Details

analyze5.2s (22.7%)

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)

sample216.0ms (0.9%)

Algorithm

1×

intervals

Results

105.0ms	57×	body	1024	valid
43.0ms	148×	body	128	valid
33.0ms	33×	body	512	valid
12.0ms	18×	body	256	valid
2.0ms	1×	body	1024	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify170.0ms (0.7%)

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

prune6.0ms (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

16.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	16.0b	(.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)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.3b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
6.9b	(.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))))
8.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite330.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

15.9b

Rules

28×	`add-exp-log_binary64`
20×	`pow1_binary64`
18×	`add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64`
12×	`prod-exp_binary64`

Counts

4 → 86

Calls

4 calls:

27.0ms	(.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))))
13.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
11.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
8.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 2850 to 2286 computations (19.8% saved)

series628.0ms (2.8%)

Error

0.1b

Counts

4 → 51

Calls

4 calls:

251.0ms	(.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))))
166.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
104.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
46.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3716 to 3004 computations (19.2% saved)

simplify249.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

945×	`times-frac_binary64`
300×	`associate-l_binary64`
218×	`associate-r_binary64`
207×	`cancel-sign-sub-inv_binary64`
151×	`*-commutative_binary64`

Counts

137 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	262	3943
1	627	3602
2	2251	3584
3	4943	3584
4	5012	3584

prune154.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	97	8	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	97	9	106

Error

0.0b

Counts

106 → 9

Alt Table

Status	Error	Program
	16.3b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	46.0b	(neg.f64 U)
	16.9b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
▶	16.1b	(.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
	21.5b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) 3)))
	39.3b	(.f64 (+.f64 (.f64 J (+.f64 (.f64 1/4 (.f64 K K)) -2)) (.f64 -1/192 (.f64 J (pow.f64 K 4)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	48.3b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
✓	16.0b	(.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))))
	28.0b	(.f64 (.f64 (.f64 (.f64 J -2) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (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 2395 to 1829 computations (23.6% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
0.9b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (*.f64 J -2) (cos.f64 (/.f64 K 2))))
14.3b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
14.3b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite360.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

19×	`*-un-lft-identity_binary64`
18×	`cbrt-prod_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`pow1_binary64`
13×	`add-cbrt-cube_binary64`

Counts

4 → 81

Calls

4 calls:

27.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (*.f64 J -2) (cos.f64 (/.f64 K 2))))
15.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
14.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
13.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 4380 to 3578 computations (18.3% saved)

series1.0s (4.4%)

Error

0.0b

Counts

4 → 50

Calls

4 calls:

240.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
234.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
220.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
208.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (*.f64 J -2) (cos.f64 (/.f64 K 2))))

Compiler

Compiled 6832 to 5723 computations (16.2% saved)

simplify267.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

593×	`*-commutative_binary64`
428×	`unswap-sqr_binary64`
254×	`times-frac_binary64`
235×	`associate-r_binary64`
208×	`associate-l_binary64`

Counts

131 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	217	4943
1	477	4533
2	1413	4389
3	3746	4294
4	5338	4294

prune311.0ms (1.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	92	9	101

Error

0.0b

Counts

101 → 9

Alt Table

Status	Error	Program
▶	16.3b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	46.0b	(neg.f64 U)
	16.9b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
✓	16.1b	(.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
	21.5b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) 3)))
	39.3b	(.f64 (+.f64 (.f64 J (+.f64 (.f64 1/4 (.f64 K K)) -2)) (.f64 -1/192 (.f64 J (pow.f64 K 4)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	48.3b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
✓	16.0b	(.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))))
	28.0b	(.f64 (.f64 (.f64 (.f64 J -2) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (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 3745 to 2956 computations (21.1% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
6.9b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite322.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`pow1_binary64`
29×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
19×	`cbrt-unprod_binary64`
19×	`prod-exp_binary64`

Counts

4 → 74

Calls

4 calls:

44.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
16.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
2.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3481 to 2847 computations (18.2% saved)

series576.0ms (2.5%)

Error

0.0b

Counts

4 → 44

Calls

4 calls:

254.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
183.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
34.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
33.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 4078 to 3320 computations (18.6% saved)

simplify198.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

735×	`times-frac_binary64`
386×	`associate-l_binary64`
281×	`associate-r_binary64`
189×	`cancel-sign-sub-inv_binary64`
167×	`distribute-rgt-in_binary64`

