/.f64 beta (+.f64 beta (+.f64 2 alpha))))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (+.f64 (.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (+.f64 (.f64 -8 (/.f64 (.f64 (pow.f64 i 3) (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 4))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 i 2) (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3))) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))))
(*.f64 1/2 (/.f64 (+.f64 beta alpha) i))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (+.f64 beta alpha)) (pow.f64 i 4))) (+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))
(*.f64 1/2 (/.f64 (+.f64 beta alpha) i))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (+.f64 beta alpha)) (pow.f64 i 4))) (+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))

Outputs
(+.f64 1 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (*.f64 2 i))))))
(+.f64 1 (/.f64 (.f64 beta beta) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i))))))
(+.f64 1 (*.f64 (/.f64 beta (fma.f64 2 i beta)) (/.f64 beta (+.f64 beta (fma.f64 2 i 2)))))
(+.f64 1 (+.f64 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i))))) (.f64 (+.f64 (/.f64 (.f64 beta (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 beta (.f64 2 i))) (.f64 -1 (/.f64 (.f64 beta (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2)))) (+.f64 beta (+.f64 2 (*.f64 2 i)))))) alpha)))
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(/.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta))) alpha)
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2
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1
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(fma.f64 (*.f64 beta beta) (+.f64 (/.f64 alpha (pow.f64 (+.f64 2 (fma.f64 2 i alpha)) 3)) (/.f64 -1 (pow.f64 (+.f64 2 (fma.f64 2 i alpha)) 2))) (fma.f64 beta (-.f64 (/.f64 1 (+.f64 2 (fma.f64 2 i alpha))) (/.f64 alpha (pow.f64 (+.f64 2 (fma.f64 2 i alpha)) 2))) (/.f64 alpha (+.f64 2 (fma.f64 2 i alpha)))))
(+.f64 (.f64 (-.f64 (/.f64 1 (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 3)) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 4))) (pow.f64 beta 3)) (+.f64 (.f64 (pow.f64 beta 2) (-.f64 (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)))) (+.f64 (/.f64 alpha (+.f64 2 (+.f64 alpha (.f64 2 i)))) (.f64 beta (-.f64 (/.f64 1 (+.f64 2 (+.f64 alpha (.f64 2 i)))) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)))))))
(fma.f64 (-.f64 (/.f64 1 (pow.f64 (+.f64 2 (+.f64 (.f64 2 i) alpha)) 3)) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 (.f64 2 i) alpha)) 4))) (pow.f64 beta 3) (fma.f64 (.f64 beta beta) (-.f64 (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 (.f64 2 i) alpha)) 3)) (/.f64 1 (pow.f64 (+.f64 2 (+.f64 (.f64 2 i) alpha)) 2))) (+.f64 (/.f64 alpha (+.f64 2 (+.f64 (.f64 2 i) alpha))) (.f64 beta (-.f64 (/.f64 1 (+.f64 2 (+.f64 (.f64 2 i) alpha))) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 (*.f64 2 i) alpha)) 2)))))))
(fma.f64 (-.f64 (/.f64 1 (pow.f64 (+.f64 2 (fma.f64 2 i alpha)) 3)) (/.f64 alpha (pow.f64 (+.f64 2 (fma.f64 2 i alpha)) 4))) (pow.f64 beta 3) (fma.f64 (*.f64 beta beta) (+.f64 (/.f64 alpha (pow.f64 (+.f64 2 (fma.f64 2 i alpha)) 3)) (/.f64 -1 (pow.f64 (+.f64 2 (fma.f64 2 i alpha)) 2))) (fma.f64 beta (-.f64 (/.f64 1 (+.f64 2 (fma.f64 2 i alpha))) (/.f64 alpha (pow.f64 (+.f64 2 (fma.f64 2 i alpha)) 2))) (/.f64 alpha (+.f64 2 (fma.f64 2 i alpha))))))
1
(+.f64 1 (.f64 -1 (/.f64 (+.f64 2 (.f64 2 i)) beta)))
(+.f64 1 (neg.f64 (/.f64 (+.f64 2 (*.f64 2 i)) beta)))
(-.f64 1 (/.f64 (fma.f64 2 i 2) beta))
(+.f64 1 (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 2 (+.f64 alpha (.f64 2 i)))) (pow.f64 beta 2)) (.f64 -1 (/.f64 (+.f64 2 (*.f64 2 i)) beta))))
(+.f64 (+.f64 1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 2 (+.f64 (.f64 2 i) alpha))) (.f64 beta beta))) (neg.f64 (/.f64 (+.f64 2 (*.f64 2 i)) beta)))
(+.f64 1 (-.f64 (*.f64 (/.f64 (fma.f64 2 i 2) beta) (/.f64 (+.f64 2 (fma.f64 2 i alpha)) beta)) (/.f64 (fma.f64 2 i 2) beta)))
(+.f64 1 (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 2 (+.f64 alpha (.f64 2 i)))) (pow.f64 beta 2)) (+.f64 (.f64 -1 (/.f64 (+.f64 2 (.f64 2 i)) beta)) (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (pow.f64 (+.f64 2 (+.f64 alpha (*.f64 2 i))) 2)) (pow.f64 beta 3))))))
(+.f64 1 (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 2 (+.f64 (.f64 2 i) alpha))) (.f64 beta beta)) (fma.f64 -1 (/.f64 (+.f64 2 (.f64 2 i)) beta) (neg.f64 (/.f64 (+.f64 2 (.f64 2 i)) (/.f64 (pow.f64 beta 3) (pow.f64 (+.f64 2 (+.f64 (*.f64 2 i) alpha)) 2)))))))
(+.f64 1 (-.f64 (-.f64 (*.f64 (/.f64 (fma.f64 2 i 2) beta) (/.f64 (+.f64 2 (fma.f64 2 i alpha)) beta)) (/.f64 (fma.f64 2 i 2) beta)) (/.f64 (fma.f64 2 i 2) (/.f64 (pow.f64 beta 3) (pow.f64 (+.f64 2 (fma.f64 2 i alpha)) 2)))))
1
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) beta)) 1)
(fma.f64 -1 (/.f64 (.f64 -1 (-.f64 alpha (+.f64 2 (+.f64 (.f64 2 i) alpha)))) beta) 1)
(-.f64 1 (/.f64 (fma.f64 -1 alpha (+.f64 2 (fma.f64 2 i alpha))) beta))
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) beta)) (+.f64 1 (/.f64 (.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) (+.f64 2 (+.f64 alpha (*.f64 2 i)))) (pow.f64 beta 2))))
(+.f64 (fma.f64 -1 (/.f64 (.f64 -1 (-.f64 alpha (+.f64 2 (+.f64 (.f64 2 i) alpha)))) beta) 1) (/.f64 (.f64 -1 (-.f64 alpha (+.f64 2 (+.f64 (.f64 2 i) alpha)))) (/.f64 (.f64 beta beta) (+.f64 2 (+.f64 (.f64 2 i) alpha)))))
(+.f64 (-.f64 1 (/.f64 (fma.f64 -1 alpha (+.f64 2 (fma.f64 2 i alpha))) beta)) (*.f64 (/.f64 (fma.f64 -1 alpha (+.f64 2 (fma.f64 2 i alpha))) beta) (/.f64 (+.f64 2 (fma.f64 2 i alpha)) beta)))
(+.f64 (.f64 -1 (/.f64 (.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)) (pow.f64 beta 3))) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) beta)) (+.f64 1 (/.f64 (.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) (+.f64 2 (+.f64 alpha (*.f64 2 i)))) (pow.f64 beta 2)))))
(fma.f64 -1 (/.f64 (.f64 -1 (-.f64 alpha (+.f64 2 (+.f64 (.f64 2 i) alpha)))) (/.f64 (pow.f64 beta 3) (pow.f64 (+.f64 2 (+.f64 (.f64 2 i) alpha)) 2))) (+.f64 (fma.f64 -1 (/.f64 (.f64 -1 (-.f64 alpha (+.f64 2 (+.f64 (.f64 2 i) alpha)))) beta) 1) (/.f64 (.f64 -1 (-.f64 alpha (+.f64 2 (+.f64 (.f64 2 i) alpha)))) (/.f64 (.f64 beta beta) (+.f64 2 (+.f64 (*.f64 2 i) alpha))))))
(-.f64 (+.f64 (-.f64 1 (/.f64 (fma.f64 -1 alpha (+.f64 2 (fma.f64 2 i alpha))) beta)) (*.f64 (/.f64 (fma.f64 -1 alpha (+.f64 2 (fma.f64 2 i alpha))) beta) (/.f64 (+.f64 2 (fma.f64 2 i alpha)) beta))) (/.f64 (fma.f64 -1 alpha (+.f64 2 (fma.f64 2 i alpha))) (/.f64 (pow.f64 beta 3) (pow.f64 (+.f64 2 (fma.f64 2 i alpha)) 2))))
(/.f64 (+.f64 beta alpha) (+.f64 beta (+.f64 2 alpha)))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (+.f64 (.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (fma.f64 -2 (/.f64 i (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2) (+.f64 beta alpha))) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (+.f64 (.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 i 2) (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3))) (/.f64 beta (+.f64 beta (+.f64 2 alpha))))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (fma.f64 -2 (/.f64 i (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2) (+.f64 beta alpha))) (fma.f64 4 (/.f64 (.f64 (+.f64 beta alpha) (.f64 i i)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3)) (/.f64 beta (+.f64 beta (+.f64 2 alpha))))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (+.f64 (.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (+.f64 (.f64 -8 (/.f64 (.f64 (pow.f64 i 3) (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 4))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 i 2) (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3))) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (fma.f64 -2 (/.f64 i (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2) (+.f64 beta alpha))) (fma.f64 -8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 i 3)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 4)) (fma.f64 4 (/.f64 (.f64 (+.f64 beta alpha) (*.f64 i i)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3)) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))))
(*.f64 1/2 (/.f64 (+.f64 beta alpha) i))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(fma.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha))) (.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(fma.f64 1/2 (/.f64 (+.f64 beta alpha) i) (.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha)))))
(+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha))) (.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 1/2 (/.f64 (+.f64 beta alpha) i) (.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha))))))
(+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (+.f64 beta alpha)) (pow.f64 i 4))) (+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))
(fma.f64 -1/16 (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (/.f64 (pow.f64 i 4) (+.f64 beta alpha))) (fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha))) (.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))
(fma.f64 -1/16 (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (/.f64 (pow.f64 i 4) (+.f64 beta alpha))) (fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 1/2 (/.f64 (+.f64 beta alpha) i) (.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha)))))))
(*.f64 1/2 (/.f64 (+.f64 beta alpha) i))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(fma.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha))) (.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(fma.f64 1/2 (/.f64 (+.f64 beta alpha) i) (.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha)))))
(+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha))) (.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 1/2 (/.f64 (+.f64 beta alpha) i) (.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha))))))
(+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (+.f64 beta alpha)) (pow.f64 i 4))) (+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))
(fma.f64 -1/16 (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (/.f64 (pow.f64 i 4) (+.f64 beta alpha))) (fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha))) (.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))
(fma.f64 -1/16 (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (/.f64 (pow.f64 i 4) (+.f64 beta alpha))) (fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 1/2 (/.f64 (+.f64 beta alpha) i) (.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha)))))))

