Details

analyze2.3s (14.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample106.0ms (0.7%)

Algorithm

1×

intervals

Results

38.0ms	453×	body	128	nan
26.0ms	256×	body	128	valid
4.0ms	44×	body	128	invalid

Compiler

Compiled 75 to 53 computations (29.3% saved)

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

716×	`neg-sub0_binary64`
716×	`neg-mul-1_binary64`
377×	`distribute-rgt-neg-out_binary64`
358×	`cancel-sign-sub-inv_binary64`
354×	`distribute-lft-neg-out_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	42
1	58	42
2	180	42
3	719	39
4	2459	39
5	3995	39
6	5181	39

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

33.2b

Counts

2 → 2

Alt Table

Status	Error	Program
	37.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
▶	34.9b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))

Status

Error

Program

37.0b

(sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (-.f64 (-.f64 t (*.f64 2 (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*)))))

▶

34.9b

(sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (+.f64 (*.f64 l -2) (*.f64 (/.f64 l Om) (*.f64 n (-.f64 U* U))))))))

Compiler

Compiled 164 to 106 computations (35.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.6b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.7b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
11.7b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
19.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))

rewrite374.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

23.8b

Rules

30×	`add-cbrt-cube_binary64`
30×	`add-exp-log_binary64`
30×	`pow1_binary64`
29×	`add-sqr-sqrt_binary64`
27×	`associate-l_binary64`

Counts

4 → 131

Calls

4 calls:

13.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
12.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
11.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))

Compiler

Compiled 4890 to 1897 computations (61.2% saved)

series1.1s (7%)

Error

18.9b

Counts

4 → 111

Calls

4 calls:

453.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
326.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))
180.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
74.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 10413 to 7360 computations (29.3% saved)

simplify237.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

630×	`*-commutative_binary64`
242×	`associate-*l/_binary64`
230×	`associate-/l*_binary64`
220×	`distribute-rgt-in_binary64`
208×	`associate-*r/_binary64`

Counts

242 → 223

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	529	8427
1	1615	7939
2	4268	7717
3	4914	7717
4	5040	7717

prune257.0ms (1.6%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	199	24	223
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	199	26	225

Error

15.1b

Counts

225 → 26

Alt Table

Status	Error	Program
	38.9b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (/.f64 (+.f64 (.f64 (-.f64 U* U) (/.f64 n Om)) -2) (/.f64 Om (*.f64 l l))))))
	37.2b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))))
	59.9b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U* U))) (/.f64 Om (/.f64 (*.f64 U n) Om)))))
	58.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))) (*.f64 (sqrt.f64 2) l)))
	37.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
	58.2b	(sqrt.f64 (.f64 2 (.f64 (.f64 (.f64 l l) n) (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om)))))))
	61.6b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))
	35.6b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2)))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (*.f64 l -2))))))))
	42.2b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))) 3))
	59.9b	(.f64 (sqrt.f64 (.f64 (.f64 U n) (.f64 (.f64 l l) (.f64 n (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
	42.9b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 t (*.f64 U n))))
	35.7b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) 1) (.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)) (/.f64 (cbrt.f64 l) Om))))))
	40.8b	(sqrt.f64 (-.f64 (.f64 2 (.f64 t (.f64 U n))) (.f64 4 (/.f64 (.f64 U (.f64 (*.f64 l l) n)) Om))))
	35.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (*.f64 l -2))))))))
	57.3b	(.f64 (sqrt.f64 (.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))) (*.f64 (sqrt.f64 2) l))
✓	34.9b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))
	61.4b	(.f64 (.f64 (sqrt.f64 2) n) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om))))))
	49.7b	(sqrt.f64 (.f64 (.f64 (.f64 U (.f64 2 n)) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2)))))) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))))
	62.2b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (.f64 U (.f64 2 n))) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (*.f64 l -2)))))))
	46.2b	(.f64 (sqrt.f64 (.f64 U (.f64 2 n))) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
	44.7b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 t (.f64 U n)))) (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om) (sqrt.f64 (/.f64 (*.f64 U n) t))))
	62.7b	(neg.f64 (.f64 U (sqrt.f64 (.f64 -2 (/.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 Om Om))))))
▶	30.7b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))
	43.2b	(sqrt.f64 (.f64 2 (.f64 U (.f64 n (-.f64 t (+.f64 (/.f64 (.f64 U (.f64 (.f64 l l) n)) (.f64 Om Om)) (.f64 2 (/.f64 (*.f64 l l) Om))))))))
	57.9b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))) (.f64 (sqrt.f64 2) l)) (.f64 1/2 (.f64 (/.f64 (.f64 t (sqrt.f64 2)) l) (sqrt.f64 (/.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))))))
	36.9b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (/.f64 (.f64 l (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))) Om))))