Counts

118 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	3622
1	582	3235
2	2255	3171
3	4692	3171
4	4969	3171
5	5010	3171

prune78.0ms (0.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	5	6
Picked	0	1	1
Done	1	1	2
Total	81	8	89

Error

0.0b

Counts

89 → 8

Alt Table

Status	Error	Program
✓	16.3b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	46.0b	(neg.f64 U)
	16.9b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
✓	16.1b	(.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
▶	16.1b	(.f64 (.f64 (sqrt.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 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
	39.3b	(.f64 (+.f64 (.f64 J (+.f64 (.f64 1/4 (.f64 K K)) -2)) (.f64 -1/192 (.f64 J (pow.f64 K 4)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	48.3b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
	28.0b	(.f64 (.f64 (.f64 (.f64 J -2) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (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 2278 to 1756 computations (22.9% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.9b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
6.9b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite157.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

32×	`sqrt-prod_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64`
10×	`sqrt-pow1_binary64`

Counts

4 → 76

Calls

4 calls:

9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
7.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
6.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 3667 to 2999 computations (18.2% saved)

series985.0ms (4.3%)

Error

0.0b

Counts

4 → 62

Calls

4 calls:

241.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
230.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
225.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
185.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 7265 to 5956 computations (18% saved)

simplify285.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

490×	`unswap-sqr_binary64`
428×	`times-frac_binary64`
289×	`associate-/l*_binary64`
223×	`associate-/r*_binary64`
196×	`associate-r_binary64`

Counts

138 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	3928
1	283	3832
2	770	3802
3	3651	3720
4	5368	3720

prune203.0ms (0.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	82	8	90

Error

0.0b

Counts

90 → 8

Alt Table

Status	Error	Program
	16.3b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	46.0b	(neg.f64 U)
	16.9b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	16.1b	(.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
	16.1b	(.f64 (.f64 (sqrt.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 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
	39.3b	(.f64 (+.f64 (.f64 J (+.f64 (.f64 1/4 (.f64 K K)) -2)) (.f64 -1/192 (.f64 J (pow.f64 K 4)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
	48.3b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
	28.0b	(.f64 (.f64 (.f64 (.f64 J -2) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (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 3117 to 2445 computations (21.6% saved)

regimes3.5s (15.5%)

Accuracy

Total 9.2b remaining (99.6%)

Threshold costs 0b (0%)

Compiler

Compiled 34705 to 28124 computations (19% saved)

bsearch20.0ms (0.1%)

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

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	147
1	49	147
2	48	147

end4.0ms (0%)

Compiler: Compiled 98 to 78 computations (20.4% saved)

sample7.5s (32.7%)

Algorithm

1×

intervals

Results

3.6s	1981×	body	1024	valid
1.4s	4496×	body	128	valid
1.1s	1031×	body	512	valid
332.0ms	491×	body	256	valid
4.0ms	1×	body	2048	valid
2.0ms	1×	body	1024	invalid
1.0ms	5×	body	128	invalid

Compiler

Compiled 401 to 324 computations (19.2% saved)

Details

analyze5.2s (22.7%)

sample216.0ms (0.9%)

simplify170.0ms (0.7%)

prune6.0ms (0%)

localize28.0ms (0.1%)

rewrite330.0ms (1.4%)

series628.0ms (2.8%)

simplify249.0ms (1.1%)

prune154.0ms (0.7%)

localize39.0ms (0.2%)

rewrite360.0ms (1.6%)

series1.0s (4.4%)

simplify267.0ms (1.2%)

prune311.0ms (1.4%)

localize40.0ms (0.2%)

rewrite322.0ms (1.4%)

series576.0ms (2.5%)

simplify198.0ms (0.9%)

prune78.0ms (0.3%)

localize20.0ms (0.1%)

rewrite157.0ms (0.7%)

series985.0ms (4.3%)

simplify285.0ms (1.2%)

prune203.0ms (0.9%)

regimes3.5s (15.5%)

bsearch20.0ms (0.1%)

simplify9.0ms (0%)

end4.0ms (0%)

sample7.5s (32.7%)

Profiling