eval282.0ms (4.8%)

Compiler: Compiled 15856 to 10100 computations (36.3% saved)

prune785.0ms (13.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	254	3	257
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	256	3	259

Error

0.1b

Counts

259 → 3

Alt Table

Click to see full alt table

Status

Error

Program

49.4b

(/.f64 (+.f64 (+.f64 (-.f64 (/.f64 beta alpha) (*.f64 (/.f64 (fma.f64 2 i beta) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha))) (-.f64 (fma.f64 2 (/.f64 i alpha) (-.f64 (/.f64 2 alpha) (*.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha)))) (*.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha)))) (/.f64 (fma.f64 2 i beta) alpha)) 2)

▶

13.5b

(/.f64 (fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)

48.5b

(/.f64 (/.f64 (-.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) (*.f64 -1 (+.f64 beta (*.f64 2 i)))) alpha) 2)

Compiler

Compiled 250 to 168 computations (32.8% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2))))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2))))))
	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))
✓	13.7b	(fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

series18.0ms (0.3%)

Counts

3 → 108

Calls

27 calls:

Time	Variable		Point	Expression
4.0ms	alpha	@	inf	(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2))))
1.0ms	alpha	@	0	(fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)
1.0ms	alpha	@	-inf	(fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)
1.0ms	alpha	@	inf	(fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)
1.0ms	beta	@	0	(fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

rewrite40.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

208×	`add-sqr-sqrt_binary64`
205×	`pow1_binary64`
204×	`*-un-lft-identity_binary64`
196×	`expm1-log1p-u_binary64`
195×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	68
1	397	68

Stop Event

1×	node limit

Counts

3 → 80

Calls

Call 1

Inputs
(fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)
(expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2))))))
(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2))))

Inputs

(fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

(expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2))))))

(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2))))

Outputs
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Outputs

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

simplify118.0ms (2%)

Algorithm

1×	egg-herbie

Rules

503×	`fma-def_binary64`
381×	`distribute-rgt-in_binary64`
376×	`distribute-lft-in_binary64`
346×	`times-frac_binary64`
184×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	544	9154
1	1933	7917