Compiler

Compiled 6141 to 2790 computations (54.6% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
5.8b	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
6.5b	(/.f64 (.f64 l (-.f64 U U)) Om)
19.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))

rewrite201.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

11.9b

Rules

31×	`pow1_binary64`
30×	`add-cbrt-cube_binary64`
30×	`add-exp-log_binary64`
17×	`pow-prod-down_binary64`
13×	`cbrt-unprod_binary64`

Counts

4 → 94

Calls

4 calls:

9.0ms	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
9.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
8.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))

Compiler

Compiled 3311 to 1331 computations (59.8% saved)

series967.0ms (6.1%)

Error

14.4b

Counts

4 → 102

Calls

4 calls:

449.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
320.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))
72.0ms	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
50.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)

Compiler

Compiled 9659 to 6777 computations (29.8% saved)

simplify199.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

594×	`associate-r_binary64`
514×	`associate-l_binary64`
210×	`associate-/l*_binary64`
174×	`associate-*r/_binary64`
171×	`*-commutative_binary64`

Counts

196 → 142

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	418	6565
1	1189	5920
2	4723	5920
3	4946	5920
4	4981	5920

prune126.0ms (0.8%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	3	21	24
Picked	1	0	1
Done	0	1	1
Total	143	25	168

Error

13.8b

Counts

168 → 25

Alt Table

Status	Error	Program
	37.2b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))))
	59.9b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U* U))) (/.f64 Om (/.f64 (*.f64 U n) Om)))))
	58.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))) (*.f64 (sqrt.f64 2) l)))
	37.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
	58.2b	(sqrt.f64 (.f64 2 (.f64 (.f64 (.f64 l l) n) (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om)))))))
	54.3b	(/.f64 (sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 (pow.f64 t 3) (pow.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2))) 3))))) (sqrt.f64 (+.f64 (.f64 t t) (.f64 (/.f64 l Om) (.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2)) (-.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))) t))))))
▶	33.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (neg.f64 (/.f64 (.f64 U l) Om))) (*.f64 l -2)))))))
	61.6b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))
	35.6b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2)))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (*.f64 l -2))))))))
	60.8b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U* U))) (/.f64 (.f64 Om Om) (.f64 U n)))))
	42.2b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))) 3))
	59.9b	(.f64 (sqrt.f64 (.f64 (.f64 U n) (.f64 (.f64 l l) (.f64 n (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
	42.9b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 t (*.f64 U n))))
	35.7b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) 1) (.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)) (/.f64 (cbrt.f64 l) Om))))))
	40.8b	(sqrt.f64 (-.f64 (.f64 2 (.f64 t (.f64 U n))) (.f64 4 (/.f64 (.f64 U (.f64 (*.f64 l l) n)) Om))))
	57.3b	(.f64 (sqrt.f64 (.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))) (*.f64 (sqrt.f64 2) l))
✓	34.9b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))
	61.4b	(.f64 (.f64 (sqrt.f64 2) n) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om))))))
	49.7b	(sqrt.f64 (.f64 (.f64 (.f64 U (.f64 2 n)) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2)))))) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))))
	62.2b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (.f64 U (.f64 2 n))) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (*.f64 l -2)))))))
	46.2b	(.f64 (sqrt.f64 (.f64 U (.f64 2 n))) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
	44.7b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 t (.f64 U n)))) (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om) (sqrt.f64 (/.f64 (*.f64 U n) t))))
	43.2b	(sqrt.f64 (.f64 2 (.f64 U (.f64 n (-.f64 t (+.f64 (/.f64 (.f64 U (.f64 (.f64 l l) n)) (.f64 Om Om)) (.f64 2 (/.f64 (*.f64 l l) Om))))))))
	57.9b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))) (.f64 (sqrt.f64 2) l)) (.f64 1/2 (.f64 (/.f64 (.f64 t (sqrt.f64 2)) l) (sqrt.f64 (/.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))))))
	36.9b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (/.f64 (.f64 l (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))) Om))))

