Details

analyze2.0s (13.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
15.6%	84.3%	0.1%	8
15.6%	84.3%	0.1%	9
15.6%	84.3%	0.1%	10
30.4%	69.4%	0.1%	11
30.4%	69.4%	0.1%	12
30.4%	69.4%	0.1%	13
39.6%	60.3%	0.1%	14

Compiler

Compiled 28 to 23 computations (17.9% saved)

sample83.0ms (0.6%)

Algorithm

1×

intervals

Results

32.0ms	56×	body	1024	valid
19.0ms	34×	body	512	valid
17.0ms	152×	body	128	valid
4.0ms	14×	body	256	valid

Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify118.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1043×	`associate-*l/_binary64`
692×	`associate-/l/_binary64`
651×	`associate-/r/_binary64`
525×	`associate-*r/_binary64`
474×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	37	37
2	81	37
3	206	37
4	726	37
5	2242	37
6	2396	37
7	2777	37
8	2829	37
9	2940	37
10	3048	37
11	4535	37
12	4712	37
13	4916	37
14	4945	37
15	4849	37

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

16.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	16.6b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))

Compiler

Compiled 81 to 66 computations (18.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
6.5b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.1b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite260.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

16.6b

Rules

32×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
16×	`*-un-lft-identity_binary64`
15×	`pow1_binary64`
13×	`add-sqr-sqrt_binary64`

Counts

4 → 91

Calls

4 calls:

14.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
6.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
6.0ms	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))

Compiler

Compiled 3022 to 2396 computations (20.7% saved)

series386.0ms (2.7%)

Error

0.1b

Counts

4 → 54

Calls

4 calls:

121.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
85.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
77.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
60.0ms	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))

Compiler

Compiled 3656 to 2954 computations (19.2% saved)

simplify147.0ms (1%)

Algorithm

1×	egg-herbie

Rules

359×	`associate-l_binary64`
265×	`associate-/l/_binary64`
253×	`associate-r_binary64`
196×	`log-prod_binary64`
177×	`distribute-rgt-in_binary64`

Counts

145 → 100

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	273	4059
1	693	3745
2	2672	3710
3	4796	3710
4	4978	3710

prune110.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	94	7	101

Error

0.0b

Counts

101 → 7

Alt Table

Status	Error	Program
✓	16.6b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	45.9b	(neg.f64 U)
	43.1b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2)))) (sqrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))))
▶	17.5b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2)))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2))))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))))
	49.9b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
	50.3b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2))) 3))
	25.4b	(/.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))

Compiler

Compiled 2401 to 1788 computations (25.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

6.5b	(.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
9.1b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.1b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.1b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite233.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`*-un-lft-identity_binary64`
16×	`pow1_binary64` `sqrt-prod_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 75

Calls

4 calls:

19.0ms	(.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 5980 to 4842 computations (19% saved)

series590.0ms (4.1%)

Error

0.0b

Counts

4 → 60

Calls

4 calls:

149.0ms	(.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
121.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
119.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
117.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 11238 to 9095 computations (19.1% saved)

simplify167.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

579×	`times-frac_binary64`
414×	`associate-/l*_binary64`
269×	`associate-/r*_binary64`
233×	`associate-*l/_binary64`
222×	`associate-*r/_binary64`

Counts

135 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	4155
1	421	3903
2	1452	3859
3	4681	3850
4	4975	3850
5	5066	3850

prune369.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	76	7	83

Error

0.0b

Counts

83 → 7

Alt Table

Status	Error	Program
✓	16.6b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	45.9b	(neg.f64 U)
	43.1b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2)))) (sqrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))))
✓	17.5b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2)))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2))))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))))
	49.9b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
	50.3b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2))) 3))
▶	25.4b	(/.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))

Compiler

Compiled 4942 to 3858 computations (21.9% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6)))
6.1b	(sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
13.2b	(-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
20.3b	(/.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))

rewrite337.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`sqrt-prod_binary64`
15×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

4 → 82

Calls

4 calls:

31.0ms	(/.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
20.0ms	(sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
13.0ms	(-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6)))

Compiler

Compiled 8371 to 6730 computations (19.6% saved)

series1.2s (8.4%)

Error

0.0b

Counts

4 → 57

Calls

4 calls:

657.0ms	(/.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
211.0ms	(-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
169.0ms	(sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2) (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) (.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
115.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6)))