Stop Event

1×	node limit

Counts

188 → 172

Calls

Call 1

Inputs
(+.f64 1 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (*.f64 2 i))))))
(+.f64 1 (+.f64 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i))))) (.f64 (+.f64 (/.f64 (.f64 beta (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 beta (.f64 2 i))) (.f64 -1 (/.f64 (.f64 beta (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2)))) (+.f64 beta (+.f64 2 (*.f64 2 i)))))) alpha)))
(+.f64 1 (+.f64 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i))))) (+.f64 (.f64 (+.f64 (/.f64 (.f64 beta (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 beta (.f64 2 i))) (.f64 -1 (/.f64 (.f64 beta (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2)))) (+.f64 beta (+.f64 2 (.f64 2 i)))))) alpha) (.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2))) (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))))) (+.f64 (/.f64 (.f64 beta (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2)))) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i))))) (/.f64 (.f64 beta (-.f64 (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2)))))
(+.f64 (.f64 (+.f64 (/.f64 (.f64 beta (-.f64 (/.f64 1 (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 3)) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 4)))) (+.f64 beta (.f64 2 i))) (+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2))) (-.f64 (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))))) (+.f64 (/.f64 (.f64 (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2))) (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 beta (.f64 2 i))) (.f64 -1 (/.f64 (.f64 beta (+.f64 (/.f64 1 (pow.f64 (+.f64 beta (.f64 2 i)) 3)) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 4)))) (+.f64 beta (+.f64 2 (.f64 2 i)))))))) (pow.f64 alpha 3)) (+.f64 1 (+.f64 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i))))) (+.f64 (.f64 (+.f64 (/.f64 (.f64 beta (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 beta (.f64 2 i))) (.f64 -1 (/.f64 (.f64 beta (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2)))) (+.f64 beta (+.f64 2 (.f64 2 i)))))) alpha) (.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2))) (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))))) (+.f64 (/.f64 (.f64 beta (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2)))) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i))))) (/.f64 (.f64 beta (-.f64 (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2))))))
(/.f64 (-.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) (.f64 -1 (+.f64 beta (*.f64 2 i)))) alpha)
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 beta (.f64 2 i)) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2))) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i)))) (pow.f64 alpha 2))) (+.f64 (.f64 2 (/.f64 i alpha)) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2))) (.f64 2 (/.f64 1 alpha))))))) (.f64 -1 (/.f64 (+.f64 beta (.f64 2 i)) alpha)))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 i alpha)) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i)))) (pow.f64 alpha 2))) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2))) (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (.f64 (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i)))) (+.f64 beta (+.f64 2 (.f64 2 i))))) (pow.f64 alpha 3)) (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)) (pow.f64 alpha 3)) (+.f64 (/.f64 (.f64 (+.f64 beta (.f64 2 i)) (.f64 (+.f64 2 (.f64 2 i)) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i)))))) (pow.f64 alpha 3)) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 beta (.f64 2 i)) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2))) (+.f64 (/.f64 (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 3)) (.f64 2 (/.f64 1 alpha))))))))))) (.f64 -1 (/.f64 (+.f64 beta (*.f64 2 i)) alpha)))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (.f64 (+.f64 beta (.f64 2 i)) (.f64 (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i)))) (+.f64 beta (+.f64 2 (.f64 2 i)))))) (pow.f64 alpha 4))) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i)))))) (pow.f64 alpha 4))) (+.f64 (.f64 2 (/.f64 i alpha)) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i)))) (pow.f64 alpha 2))) (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 3) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 4))) (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (.f64 (+.f64 beta (.f64 2 i)) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i)))))) (pow.f64 alpha 3)) (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (.f64 (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i)))) (+.f64 beta (+.f64 2 (.f64 2 i))))) (pow.f64 alpha 3)) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2))) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 3)) (pow.f64 alpha 4))) (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)) (pow.f64 alpha 3)) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 beta (.f64 2 i)) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 2))) (+.f64 (/.f64 (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i))))) (pow.f64 alpha 3)) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (.f64 (-.f64 beta (.f64 -1 (+.f64 beta (.f64 2 i)))) (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))) (pow.f64 alpha 4))) (.f64 2 (/.f64 1 alpha)))))))))))))))) (.f64 -1 (/.f64 (+.f64 beta (*.f64 2 i)) alpha)))
(.f64 -1 (/.f64 (-.f64 (+.f64 (.f64 -1 beta) (.f64 -1 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (.f64 2 i))))))) (+.f64 beta (*.f64 2 i))) alpha))
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2
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1
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1
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1
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1
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(+.f64 (/.f64 (.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (.f64 2 i))))) (+.f64 beta (+.f64 2 (.f64 2 i)))) (pow.f64 alpha 2)) (+.f64 1 (.f64 -1 (/.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (*.f64 2 i))))) alpha))))
(+.f64 (/.f64 (.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (.f64 2 i))))) (+.f64 beta (+.f64 2 (.f64 2 i)))) (pow.f64 alpha 2)) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (.f64 2 i))))) alpha)) (.f64 -1 (/.f64 (.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (.f64 2 i))))) (pow.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) 2)) (pow.f64 alpha 3))))))
(/.f64 alpha (+.f64 2 (+.f64 alpha (*.f64 2 i))))
(+.f64 (/.f64 alpha (+.f64 2 (+.f64 alpha (.f64 2 i)))) (.f64 beta (-.f64 (/.f64 1 (+.f64 2 (+.f64 alpha (.f64 2 i)))) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)))))
(+.f64 (.f64 (pow.f64 beta 2) (-.f64 (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)))) (+.f64 (/.f64 alpha (+.f64 2 (+.f64 alpha (.f64 2 i)))) (.f64 beta (-.f64 (/.f64 1 (+.f64 2 (+.f64 alpha (.f64 2 i)))) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (*.f64 2 i))) 2))))))
(+.f64 (.f64 (-.f64 (/.f64 1 (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 3)) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 4))) (pow.f64 beta 3)) (+.f64 (.f64 (pow.f64 beta 2) (-.f64 (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)))) (+.f64 (/.f64 alpha (+.f64 2 (+.f64 alpha (.f64 2 i)))) (.f64 beta (-.f64 (/.f64 1 (+.f64 2 (+.f64 alpha (.f64 2 i)))) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)))))))
1
(+.f64 1 (.f64 -1 (/.f64 (+.f64 2 (.f64 2 i)) beta)))
(+.f64 1 (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 2 (+.f64 alpha (.f64 2 i)))) (pow.f64 beta 2)) (.f64 -1 (/.f64 (+.f64 2 (*.f64 2 i)) beta))))
(+.f64 1 (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 2 (+.f64 alpha (.f64 2 i)))) (pow.f64 beta 2)) (+.f64 (.f64 -1 (/.f64 (+.f64 2 (.f64 2 i)) beta)) (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (pow.f64 (+.f64 2 (+.f64 alpha (*.f64 2 i))) 2)) (pow.f64 beta 3))))))
1
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) beta)) 1)
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) beta)) (+.f64 1 (/.f64 (.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) (+.f64 2 (+.f64 alpha (*.f64 2 i)))) (pow.f64 beta 2))))
(+.f64 (.f64 -1 (/.f64 (.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)) (pow.f64 beta 3))) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) beta)) (+.f64 1 (/.f64 (.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) (+.f64 2 (+.f64 alpha (*.f64 2 i)))) (pow.f64 beta 2)))))
(/.f64 (+.f64 beta alpha) (+.f64 beta (+.f64 2 alpha)))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (+.f64 (.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (+.f64 (.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 i 2) (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3))) (/.f64 beta (+.f64 beta (+.f64 2 alpha))))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (+.f64 (.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (+.f64 (.f64 -8 (/.f64 (.f64 (pow.f64 i 3) (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 4))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 i 2) (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3))) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))))
(*.f64 1/2 (/.f64 (+.f64 beta alpha) i))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (+.f64 beta alpha)) (pow.f64 i 4))) (+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))
(*.f64 1/2 (/.f64 (+.f64 beta alpha) i))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (+.f64 beta alpha)) (pow.f64 i 4))) (+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))
(/.f64 beta (+.f64 beta (+.f64 2 (*.f64 2 i))))
(+.f64 (.f64 alpha (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (/.f64 beta (+.f64 beta (+.f64 2 (.f64 2 i)))))
(+.f64 (.f64 alpha (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 (.f64 (-.f64 (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))) (pow.f64 alpha 2)) (/.f64 beta (+.f64 beta (+.f64 2 (*.f64 2 i))))))
(+.f64 (.f64 alpha (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 (.f64 (-.f64 (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))) (pow.f64 alpha 2)) (+.f64 (/.f64 beta (+.f64 beta (+.f64 2 (.f64 2 i)))) (.f64 (-.f64 (/.f64 1 (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 3)) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 4))) (pow.f64 alpha 3)))))
1
(+.f64 1 (.f64 -1 (/.f64 (+.f64 2 (.f64 2 i)) alpha)))
(+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i)))) (pow.f64 alpha 2)) (+.f64 1 (.f64 -1 (/.f64 (+.f64 2 (*.f64 2 i)) alpha))))
(+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i)))) (pow.f64 alpha 2)) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)) (pow.f64 alpha 3))) (.f64 -1 (/.f64 (+.f64 2 (*.f64 2 i)) alpha)))))
1
(+.f64 1 (.f64 -1 (/.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (.f64 2 i))))) alpha)))
(+.f64 (/.f64 (.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (.f64 2 i))))) (+.f64 beta (+.f64 2 (.f64 2 i)))) (pow.f64 alpha 2)) (+.f64 1 (.f64 -1 (/.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (*.f64 2 i))))) alpha))))
(+.f64 (/.f64 (.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (.f64 2 i))))) (+.f64 beta (+.f64 2 (.f64 2 i)))) (pow.f64 alpha 2)) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (.f64 2 i))))) alpha)) (.f64 -1 (/.f64 (.f64 (-.f64 (.f64 -1 beta) (.f64 -1 (+.f64 beta (+.f64 2 (.f64 2 i))))) (pow.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) 2)) (pow.f64 alpha 3))))))
(/.f64 alpha (+.f64 2 (+.f64 alpha (*.f64 2 i))))
(+.f64 (/.f64 alpha (+.f64 2 (+.f64 alpha (.f64 2 i)))) (.f64 beta (-.f64 (/.f64 1 (+.f64 2 (+.f64 alpha (.f64 2 i)))) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)))))
(+.f64 (.f64 (pow.f64 beta 2) (-.f64 (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)))) (+.f64 (/.f64 alpha (+.f64 2 (+.f64 alpha (.f64 2 i)))) (.f64 beta (-.f64 (/.f64 1 (+.f64 2 (+.f64 alpha (.f64 2 i)))) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (*.f64 2 i))) 2))))))
(+.f64 (.f64 (-.f64 (/.f64 1 (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 3)) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 4))) (pow.f64 beta 3)) (+.f64 (.f64 (pow.f64 beta 2) (-.f64 (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 3)) (/.f64 1 (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)))) (+.f64 (/.f64 alpha (+.f64 2 (+.f64 alpha (.f64 2 i)))) (.f64 beta (-.f64 (/.f64 1 (+.f64 2 (+.f64 alpha (.f64 2 i)))) (/.f64 alpha (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)))))))
1
(+.f64 1 (.f64 -1 (/.f64 (+.f64 2 (.f64 2 i)) beta)))
(+.f64 1 (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 2 (+.f64 alpha (.f64 2 i)))) (pow.f64 beta 2)) (.f64 -1 (/.f64 (+.f64 2 (*.f64 2 i)) beta))))
(+.f64 1 (+.f64 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (+.f64 2 (+.f64 alpha (.f64 2 i)))) (pow.f64 beta 2)) (+.f64 (.f64 -1 (/.f64 (+.f64 2 (.f64 2 i)) beta)) (.f64 -1 (/.f64 (.f64 (+.f64 2 (.f64 2 i)) (pow.f64 (+.f64 2 (+.f64 alpha (*.f64 2 i))) 2)) (pow.f64 beta 3))))))
1
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) beta)) 1)
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) beta)) (+.f64 1 (/.f64 (.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) (+.f64 2 (+.f64 alpha (*.f64 2 i)))) (pow.f64 beta 2))))
(+.f64 (.f64 -1 (/.f64 (.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) (pow.f64 (+.f64 2 (+.f64 alpha (.f64 2 i))) 2)) (pow.f64 beta 3))) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) beta)) (+.f64 1 (/.f64 (.f64 (-.f64 (.f64 -1 alpha) (.f64 -1 (+.f64 2 (+.f64 alpha (.f64 2 i))))) (+.f64 2 (+.f64 alpha (*.f64 2 i)))) (pow.f64 beta 2)))))
(/.f64 (+.f64 beta alpha) (+.f64 beta (+.f64 2 alpha)))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (+.f64 (.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (+.f64 (.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 i 2) (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3))) (/.f64 beta (+.f64 beta (+.f64 2 alpha))))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (+.f64 (.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (+.f64 (.f64 -8 (/.f64 (.f64 (pow.f64 i 3) (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 4))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 i 2) (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3))) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))))
(*.f64 1/2 (/.f64 (+.f64 beta alpha) i))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (+.f64 beta alpha)) (pow.f64 i 4))) (+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))
(*.f64 1/2 (/.f64 (+.f64 beta alpha) i))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (+.f64 beta alpha)) (pow.f64 i 4))) (+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))