Compiler

Compiled 3668 to 1845 computations (49.7% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.1b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (neg.f64 (/.f64 (.f64 U l) Om))) (*.f64 l -2))))))
6.1b	(.f64 n (neg.f64 (/.f64 (.f64 U l) Om)))
6.4b	(/.f64 (*.f64 U l) Om)
15.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (neg.f64 (/.f64 (.f64 U l) Om))) (*.f64 l -2)))))))

rewrite196.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

11.9b

Rules

31×	`pow1_binary64`
23×	`add-cbrt-cube_binary64`
23×	`add-exp-log_binary64`
19×	`associate-r_binary64`
17×	`pow-prod-down_binary64`

Counts

4 → 100

Calls

4 calls:

9.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (neg.f64 (/.f64 (.f64 U l) Om))) (*.f64 l -2))))))
8.0ms	(.f64 n (neg.f64 (/.f64 (.f64 U l) Om)))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (neg.f64 (/.f64 (.f64 U l) Om))) (*.f64 l -2)))))))
5.0ms	(/.f64 (*.f64 U l) Om)

Compiler

Compiled 3284 to 1416 computations (56.9% saved)

series537.0ms (3.4%)

Error

13.5b

Counts

4 → 73

Calls

4 calls:

259.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (neg.f64 (/.f64 (.f64 U l) Om))) (*.f64 l -2))))))
168.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (neg.f64 (/.f64 (.f64 U l) Om))) (*.f64 l -2)))))))
46.0ms	(.f64 n (neg.f64 (/.f64 (.f64 U l) Om)))
28.0ms	(/.f64 (*.f64 U l) Om)

Compiler

Compiled 5484 to 4011 computations (26.9% saved)

simplify162.0ms (1%)

Algorithm

1×	egg-herbie

Rules

521×	`associate-r_binary64`
476×	`associate-l_binary64`
271×	`*-commutative_binary64`
205×	`distribute-neg-frac_binary64`
161×	`log-prod_binary64`

Counts

173 → 123

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	324	4848
1	904	4241
2	3784	4241
3	4895	4241
4	4967	4241

prune147.0ms (0.9%)

Pruning

28 alts after pruning (26 fresh and 2 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	3	20	23
Picked	0	1	1
Done	0	1	1
Total	120	28	148

Error

11.6b

Counts

148 → 28

Alt Table

Status	Error	Program
	59.9b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U* U))) (/.f64 Om (/.f64 (*.f64 U n) Om)))))
	58.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))) (*.f64 (sqrt.f64 2) l)))
	37.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
	58.2b	(sqrt.f64 (.f64 2 (.f64 (.f64 (.f64 l l) n) (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om)))))))
	54.3b	(/.f64 (sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 (pow.f64 t 3) (pow.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2))) 3))))) (sqrt.f64 (+.f64 (.f64 t t) (.f64 (/.f64 l Om) (.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2)) (-.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))) t))))))
✓	33.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (neg.f64 (/.f64 (.f64 U l) Om))) (*.f64 l -2)))))))
	61.6b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))
	35.4b	(sqrt.f64 (exp.f64 (log.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (*.f64 U l) Om))))))))))
	35.6b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2)))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (*.f64 l -2))))))))
	60.8b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U* U))) (/.f64 (.f64 Om Om) (.f64 U n)))))
	59.9b	(.f64 (sqrt.f64 (.f64 (.f64 U n) (.f64 (.f64 l l) (.f64 n (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
	42.9b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 t (*.f64 U n))))
	35.7b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) 1) (.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)) (/.f64 (cbrt.f64 l) Om))))))
	40.8b	(sqrt.f64 (-.f64 (.f64 2 (.f64 t (.f64 U n))) (.f64 4 (/.f64 (.f64 U (.f64 (*.f64 l l) n)) Om))))
	57.3b	(.f64 (sqrt.f64 (.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))) (*.f64 (sqrt.f64 2) l))
	44.0b	(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (*.f64 U l) Om))))))))
✓	34.9b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))
	61.4b	(.f64 (.f64 (sqrt.f64 2) n) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om))))))
	58.4b	(/.f64 (sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (.f64 t t) (.f64 (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (.f64 U l) Om)))) (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (.f64 U l) Om))))))))) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (*.f64 U l) Om)))))))
▶	35.4b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (*.f64 U l) Om))))))))))
	49.7b	(sqrt.f64 (.f64 (.f64 (.f64 U (.f64 2 n)) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2)))))) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))))
	62.2b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (.f64 U (.f64 2 n))) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (*.f64 l -2)))))))
	46.2b	(.f64 (sqrt.f64 (.f64 U (.f64 2 n))) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
	44.7b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 t (.f64 U n)))) (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om) (sqrt.f64 (/.f64 (*.f64 U n) t))))
	57.9b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))) (.f64 (sqrt.f64 2) l)) (.f64 1/2 (.f64 (/.f64 (.f64 t (sqrt.f64 2)) l) (sqrt.f64 (/.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))))))
	59.0b	(neg.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 U (.f64 n (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om)))))) (.f64 (sqrt.f64 2) l)))
	36.9b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (/.f64 (.f64 l (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))) Om))))
	39.6b	(sqrt.f64 (.f64 U (-.f64 (.f64 2 (.f64 t n)) (.f64 4 (/.f64 (.f64 (.f64 l l) n) Om)))))