Compiler

Compiled 8585 to 7070 computations (17.6% saved)

simplify239.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

276×	`distribute-rgt-in_binary64`
253×	`associate-r_binary64`
241×	`cancel-sign-sub-inv_binary64`
230×	`associate-l_binary64`
174×	`associate-/l*_binary64`

Counts

139 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	304	8417
1	794	7388
2	3049	7317
3	4976	7317
4	4936	7317

prune195.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	113	7	120

Error

0.0b

Counts

120 → 7

Alt Table

Status	Error	Program
✓	16.6b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	45.9b	(neg.f64 U)
	43.1b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2)))) (sqrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))))
✓	17.5b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2)))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2))))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))))
	49.9b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
	50.3b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2))) 3))
▶	25.5b	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (/.f64 (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 4) (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 -2 J))))

Compiler

Compiled 5757 to 4537 computations (21.2% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6)))
6.1b	(sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 4) (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))))
13.2b	(-.f64 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 4) (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))
21.6b	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (/.f64 (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 4) (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 -2 J))))

rewrite632.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

151×	`times-frac_binary64`
134×	`*-un-lft-identity_binary64`
101×	`sqrt-prod_binary64`
75×	`add-sqr-sqrt_binary64`
59×	`add-cube-cbrt_binary64`

Counts

4 → 193

Calls

4 calls:

37.0ms	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (/.f64 (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 4) (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 -2 J))))
23.0ms	(sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 4) (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))))
16.0ms	(-.f64 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 4) (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))
7.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6)))

Compiler

Compiled 12333 to 9869 computations (20% saved)

series1.2s (8.3%)

Error

0.0b

Counts

4 → 57

Calls

4 calls:

653.0ms	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (/.f64 (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 4) (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 -2 J))))
212.0ms	(-.f64 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 4) (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))
174.0ms	(sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 4) (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2))))
107.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6)))

Compiler

Compiled 8138 to 6692 computations (17.8% saved)

simplify509.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

281×	`associate-r_binary64`
209×	`associate-/r*_binary64`
200×	`*-commutative_binary64`
188×	`associate-l_binary64`
180×	`unswap-sqr_binary64`

Counts

250 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	450	21161
1	1105	19983
2	3868	19960
3	4730	19960
4	4933	19960

prune283.0ms (2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	211	7	218

Error

0.0b

Counts

218 → 7

Alt Table

Status	Error	Program
	16.6b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	45.9b	(neg.f64 U)
	43.1b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2)))) (sqrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))))
	17.5b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2)))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 J -2))))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))))
	49.9b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
	25.5b	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 6))) (/.f64 (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 4) (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (.f64 -2 J))))
	25.5b	(/.f64 (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 6)))) (/.f64 (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 4) (pow.f64 (/.f64 U (.f64 (.f64 J 2) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 -2 J)))

Compiler

Compiled 8061 to 6372 computations (21% saved)

regimes2.2s (15.6%)

Accuracy

Total 9.4b remaining (99.6%)

Threshold costs 0b (0%)

Compiler

Compiled 38509 to 31156 computations (19.1% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 27 to 22 computations (18.5% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
3×	`+-commutative_binary64`
1×	`1-exp_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	148
1	50	148
2	52	148
3	53	148
4	52	148

end3.0ms (0%)

Compiler: Compiled 99 to 78 computations (21.2% saved)

sample3.0s (20.6%)

Algorithm

1×

intervals

Results

1.2s	2006×	body	1024	valid
539.0ms	4444×	body	128	valid
433.0ms	1057×	body	512	valid
128.0ms	491×	body	256	valid
2.0ms	2×	body	2048	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 427 to 343 computations (19.7% saved)

Details

analyze2.0s (13.9%)

sample83.0ms (0.6%)

simplify118.0ms (0.8%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite260.0ms (1.8%)

series386.0ms (2.7%)

simplify147.0ms (1%)

prune110.0ms (0.8%)

localize23.0ms (0.2%)

rewrite233.0ms (1.6%)

series590.0ms (4.1%)

simplify167.0ms (1.2%)

prune369.0ms (2.6%)

localize30.0ms (0.2%)

rewrite337.0ms (2.3%)

series1.2s (8.4%)

simplify239.0ms (1.7%)

prune195.0ms (1.4%)

localize32.0ms (0.2%)

rewrite632.0ms (4.4%)

series1.2s (8.3%)

simplify509.0ms (3.5%)

prune283.0ms (2%)

regimes2.2s (15.6%)

bsearch8.0ms (0.1%)

simplify6.0ms (0%)

end3.0ms (0%)

sample3.0s (20.6%)

Profiling