Outputs
(+.f64 1 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (*.f64 2 i))))))
(+.f64 1 (/.f64 (.f64 beta beta) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i))))))
(+.f64 1 (*.f64 (/.f64 beta (+.f64 beta (fma.f64 2 i 2))) (/.f64 beta (fma.f64 2 i beta))))
(+.f64 1 (+.f64 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i))))) (.f64 (+.f64 (/.f64 (.f64 beta (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2)))) (+.f64 beta (.f64 2 i))) (.f64 -1 (/.f64 (.f64 beta (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (.f64 2 i)) 2)))) (+.f64 beta (+.f64 2 (*.f64 2 i)))))) alpha)))
(+.f64 (+.f64 1 (/.f64 (.f64 beta beta) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i)))))) (.f64 (+.f64 (/.f64 beta (/.f64 (+.f64 beta (.f64 2 i)) (-.f64 (/.f64 1 (+.f64 beta (+.f64 2 (.f64 2 i)))) (/.f64 beta (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))))) (neg.f64 (/.f64 beta (/.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) (+.f64 (/.f64 1 (+.f64 beta (.f64 2 i))) (/.f64 beta (pow.f64 (+.f64 beta (*.f64 2 i)) 2))))))) alpha))
(+.f64 1 (fma.f64 (-.f64 (/.f64 beta (/.f64 (fma.f64 2 i beta) (-.f64 (/.f64 1 (+.f64 beta (fma.f64 2 i 2))) (/.f64 beta (pow.f64 (+.f64 beta (fma.f64 2 i 2)) 2))))) (/.f64 beta (/.f64 (+.f64 beta (fma.f64 2 i 2)) (+.f64 (/.f64 1 (fma.f64 2 i beta)) (/.f64 beta (pow.f64 (fma.f64 2 i beta) 2)))))) alpha (*.f64 (/.f64 beta (+.f64 beta (fma.f64 2 i 2))) (/.f64 beta (fma.f64 2 i beta)))))
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1
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1
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1
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1
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1
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1
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(-.f64 (+.f64 (-.f64 1 (/.f64 (fma.f64 -1 alpha (+.f64 2 (fma.f64 2 i alpha))) beta)) (.f64 (/.f64 (fma.f64 -1 alpha (+.f64 2 (fma.f64 2 i alpha))) beta) (/.f64 (+.f64 2 (fma.f64 2 i alpha)) beta))) (/.f64 (.f64 (pow.f64 (+.f64 2 (fma.f64 2 i alpha)) 2) (fma.f64 -1 alpha (+.f64 2 (fma.f64 2 i alpha)))) (pow.f64 beta 3)))
(/.f64 (+.f64 beta alpha) (+.f64 beta (+.f64 2 alpha)))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (+.f64 (.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (fma.f64 -2 (/.f64 (*.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (fma.f64 -2 (/.f64 i (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2) (+.f64 beta alpha))) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (+.f64 (.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 i 2) (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3))) (/.f64 beta (+.f64 beta (+.f64 2 alpha))))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (fma.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (fma.f64 4 (/.f64 (.f64 i i) (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (+.f64 beta alpha))) (/.f64 beta (+.f64 beta (+.f64 2 alpha))))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (fma.f64 -2 (/.f64 i (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2) (+.f64 beta alpha))) (fma.f64 4 (/.f64 (.f64 (+.f64 beta alpha) (.f64 i i)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3)) (/.f64 beta (+.f64 beta (+.f64 2 alpha))))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (+.f64 (.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (+.f64 (.f64 -8 (/.f64 (.f64 (pow.f64 i 3) (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 4))) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 i 2) (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3))) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (fma.f64 -2 (/.f64 (.f64 i (+.f64 beta alpha)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (fma.f64 -8 (/.f64 (pow.f64 i 3) (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 4) (+.f64 beta alpha))) (fma.f64 4 (/.f64 (.f64 i i) (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (+.f64 beta alpha))) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))))
(+.f64 (/.f64 alpha (+.f64 beta (+.f64 2 alpha))) (fma.f64 -2 (/.f64 i (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2) (+.f64 beta alpha))) (fma.f64 -8 (/.f64 (pow.f64 i 3) (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 4) (+.f64 beta alpha))) (fma.f64 4 (/.f64 (.f64 (+.f64 beta alpha) (.f64 i i)) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3)) (/.f64 beta (+.f64 beta (+.f64 2 alpha)))))))
(*.f64 1/2 (/.f64 (+.f64 beta alpha) i))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(fma.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha))) (.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(fma.f64 -1/4 (.f64 (/.f64 (+.f64 beta alpha) i) (/.f64 (+.f64 beta (+.f64 2 alpha)) i)) (.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha))) (.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 -1/4 (.f64 (/.f64 (+.f64 beta alpha) i) (/.f64 (+.f64 beta (+.f64 2 alpha)) i)) (.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (+.f64 beta alpha)) (pow.f64 i 4))) (+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))
(fma.f64 -1/16 (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (/.f64 (pow.f64 i 4) (+.f64 beta alpha))) (fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha))) (.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))
(fma.f64 -1/16 (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (/.f64 (pow.f64 i 4) (+.f64 beta alpha))) (fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 -1/4 (.f64 (/.f64 (+.f64 beta alpha) i) (/.f64 (+.f64 beta (+.f64 2 alpha)) i)) (.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))
(*.f64 1/2 (/.f64 (+.f64 beta alpha) i))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(fma.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha))) (.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(fma.f64 -1/4 (.f64 (/.f64 (+.f64 beta alpha) i) (/.f64 (+.f64 beta (+.f64 2 alpha)) i)) (.f64 1/2 (/.f64 (+.f64 beta alpha) i)))
(+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha))) (.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 -1/4 (.f64 (/.f64 (+.f64 beta alpha) i) (/.f64 (+.f64 beta (+.f64 2 alpha)) i)) (.f64 1/2 (/.f64 (+.f64 beta alpha) i))))
(+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (+.f64 beta alpha)) (pow.f64 i 4))) (+.f64 (.f64 1/8 (/.f64 (.f64 (+.f64 beta alpha) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2)) (pow.f64 i 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 beta (+.f64 2 alpha)) (+.f64 beta alpha)) (pow.f64 i 2))) (*.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))
(fma.f64 -1/16 (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (/.f64 (pow.f64 i 4) (+.f64 beta alpha))) (fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 -1/4 (/.f64 (+.f64 beta (+.f64 2 alpha)) (/.f64 (.f64 i i) (+.f64 beta alpha))) (.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))
(fma.f64 -1/16 (/.f64 (pow.f64 (+.f64 beta (+.f64 2 alpha)) 3) (/.f64 (pow.f64 i 4) (+.f64 beta alpha))) (fma.f64 1/8 (/.f64 (+.f64 beta alpha) (/.f64 (pow.f64 i 3) (pow.f64 (+.f64 beta (+.f64 2 alpha)) 2))) (fma.f64 -1/4 (.f64 (/.f64 (+.f64 beta alpha) i) (/.f64 (+.f64 beta (+.f64 2 alpha)) i)) (.f64 1/2 (/.f64 (+.f64 beta alpha) i)))))

eval272.0ms (4.6%)

Compiler: Compiled 16031 to 10369 computations (35.3% saved)

prune812.0ms (13.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	258	3	261

Error

0.1b

Counts

261 → 3

Alt Table

Click to see full alt table

Status

Error

Program

✓

13.5b

(/.f64 (fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)

▶

48.5b

(/.f64 (/.f64 (-.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) (*.f64 -1 (+.f64 beta (*.f64 2 i)))) alpha) 2)

49.4b

(/.f64 (+.f64 (+.f64 (-.f64 (/.f64 beta alpha) (*.f64 (/.f64 (fma.f64 2 i beta) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha))) (-.f64 (fma.f64 2 (/.f64 i alpha) (-.f64 (/.f64 2 alpha) (*.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha)))) (*.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha)))) (/.f64 (fma.f64 2 i beta) alpha)) 2)