Compiler

Compiled 3967 to 2079 computations (47.6% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.1b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (*.f64 U l) Om)))))))
6.1b	(.f64 n (/.f64 (.f64 U l) Om))
6.4b	(/.f64 (*.f64 U l) Om)
15.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (*.f64 U l) Om))))))))

rewrite308.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

11.6b

Rules

31×	`pow1_binary64`
30×	`add-cbrt-cube_binary64`
30×	`add-exp-log_binary64`
17×	`pow-prod-down_binary64`
13×	`cbrt-unprod_binary64`

Counts

4 → 92

Calls

4 calls:

12.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (*.f64 U l) Om)))))))
7.0ms	(.f64 n (/.f64 (.f64 U l) Om))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (*.f64 U l) Om))))))))
5.0ms	(/.f64 (*.f64 U l) Om)

Compiler

Compiled 3131 to 1451 computations (53.7% saved)

series544.0ms (3.4%)

Error

11.6b

Counts

4 → 73

Calls

4 calls:

260.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (*.f64 U l) Om)))))))
173.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (*.f64 U l) Om))))))))
46.0ms	(.f64 n (/.f64 (.f64 U l) Om))
29.0ms	(/.f64 (*.f64 U l) Om)

Compiler

Compiled 5713 to 4240 computations (25.8% saved)

simplify129.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

934×	`distribute-rgt-in_binary64`
497×	`associate-r_binary64`
449×	`associate-l_binary64`
255×	`*-commutative_binary64`
208×	`distribute-rgt-neg-in_binary64`

Counts

165 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	304	4633
1	847	4094
2	3427	4076
3	6354	4076

prune82.0ms (0.5%)

Pruning

29 alts after pruning (27 fresh and 2 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	1	24	25
Picked	1	0	1
Done	0	2	2
Total	102	29	131

Error

11.6b

Counts

131 → 29

Alt Table

Status	Error	Program
	59.9b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U* U))) (/.f64 Om (/.f64 (*.f64 U n) Om)))))
	58.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))) (*.f64 (sqrt.f64 2) l)))
	59.4b	(exp.f64 (log.f64 (neg.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 U (.f64 n (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om)))))) (.f64 (sqrt.f64 2) l)))))
	37.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
	58.2b	(sqrt.f64 (.f64 2 (.f64 (.f64 (.f64 l l) n) (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om)))))))
	44.1b	(exp.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 t (*.f64 U n))))))
	54.3b	(/.f64 (sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 (pow.f64 t 3) (pow.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2))) 3))))) (sqrt.f64 (+.f64 (.f64 t t) (.f64 (/.f64 l Om) (.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2)) (-.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))) t))))))
	33.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (neg.f64 (/.f64 (.f64 U l) Om))) (*.f64 l -2)))))))
	61.6b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))
	35.4b	(sqrt.f64 (exp.f64 (log.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (*.f64 U l) Om))))))))))
	35.6b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2)))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (*.f64 l -2))))))))
	60.8b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (.f64 l l) (.f64 n (-.f64 U* U))) (/.f64 (.f64 Om Om) (.f64 U n)))))
	59.9b	(.f64 (sqrt.f64 (.f64 (.f64 U n) (.f64 (.f64 l l) (.f64 n (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
	39.0b	(exp.f64 (log.f64 (sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (.f64 U (.f64 l l)) Om)))))))
	42.9b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 t (*.f64 U n))))
	35.7b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) 1) (.f64 (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)) (/.f64 (cbrt.f64 l) Om))))))
	57.3b	(.f64 (sqrt.f64 (.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))) (*.f64 (sqrt.f64 2) l))
	44.0b	(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (*.f64 U l) Om))))))))
	34.9b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))
	61.4b	(.f64 (.f64 (sqrt.f64 2) n) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om))))))
	58.4b	(/.f64 (sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (.f64 t t) (.f64 (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (.f64 U l) Om)))) (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (.f64 U l) Om))))))))) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (-.f64 (.f64 l -2) (.f64 n (/.f64 (*.f64 U l) Om)))))))
	49.7b	(sqrt.f64 (.f64 (.f64 (.f64 U (.f64 2 n)) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2)))))) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))))
	62.2b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (.f64 U (.f64 2 n))) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (*.f64 l -2)))))))
	46.2b	(.f64 (sqrt.f64 (.f64 U (.f64 2 n))) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
	44.7b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 t (.f64 U n)))) (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om) (sqrt.f64 (/.f64 (*.f64 U n) t))))
	57.9b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))) (.f64 (sqrt.f64 2) l)) (.f64 1/2 (.f64 (/.f64 (.f64 t (sqrt.f64 2)) l) (sqrt.f64 (/.f64 (.f64 U n) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om))))))))
	59.0b	(neg.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 U (.f64 n (+.f64 (/.f64 (.f64 U n) (.f64 Om Om)) (/.f64 2 Om)))))) (.f64 (sqrt.f64 2) l)))
	36.9b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (/.f64 (.f64 l (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))) Om))))
	39.6b	(sqrt.f64 (.f64 U (-.f64 (.f64 2 (.f64 t n)) (.f64 4 (/.f64 (.f64 (.f64 l l) n) Om)))))