Compiler

Compiled 219 to 147 computations (32.9% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) (.f64 -1 (+.f64 beta (*.f64 2 i))))
✓	0.0b	(/.f64 (-.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) (.f64 -1 (+.f64 beta (*.f64 2 i)))) alpha)

series13.0ms (0.2%)

Counts

2 → 48

Calls

15 calls:

Time	Variable		Point	Expression
3.0ms	alpha	@	inf	(/.f64 (-.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) (.f64 -1 (+.f64 beta (*.f64 2 i)))) alpha)
3.0ms	beta	@	-inf	(/.f64 (-.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) (.f64 -1 (+.f64 beta (*.f64 2 i)))) alpha)
1.0ms	alpha	@	0	(/.f64 (-.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) (.f64 -1 (+.f64 beta (*.f64 2 i)))) alpha)
1.0ms	beta	@	0	(/.f64 (-.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) (.f64 -1 (+.f64 beta (*.f64 2 i)))) alpha)
1.0ms	i	@	inf	(/.f64 (-.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) (.f64 -1 (+.f64 beta (*.f64 2 i)))) alpha)

rewrite38.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

168×	`add-sqr-sqrt_binary64`
164×	`*-un-lft-identity_binary64`
164×	`pow1_binary64`
157×	`add-cbrt-cube_binary64`
157×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	41
1	315	33

Stop Event

1×	node limit

Counts

2 → 91

Calls

Call 1

Inputs
(/.f64 (-.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) (.f64 -1 (+.f64 beta (*.f64 2 i)))) alpha)
(-.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) (.f64 -1 (+.f64 beta (*.f64 2 i))))

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 beta (*.f64 (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 2 i 2) (-.f64 beta (fma.f64 2 i beta)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 2 i 2) (+.f64 beta (fma.f64 2 i beta)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 beta (fma.f64 2 i 2)) (fma.f64 2 i beta))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 2 i beta) (+.f64 beta (fma.f64 2 i 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta))) (fma.f64 (fma.f64 2 i beta) -1 (fma.f64 2 i beta)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta))) (fma.f64 1 (fma.f64 2 i beta) (fma.f64 2 i beta)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) 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(fma.f64 2 i 2) (fma.f64 2 i beta)))) (sqrt.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 beta (fma.f64 2 i 2)) 3) (pow.f64 (fma.f64 2 i beta) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta))) 2) (*.f64 (+.f64 beta (fma.f64 2 i 2)) (fma.f64 2 i beta)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 beta (fma.f64 2 i 2))) (sqrt.f64 (fma.f64 2 i beta))) (-.f64 (sqrt.f64 (+.f64 beta (fma.f64 2 i 2))) (sqrt.f64 (fma.f64 2 i beta))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta))) 2) (*.f64 (+.f64 beta (fma.f64 2 i 2)) (fma.f64 2 i beta))) (+.f64 (pow.f64 (+.f64 beta (fma.f64 2 i 2)) 3) (pow.f64 (fma.f64 2 i beta) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta))) (pow.f64 (+.f64 beta (+.f64 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(fma.f64 2 i 2)) (fma.f64 2 i beta)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta))) 2)) (neg.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (+.f64 (pow.f64 beta 3) (pow.f64 (fma.f64 2 i 2) 3)) (fma.f64 beta beta (*.f64 (*.f64 2 i) (-.f64 (*.f64 2 i) beta)))) (*.f64 (fma.f64 beta beta (*.f64 (fma.f64 2 i 2) (-.f64 (fma.f64 2 i 2) beta))) (+.f64 (pow.f64 beta 3) (*.f64 8 (pow.f64 i 3))))) (*.f64 (fma.f64 beta beta (*.f64 (fma.f64 2 i 2) (-.f64 (fma.f64 2 i 2) beta))) (fma.f64 beta beta (*.f64 (*.f64 2 i) (-.f64 (*.f64 2 i) beta)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (-.f64 (*.f64 beta beta) (pow.f64 (fma.f64 2 i 2) 2)) (fma.f64 beta beta (*.f64 (*.f64 2 i) (-.f64 (*.f64 2 i) beta)))) (*.f64 (-.f64 beta (fma.f64 2 i 2)) (+.f64 (pow.f64 beta 3) (*.f64 8 (pow.f64 i 3))))) (*.f64 (-.f64 beta (fma.f64 2 i 2)) (fma.f64 beta beta (*.f64 (*.f64 2 i) (-.f64 (*.f64 2 i) beta)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (+.f64 (pow.f64 beta 3) (pow.f64 (fma.f64 2 i 2) 3)) (+.f64 beta (*.f64 i -2))) (*.f64 (fma.f64 beta beta (*.f64 (fma.f64 2 i 2) (-.f64 (fma.f64 2 i 2) beta))) (-.f64 (*.f64 beta beta) (*.f64 i (*.f64 4 i))))) (*.f64 (fma.f64 beta beta (*.f64 (fma.f64 2 i 2) (-.f64 (fma.f64 2 i 2) beta))) (+.f64 beta (*.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (-.f64 (*.f64 beta beta) (pow.f64 (fma.f64 2 i 2) 2)) (+.f64 beta (*.f64 i -2))) (*.f64 (-.f64 beta (fma.f64 2 i 2)) (-.f64 (*.f64 beta beta) (*.f64 i (*.f64 4 i))))) (*.f64 (-.f64 beta (fma.f64 2 i 2)) (+.f64 beta (*.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 beta 3) (pow.f64 (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)) 3)) (+.f64 (*.f64 beta beta) (-.f64 (*.f64 (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)) (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta))) (*.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 beta beta) (*.f64 (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)) (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)))) (-.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 beta (fma.f64 2 i 2)) (fma.f64 2 i beta))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 beta) 2) (cbrt.f64 beta) (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 beta (fma.f64 2 i 2))) 2) (cbrt.f64 (+.f64 beta (fma.f64 2 i 2))) (fma.f64 2 i beta))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 beta) (sqrt.f64 beta) (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 beta (fma.f64 2 i 2))) (sqrt.f64 (+.f64 beta (fma.f64 2 i 2))) (fma.f64 2 i beta))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 beta (+.f64 (fma.f64 2 i 2) (fma.f64 2 i beta)))))))))

simplify61.0ms (1%)

Algorithm

1×	egg-herbie

Rules

526×	`fma-def_binary64`
350×	`sub-neg_binary64`
279×	`fma-neg_binary64`
250×	`unsub-neg_binary64`
164×	`associate-+l-_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	868
1	169	740
2	382	538
3	989	502
4	3090	502
5	4863	502

Stop Event

1×	node limit

Counts

139 → 117

Calls

Call 1

Inputs
(/.f64 (-.f64 (+.f64 2 (.f64 2 i)) (.f64 -2 i)) alpha)
(-.f64 (+.f64 (.f64 2 (/.f64 i alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (.f64 2 (/.f64 1 alpha)))) (.f64 -2 (/.f64 i alpha)))
(-.f64 (+.f64 (.f64 2 (/.f64 i alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (.f64 2 (/.f64 1 alpha)))) (.f64 -2 (/.f64 i alpha)))
(-.f64 (+.f64 (.f64 2 (/.f64 i alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (.f64 2 (/.f64 1 alpha)))) (.f64 -2 (/.f64 i alpha)))
(*.f64 2 (/.f64 beta alpha))
(-.f64 (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 beta alpha)))) (.f64 -2 (/.f64 i alpha)))
(-.f64 (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 beta alpha)))) (.f64 -2 (/.f64 i alpha)))
(-.f64 (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 beta alpha)))) (.f64 -2 (/.f64 i alpha)))
(*.f64 2 (/.f64 beta alpha))
(-.f64 (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 beta alpha)))) (.f64 -2 (/.f64 i alpha)))
(-.f64 (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 beta alpha)))) (.f64 -2 (/.f64 i alpha)))
(-.f64 (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 beta alpha)))) (.f64 -2 (/.f64 i alpha)))
(/.f64 (-.f64 (+.f64 beta 2) (*.f64 -1 beta)) alpha)
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 4 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 4 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 4 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(*.f64 4 (/.f64 i alpha))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 1 alpha)) (.f64 4 (/.f64 i alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 1 alpha)) (.f64 4 (/.f64 i alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 1 alpha)) (.f64 4 (/.f64 i alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(*.f64 4 (/.f64 i alpha))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 1 alpha)) (.f64 4 (/.f64 i alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 1 alpha)) (.f64 4 (/.f64 i alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 1 alpha)) (.f64 4 (/.f64 i alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(-.f64 (+.f64 2 (.f64 2 i)) (.f64 -2 i))
(-.f64 (+.f64 2 (+.f64 (.f64 2 beta) (.f64 2 i))) (*.f64 -2 i))
(-.f64 (+.f64 2 (+.f64 (.f64 2 beta) (.f64 2 i))) (*.f64 -2 i))
(-.f64 (+.f64 2 (+.f64 (.f64 2 beta) (.f64 2 i))) (*.f64 -2 i))
(*.f64 2 beta)
(-.f64 (+.f64 2 (+.f64 (.f64 2 i) (.f64 2 beta))) (*.f64 -2 i))
(-.f64 (+.f64 2 (+.f64 (.f64 2 i) (.f64 2 beta))) (*.f64 -2 i))
(-.f64 (+.f64 2 (+.f64 (.f64 2 i) (.f64 2 beta))) (*.f64 -2 i))
(*.f64 2 beta)
(-.f64 (+.f64 2 (+.f64 (.f64 2 i) (.f64 2 beta))) (*.f64 -2 i))
(-.f64 (+.f64 2 (+.f64 (.f64 2 i) (.f64 2 beta))) (*.f64 -2 i))
(-.f64 (+.f64 2 (+.f64 (.f64 2 i) (.f64 2 beta))) (*.f64 -2 i))
(-.f64 (+.f64 beta 2) (*.f64 -1 beta))
(-.f64 (+.f64 (.f64 4 i) (+.f64 beta 2)) (.f64 -1 beta))
(-.f64 (+.f64 (.f64 4 i) (+.f64 beta 2)) (.f64 -1 beta))
(-.f64 (+.f64 (.f64 4 i) (+.f64 beta 2)) (.f64 -1 beta))
(*.f64 4 i)
(-.f64 (+.f64 beta (+.f64 (.f64 4 i) 2)) (.f64 -1 beta))
(-.f64 (+.f64 beta (+.f64 (.f64 4 i) 2)) (.f64 -1 beta))
(-.f64 (+.f64 beta (+.f64 (.f64 4 i) 2)) (.f64 -1 beta))
(*.f64 4 i)
(-.f64 (+.f64 beta (+.f64 (.f64 4 i) 2)) (.f64 -1 beta))
(-.f64 (+.f64 beta (+.f64 (.f64 4 i) 2)) (.f64 -1 beta))
(-.f64 (+.f64 beta (+.f64 (.f64 4 i) 2)) (.f64 -1 beta))

Outputs
(/.f64 (-.f64 (+.f64 2 (.f64 2 i)) (.f64 -2 i)) alpha)
(/.f64 (+.f64 (+.f64 2 (.f64 2 i)) (.f64 2 i)) alpha)
(/.f64 (fma.f64 i 4 2) alpha)
(-.f64 (+.f64 (.f64 2 (/.f64 i alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (.f64 2 (/.f64 1 alpha)))) (.f64 -2 (/.f64 i alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(-.f64 (+.f64 (.f64 2 (/.f64 i alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (.f64 2 (/.f64 1 alpha)))) (.f64 -2 (/.f64 i alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(-.f64 (+.f64 (.f64 2 (/.f64 i alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (.f64 2 (/.f64 1 alpha)))) (.f64 -2 (/.f64 i alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(*.f64 2 (/.f64 beta alpha))
(*.f64 (/.f64 2 alpha) beta)
(*.f64 beta (/.f64 2 alpha))
(-.f64 (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 beta alpha)))) (.f64 -2 (/.f64 i alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(-.f64 (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 beta alpha)))) (.f64 -2 (/.f64 i alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(-.f64 (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 beta alpha)))) (.f64 -2 (/.f64 i alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(*.f64 2 (/.f64 beta alpha))
(*.f64 (/.f64 2 alpha) beta)
(*.f64 beta (/.f64 2 alpha))
(-.f64 (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 beta alpha)))) (.f64 -2 (/.f64 i alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(-.f64 (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 beta alpha)))) (.f64 -2 (/.f64 i alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(-.f64 (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 beta alpha)))) (.f64 -2 (/.f64 i alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(/.f64 (-.f64 (+.f64 beta 2) (*.f64 -1 beta)) alpha)
(/.f64 (-.f64 (+.f64 2 beta) (neg.f64 beta)) alpha)
(/.f64 (+.f64 beta (+.f64 2 beta)) alpha)
(/.f64 (fma.f64 2 beta 2) alpha)
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 4 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 4 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 4 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(*.f64 4 (/.f64 i alpha))
(*.f64 (/.f64 i alpha) 4)
(*.f64 i (/.f64 4 alpha))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 1 alpha)) (.f64 4 (/.f64 i alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 1 alpha)) (.f64 4 (/.f64 i alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 1 alpha)) (.f64 4 (/.f64 i alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(*.f64 4 (/.f64 i alpha))
(*.f64 (/.f64 i alpha) 4)
(*.f64 i (/.f64 4 alpha))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 1 alpha)) (.f64 4 (/.f64 i alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 1 alpha)) (.f64 4 (/.f64 i alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(-.f64 (+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 1 alpha)) (.f64 4 (/.f64 i alpha)))) (*.f64 -1 (/.f64 beta alpha)))
(+.f64 (fma.f64 2 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha))) (*.f64 2 (/.f64 i alpha)))
(fma.f64 2 (/.f64 i alpha) (fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 beta alpha)) (/.f64 2 alpha)))
(+.f64 (*.f64 (/.f64 i alpha) 4) (/.f64 (fma.f64 2 beta 2) alpha))
(fma.f64 (/.f64 i alpha) 4 (/.f64 (fma.f64 2 beta 2) alpha))
(-.f64 (+.f64 2 (.f64 2 i)) (.f64 -2 i))
(+.f64 (+.f64 2 (.f64 2 i)) (.f64 2 i))
(fma.f64 i 4 2)
(-.f64 (+.f64 2 (+.f64 (.f64 2 beta) (.f64 2 i))) (*.f64 -2 i))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(-.f64 (+.f64 2 (+.f64 (.f64 2 beta) (.f64 2 i))) (*.f64 -2 i))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(-.f64 (+.f64 2 (+.f64 (.f64 2 beta) (.f64 2 i))) (*.f64 -2 i))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(*.f64 2 beta)
(+.f64 beta beta)
(-.f64 (+.f64 2 (+.f64 (.f64 2 i) (.f64 2 beta))) (*.f64 -2 i))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(-.f64 (+.f64 2 (+.f64 (.f64 2 i) (.f64 2 beta))) (*.f64 -2 i))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(-.f64 (+.f64 2 (+.f64 (.f64 2 i) (.f64 2 beta))) (*.f64 -2 i))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(*.f64 2 beta)
(+.f64 beta beta)
(-.f64 (+.f64 2 (+.f64 (.f64 2 i) (.f64 2 beta))) (*.f64 -2 i))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(-.f64 (+.f64 2 (+.f64 (.f64 2 i) (.f64 2 beta))) (*.f64 -2 i))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(-.f64 (+.f64 2 (+.f64 (.f64 2 i) (.f64 2 beta))) (*.f64 -2 i))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(-.f64 (+.f64 beta 2) (*.f64 -1 beta))
(-.f64 (+.f64 2 beta) (neg.f64 beta))
(+.f64 beta (+.f64 2 beta))
(fma.f64 2 beta 2)
(-.f64 (+.f64 (.f64 4 i) (+.f64 beta 2)) (.f64 -1 beta))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(-.f64 (+.f64 (.f64 4 i) (+.f64 beta 2)) (.f64 -1 beta))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(-.f64 (+.f64 (.f64 4 i) (+.f64 beta 2)) (.f64 -1 beta))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(*.f64 4 i)
(*.f64 i 4)
(-.f64 (+.f64 beta (+.f64 (.f64 4 i) 2)) (.f64 -1 beta))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(-.f64 (+.f64 beta (+.f64 (.f64 4 i) 2)) (.f64 -1 beta))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(-.f64 (+.f64 beta (+.f64 (.f64 4 i) 2)) (.f64 -1 beta))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(*.f64 4 i)
(*.f64 i 4)
(-.f64 (+.f64 beta (+.f64 (.f64 4 i) 2)) (.f64 -1 beta))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(-.f64 (+.f64 beta (+.f64 (.f64 4 i) 2)) (.f64 -1 beta))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))
(-.f64 (+.f64 beta (+.f64 (.f64 4 i) 2)) (.f64 -1 beta))
(+.f64 2 (-.f64 (.f64 2 (+.f64 i beta)) (.f64 i -2)))
(+.f64 2 (+.f64 (.f64 2 beta) (.f64 i 4)))
(fma.f64 i 4 (fma.f64 2 beta 2))

eval58.0ms (1%)