Compiler

Compiled 2276 to 1251 computations (45% saved)

regimes3.9s (24.3%)

Accuracy

Total 16.6b remaining (58.9%)

Threshold costs 0b (0%)

Compiler

Compiled 62498 to 39282 computations (37.1% saved)

bsearch188.0ms (1.2%)

Steps

Iters	Range		Point
8	3.763280731456008e+172	1.4529307913910292e+177	4.0389359801185104e+172
1	1.1437227837401678e-98	4.068547193494323e-96	2.135898270312147e-97
1	-1.3023605083010555e-169	-4.601994780863841e-174	-8.032622395303857e-172
9	-8.091659375798518e+232	-8.649397865091358e+227	-8.771456429987835e+227

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

48×	`*-commutative_binary64`
29×	`+-commutative_binary64`
21×	`sub-neg_binary64`
19×	`neg-sub0_binary64`
19×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	301
1	134	301
2	165	299
3	207	299
4	243	299
5	269	299
6	281	299
7	285	299
8	286	299
9	282	299

end6.0ms (0%)

Compiler: Compiled 203 to 123 computations (39.4% saved)

sample3.7s (23.3%)

Algorithm

1×

intervals

Results

1.2s	13297×	body	128	nan
723.0ms	8000×	body	128	valid
108.0ms	1229×	body	128	invalid

Compiler

Compiled 1323 to 815 computations (38.4% saved)

Iter	Nodes	Cost
0	85	301
1	134	301
2	165	299
3	207	299
4	243	299
5	269	299
6	281	299
7	285	299
8	286	299
9	282	299

Iter	Nodes	Cost
0	85	301
1	134	301
2	165	299
3	207	299
4	243	299
5	269	299
6	281	299
7	285	299
8	286	299
9	282	299

Details

analyze2.3s (14.5%)

sample106.0ms (0.7%)

simplify56.0ms (0.3%)

prune6.0ms (0%)

localize17.0ms (0.1%)

rewrite374.0ms (2.3%)

series1.1s (7%)

simplify237.0ms (1.5%)

prune257.0ms (1.6%)

localize21.0ms (0.1%)

rewrite201.0ms (1.3%)

series967.0ms (6.1%)

simplify199.0ms (1.2%)

prune126.0ms (0.8%)

localize20.0ms (0.1%)

rewrite196.0ms (1.2%)

series537.0ms (3.4%)

simplify162.0ms (1%)

prune147.0ms (0.9%)

localize21.0ms (0.1%)

rewrite308.0ms (1.9%)

series544.0ms (3.4%)

simplify129.0ms (0.8%)

prune82.0ms (0.5%)

regimes3.9s (24.3%)

bsearch188.0ms (1.2%)

simplify18.0ms (0.1%)

end6.0ms (0%)

sample3.7s (23.3%)

Profiling

Iter	Nodes	Cost
0	85	301
1	134	301
2	165	299
3	207	299
4	243	299
5	269	299
6	281	299
7	285	299
8	286	299
9	282	299