Compiler: Compiled 2635 to 1830 computations (30.6% saved)

prune98.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	116	4	120

Error

0.1b

Counts

120 → 4

Alt Table

Click to see full alt table

Status	Error	Program
	49.4b	(/.f64 (+.f64 (+.f64 (-.f64 (/.f64 beta alpha) (.f64 (/.f64 (fma.f64 2 i beta) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha))) (-.f64 (fma.f64 2 (/.f64 i alpha) (-.f64 (/.f64 2 alpha) (.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha)))) (*.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha)))) (/.f64 (fma.f64 2 i beta) alpha)) 2)
	48.6b	(/.f64 (/.f64 (fma.f64 (sqrt.f64 (+.f64 beta (fma.f64 2 i 2))) (sqrt.f64 (+.f64 beta (fma.f64 2 i 2))) (fma.f64 2 i beta)) alpha) 2)
✓	13.5b	(/.f64 (fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)
▶	48.5b	(/.f64 (+.f64 (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha) (/.f64 (fma.f64 2 i beta) alpha)) 2)

Compiler

Compiled 267 to 179 computations (33% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha)
✓	0.0b	(/.f64 (fma.f64 2 i beta) alpha)
✓	0.0b	(+.f64 (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha) (/.f64 (fma.f64 2 i beta) alpha))

series15.0ms (0.3%)

Counts

3 → 108

Calls

27 calls:

Time	Variable		Point	Expression
2.0ms	alpha	@	-inf	(/.f64 (fma.f64 2 i beta) alpha)
1.0ms	alpha	@	0	(+.f64 (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha) (/.f64 (fma.f64 2 i beta) alpha))
1.0ms	beta	@	0	(+.f64 (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha) (/.f64 (fma.f64 2 i beta) alpha))
1.0ms	alpha	@	inf	(+.f64 (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha) (/.f64 (fma.f64 2 i beta) alpha))
1.0ms	i	@	-inf	(+.f64 (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha) (/.f64 (fma.f64 2 i beta) alpha))

rewrite68.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

310×	`fma-neg_binary64`
241×	`expm1-udef_binary64`
241×	`log1p-udef_binary64`
136×	`add-sqr-sqrt_binary64`
133×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	254	40
2	3957	40

Stop Event

1×	node limit

Counts

3 → 124

Calls

Call 1

Inputs
(+.f64 (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha) (/.f64 (fma.f64 2 i beta) alpha))
(/.f64 (fma.f64 2 i beta) alpha)
(/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha)

Outputs

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

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

617×	`div-sub_binary64`
489×	`fma-neg_binary64`
247×	`fma-def_binary64`
220×	`sub-neg_binary64`
208×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	44	1550
1	113	1464
2	269	1428
3	620	1428
4	1805	1139
5	4613	1139

Stop Event

1×	node limit

Counts

232 → 152

Calls

Call 1

Inputs
(+.f64 (.f64 4 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha)))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (*.f64 4 (/.f64 i alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (*.f64 4 (/.f64 i alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (*.f64 4 (/.f64 i alpha))))
(*.f64 2 (/.f64 beta alpha))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 4 (/.f64 i alpha)) (*.f64 2 (/.f64 beta alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 4 (/.f64 i alpha)) (*.f64 2 (/.f64 beta alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 4 (/.f64 i alpha)) (*.f64 2 (/.f64 beta alpha))))
(*.f64 2 (/.f64 beta alpha))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 4 (/.f64 i alpha)) (*.f64 2 (/.f64 beta alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 4 (/.f64 i alpha)) (*.f64 2 (/.f64 beta alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 4 (/.f64 i alpha)) (*.f64 2 (/.f64 beta alpha))))
(+.f64 (.f64 2 (/.f64 beta alpha)) (.f64 2 (/.f64 1 alpha)))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 4 (/.f64 i alpha)) (*.f64 2 (/.f64 beta alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 4 (/.f64 i alpha)) (*.f64 2 (/.f64 beta alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 4 (/.f64 i alpha)) (*.f64 2 (/.f64 beta alpha))))
(*.f64 4 (/.f64 i alpha))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (*.f64 4 (/.f64 i alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (*.f64 4 (/.f64 i alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (*.f64 4 (/.f64 i alpha))))
(*.f64 4 (/.f64 i alpha))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (*.f64 4 (/.f64 i alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (*.f64 4 (/.f64 i alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (*.f64 4 (/.f64 i alpha))))
(/.f64 (+.f64 (.f64 4 i) (+.f64 2 (.f64 2 beta))) alpha)
(/.f64 (+.f64 (.f64 4 i) (+.f64 2 (.f64 2 beta))) alpha)
(/.f64 (+.f64 (.f64 4 i) (+.f64 2 (.f64 2 beta))) alpha)
(/.f64 (+.f64 (.f64 4 i) (+.f64 2 (.f64 2 beta))) alpha)
(/.f64 (+.f64 (.f64 4 i) (+.f64 2 (.f64 2 beta))) alpha)
(/.f64 (+.f64 (.f64 4 i) (+.f64 2 (.f64 2 beta))) alpha)
(/.f64 (+.f64 (.f64 4 i) (+.f64 2 (.f64 2 beta))) alpha)
(/.f64 (+.f64 (.f64 4 i) (+.f64 2 (.f64 2 beta))) alpha)
(.f64 -1 (/.f64 (+.f64 (.f64 -1 (+.f64 beta (.f64 2 i))) (.f64 -1 (+.f64 beta (+.f64 2 (*.f64 2 i))))) alpha))
(.f64 -1 (/.f64 (+.f64 (.f64 -1 (+.f64 beta (.f64 2 i))) (.f64 -1 (+.f64 beta (+.f64 2 (*.f64 2 i))))) alpha))
(.f64 -1 (/.f64 (+.f64 (.f64 -1 (+.f64 beta (.f64 2 i))) (.f64 -1 (+.f64 beta (+.f64 2 (*.f64 2 i))))) alpha))
(.f64 -1 (/.f64 (+.f64 (.f64 -1 (+.f64 beta (.f64 2 i))) (.f64 -1 (+.f64 beta (+.f64 2 (*.f64 2 i))))) alpha))
(/.f64 beta alpha)
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(*.f64 2 (/.f64 i alpha))
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(*.f64 2 (/.f64 i alpha))
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(*.f64 2 (/.f64 i alpha))
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(/.f64 beta alpha)
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(/.f64 beta alpha)
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(+.f64 (/.f64 beta alpha) (*.f64 2 (/.f64 i alpha)))
(/.f64 (+.f64 beta (*.f64 2 i)) alpha)
(/.f64 (+.f64 beta (*.f64 2 i)) alpha)
(/.f64 (+.f64 beta (*.f64 2 i)) alpha)
(/.f64 (+.f64 beta (*.f64 2 i)) alpha)
(/.f64 (+.f64 beta (*.f64 2 i)) alpha)
(/.f64 (+.f64 beta (*.f64 2 i)) alpha)
(/.f64 (+.f64 beta (*.f64 2 i)) alpha)
(/.f64 (+.f64 beta (*.f64 2 i)) alpha)
(/.f64 (+.f64 beta (*.f64 2 i)) alpha)
(/.f64 (+.f64 beta (*.f64 2 i)) alpha)
(/.f64 (+.f64 beta (*.f64 2 i)) alpha)
(/.f64 (+.f64 beta (*.f64 2 i)) alpha)
(/.f64 (+.f64 2 (*.f64 2 i)) alpha)
(+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha))))
(+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha))))
(+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha))))
(/.f64 beta alpha)
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(/.f64 beta alpha)
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(/.f64 (+.f64 beta 2) alpha)
(+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha))))
(+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha))))
(+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha))))
(*.f64 2 (/.f64 i alpha))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(*.f64 2 (/.f64 i alpha))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)

Outputs
(+.f64 (.f64 4 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha)))
(fma.f64 4 (/.f64 i alpha) (/.f64 2 alpha))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (*.f64 4 (/.f64 i alpha))))
(+.f64 (/.f64 2 alpha) (fma.f64 4 (/.f64 i alpha) (*.f64 2 (/.f64 beta alpha))))
(+.f64 (*.f64 4 (/.f64 i alpha)) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha)))
(fma.f64 4 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha)))
(fma.f64 4 (/.f64 i alpha) (*.f64 (+.f64 1 beta) (/.f64 2 alpha)))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (*.f64 4 (/.f64 i alpha))))
(+.f64 (/.f64 2 alpha) (fma.f64 4 (/.f64 i alpha) (*.f64 2 (/.f64 beta alpha))))
(+.f64 (*.f64 4 (/.f64 i alpha)) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha)))
(fma.f64 4 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha)))
(fma.f64 4 (/.f64 i alpha) (*.f64 (+.f64 1 beta) (/.f64 2 alpha)))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (*.f64 4 (/.f64 i alpha))))
(+.f64 (/.f64 2 alpha) (fma.f64 4 (/.f64 i alpha) (*.f64 2 (/.f64 beta alpha))))
(+.f64 (*.f64 4 (/.f64 i alpha)) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha)))
(fma.f64 4 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 2 alpha)))
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(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(/.f64 beta alpha)
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(/.f64 (+.f64 beta 2) alpha)
(/.f64 (+.f64 2 beta) alpha)
(+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha))))
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha))))
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(+.f64 (/.f64 beta alpha) (+.f64 (.f64 2 (/.f64 i alpha)) (.f64 2 (/.f64 1 alpha))))
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(*.f64 2 (/.f64 i alpha))
(*.f64 (/.f64 i alpha) 2)
(/.f64 (*.f64 i 2) alpha)
(*.f64 i (/.f64 2 alpha))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(*.f64 2 (/.f64 i alpha))
(*.f64 (/.f64 i alpha) 2)
(/.f64 (*.f64 i 2) alpha)
(*.f64 i (/.f64 2 alpha))
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (/.f64 beta alpha) (.f64 2 (/.f64 i alpha))))
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)
(/.f64 (+.f64 beta (+.f64 2 (*.f64 2 i))) alpha)
(+.f64 (/.f64 beta alpha) (fma.f64 2 (/.f64 i alpha) (/.f64 2 alpha)))
(fma.f64 2 (+.f64 (/.f64 i alpha) (/.f64 1 alpha)) (/.f64 beta alpha))
(+.f64 (/.f64 2 alpha) (fma.f64 (/.f64 i alpha) 2 (/.f64 beta alpha)))
(/.f64 (+.f64 beta (fma.f64 i 2 2)) alpha)

eval81.0ms (1.4%)

Compiler: Compiled 3577 to 2395 computations (33% saved)

prune103.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	152	4	156

Error

0.1b

Counts

156 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	13.5b	(/.f64 (fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)
	48.6b	(/.f64 (fma.f64 (sqrt.f64 (/.f64 (+.f64 (fma.f64 2 i beta) 2) alpha)) (sqrt.f64 (/.f64 (+.f64 (fma.f64 2 i beta) 2) alpha)) (/.f64 (fma.f64 2 i beta) alpha)) 2)
	49.4b	(/.f64 (+.f64 (+.f64 (-.f64 (/.f64 beta alpha) (.f64 (/.f64 (fma.f64 2 i beta) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha))) (-.f64 (fma.f64 2 (/.f64 i alpha) (-.f64 (/.f64 2 alpha) (.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha)))) (*.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha)))) (/.f64 (fma.f64 2 i beta) alpha)) 2)
✓	48.5b	(/.f64 (+.f64 (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha) (/.f64 (fma.f64 2 i beta) alpha)) 2)

Compiler

Compiled 153 to 102 computations (33.3% saved)

regimes72.0ms (1.2%)

Accuracy

Total -62.2b remaining (-4003.2%)

Threshold costs -62.2b (-4003.2%)

Counts

9 → 2

Calls

Call 1

Inputs
(/.f64 (fma.f64 (sqrt.f64 (/.f64 (+.f64 (fma.f64 2 i beta) 2) alpha)) (sqrt.f64 (/.f64 (+.f64 (fma.f64 2 i beta) 2) alpha)) (/.f64 (fma.f64 2 i beta) alpha)) 2)
(/.f64 (/.f64 (fma.f64 (sqrt.f64 (+.f64 beta (fma.f64 2 i 2))) (sqrt.f64 (+.f64 beta (fma.f64 2 i 2))) (fma.f64 2 i beta)) alpha) 2)
(/.f64 (+.f64 (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha) (/.f64 (fma.f64 2 i beta) alpha)) 2)
(/.f64 (+.f64 (+.f64 (-.f64 (/.f64 beta alpha) (.f64 (/.f64 (fma.f64 2 i beta) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha))) (-.f64 (fma.f64 2 (/.f64 i alpha) (-.f64 (/.f64 2 alpha) (.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha)))) (*.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha)))) (/.f64 (fma.f64 2 i beta) alpha)) 2)
(/.f64 (+.f64 (+.f64 (-.f64 (/.f64 beta alpha) (.f64 (/.f64 (fma.f64 2 i beta) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha))) (-.f64 (fma.f64 2 (/.f64 i alpha) (-.f64 (/.f64 2 alpha) (.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha)))) (*.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha)))) (/.f64 (fma.f64 2 i beta) alpha)) 2)
(/.f64 (fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)
(/.f64 (/.f64 (-.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) (.f64 -1 (+.f64 beta (*.f64 2 i)))) alpha) 2)
(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)
(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)

Outputs

(/.f64 (+.f64 (+.f64 (-.f64 (/.f64 beta alpha) (*.f64 (/.f64 (fma.f64 2 i beta) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha))) (-.f64 (fma.f64 2 (/.f64 i alpha) (-.f64 (/.f64 2 alpha) (*.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha)))) (*.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha)))) (/.f64 (fma.f64 2 i beta) alpha)) 2)

(/.f64 (fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)

Results

Time	Error	Segments	Branch
21.0ms	5.1b	4	`alpha`
6.0ms	13.5b	1	`beta`
7.0ms	13.5b	1	`i`
4.0ms	1.6b	2	`(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)`
4.0ms	1.6b	2	`(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)`
7.0ms	1.6b	2	`(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))`
6.0ms	13.5b	1	`(*.f64 2 i)`
9.0ms	13.5b	1	`(*.f64 2 i)`

Compiler

Compiled 424 to 265 computations (37.5% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Point		Range
0.0ms	-0.5	∈ [	-0.9999999999999999	,	-0.00030200273719058115	]

Compiler

Compiled 38 to 25 computations (34.2% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

27×	`+-commutative_binary64`
18×	`*-commutative_binary64`
17×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	182
1	82	182
2	117	182
3	141	182
4	164	182
5	178	182
6	182	182
7	183	182

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) -2147483648/4294967296) (/.f64 (+.f64 (+.f64 (-.f64 (/.f64 beta alpha) (*.f64 (/.f64 (fma.f64 2 i beta) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha))) (-.f64 (fma.f64 2 (/.f64 i alpha) (-.f64 (/.f64 2 alpha) (*.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha)))) (*.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha)))) (/.f64 (fma.f64 2 i beta) alpha)) 2) (/.f64 (fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2))

Outputs

(if (<=.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) -2147483648/4294967296) (/.f64 (+.f64 (+.f64 (-.f64 (/.f64 beta alpha) (*.f64 (/.f64 (fma.f64 2 i beta) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha))) (-.f64 (fma.f64 2 (/.f64 i alpha) (-.f64 (/.f64 2 alpha) (*.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha)))) (*.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha)))) (/.f64 (fma.f64 2 i beta) alpha)) 2) (/.f64 (fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2))

(if (<=.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) -1/2) (/.f64 (+.f64 (/.f64 (fma.f64 2 i beta) alpha) (+.f64 (-.f64 (/.f64 beta alpha) (*.f64 (/.f64 (fma.f64 2 i beta) alpha) (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha))) (-.f64 (fma.f64 2 (/.f64 i alpha) (-.f64 (/.f64 2 alpha) (*.f64 (/.f64 (+.f64 beta (fma.f64 2 i beta)) alpha) (/.f64 (fma.f64 2 i 2) alpha)))) (*.f64 (/.f64 (fma.f64 2 i 2) alpha) (/.f64 (+.f64 beta (fma.f64 2 i 2)) alpha))))) 2) (/.f64 (fma.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2))

end58.0ms (1%)

Stop Event

1×

fuel

Compiler

Compiled 256 to 156 computations (39.1% saved)

Details

analyze505.0ms (8.6%)

sample2.0s (33.8%)

preprocess29.0ms (0.5%)

simplify28.0ms (0.5%)

eval1.0ms (0%)

prune3.0ms (0.1%)

localize16.0ms (0.3%)

series43.0ms (0.7%)

rewrite42.0ms (0.7%)

simplify106.0ms (1.8%)

eval282.0ms (4.8%)

prune785.0ms (13.4%)

localize20.0ms (0.3%)

series18.0ms (0.3%)

rewrite40.0ms (0.7%)

simplify118.0ms (2%)

eval272.0ms (4.6%)

prune812.0ms (13.8%)

localize10.0ms (0.2%)

series13.0ms (0.2%)

rewrite38.0ms (0.7%)

simplify61.0ms (1%)

eval58.0ms (1%)

prune98.0ms (1.7%)

localize11.0ms (0.2%)

series15.0ms (0.3%)

rewrite68.0ms (1.2%)

simplify66.0ms (1.1%)

eval81.0ms (1.4%)

prune103.0ms (1.8%)

regimes72.0ms (1.2%)

bsearch0.0ms (0%)

simplify9.0ms (0.2%)

end58.0ms (1%)

Profiling