Details

analyze2.0s (14.7%)

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)

sample91.0ms (0.7%)

Algorithm

1×

intervals

Results

44.0ms	64×	body	1024	valid
16.0ms	149×	body	128	valid
14.0ms	32×	body	512	valid
3.0ms	11×	body	256	valid

Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify114.0ms (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

13.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	13.9b	(.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))))

Compiler

Compiled 81 to 66 computations (18.5% saved)

localize15.0ms (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)
4.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.3b	(.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))))

rewrite263.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

13.8b

Rules

28×	`add-exp-log_binary64`
20×	`pow1_binary64`
18×	`add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

4 → 86

Calls

4 calls:

16.0ms	(.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))))
11.0ms	(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)))
5.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 2850 to 2286 computations (19.8% saved)

series413.0ms (3.1%)

Error

0.1b

Counts

4 → 55

Calls

4 calls:

179.0ms	(.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))))
101.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
63.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
27.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3915 to 3164 computations (19.2% saved)

simplify143.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

929×	`times-frac_binary64`
292×	`associate-l_binary64`
221×	`associate-r_binary64`
185×	`cancel-sign-sub-inv_binary64`
159×	`*-commutative_binary64`

Counts

141 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	253	4095
1	636	3767
2	2252	3749
3	4878	3749
4	4949	3749

prune123.0ms (0.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	93	8	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	93	9	102

Error

0.0b

Counts

102 → 9

Alt Table

Status	Error	Program
	35.6b	(.f64 (sqrt.f64 (.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))))) (sqrt.f64 (.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))))))
	14.8b	(.f64 (.f64 (cbrt.f64 (.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))))) (cbrt.f64 (.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)))))) (cbrt.f64 (.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))))))
	51.4b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
	48.8b	(neg.f64 U)
	37.3b	(.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))))
	25.2b	(.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))))
✓	13.9b	(.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))))
▶	14.3b	(.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))))
	22.9b	(/.f64 (.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)))) 6)))) (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 2614 to 1991 computations (23.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
4.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.3b	(.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))))

rewrite252.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

39×	`add-exp-log_binary64`
31×	`pow1_binary64`
22×	`prod-exp_binary64`
20×	`add-cbrt-cube_binary64`
19×	`cbrt-unprod_binary64`

Counts

4 → 88

Calls

4 calls:

25.0ms	(.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))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 4095 to 3339 computations (18.5% saved)

series433.0ms (3.2%)

Error

0.0b

Counts

4 → 52

Calls

4 calls:

184.0ms	(.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))))
109.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
70.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
23.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 4644 to 3794 computations (18.3% saved)

simplify149.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

800×	`times-frac_binary64`
387×	`associate-l_binary64`
281×	`associate-r_binary64`
187×	`cancel-sign-sub-inv_binary64`
178×	`log-prod_binary64`

Counts

140 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	285	4362
1	687	3950
2	2524	3932
3	4862	3932
4	4969	3932

prune148.0ms (1.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	109	9	118

Error

0.0b

Counts

118 → 9

Alt Table

Status	Error	Program
	35.6b	(.f64 (sqrt.f64 (.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))))) (sqrt.f64 (.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))))))
▶	14.8b	(.f64 (.f64 (cbrt.f64 (.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))))) (cbrt.f64 (.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)))))) (cbrt.f64 (.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))))))
	51.4b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
	48.8b	(neg.f64 U)
	37.3b	(.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))))
	25.2b	(.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))))
✓	13.9b	(.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))))
✓	14.3b	(.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))))
	22.9b	(/.f64 (.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)))) 6)))) (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 3172 to 2461 computations (22.4% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.3b	(.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))))
8.3b	(.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))))
8.3b	(.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))))

rewrite363.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

32×	`pow1_binary64`
31×	`add-cbrt-cube_binary64`
31×	`add-exp-log_binary64`
21×	`associate-r_binary64`
19×	`*-un-lft-identity_binary64`

Counts

4 → 97

Calls

4 calls:

17.0ms	(.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))))
16.0ms	(.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))))
16.0ms	(.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))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 7811 to 6314 computations (19.2% saved)

series894.0ms (6.6%)

Error

0.0b

Counts

4 → 78

Calls

4 calls:

216.0ms	(.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))))
216.0ms	(.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))))
215.0ms	(.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))))
133.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 14415 to 11675 computations (19% saved)

simplify152.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

720×	`times-frac_binary64`
501×	`associate-/l*_binary64`
263×	`associate-l_binary64`
195×	`associate-r_binary64`
166×	`distribute-rgt-in_binary64`

Counts

175 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	6832
1	497	6222
2	1859	6072
3	4970	6072

prune254.0ms (1.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	144	10	154

Error

0.0b

Counts

154 → 10

Alt Table

Status	Error	Program
▶	14.8b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 2 J))) 2))))) (cbrt.f64 (.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 2 J))) 2)))))) (cbrt.f64 (.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 2 J))) 2))))))) (cbrt.f64 (.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)))))) (cbrt.f64 (.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))))))
	35.6b	(.f64 (sqrt.f64 (.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))))) (sqrt.f64 (.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))))))
✓	14.8b	(.f64 (.f64 (cbrt.f64 (.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))))) (cbrt.f64 (.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)))))) (cbrt.f64 (.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))))))
	51.4b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
	48.8b	(neg.f64 U)
	37.3b	(.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))))
	25.2b	(.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))))
✓	13.9b	(.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))))
✓	14.3b	(.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))))
	22.9b	(/.f64 (.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)))) 6)))) (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 8542 to 6659 computations (22% saved)

localize46.0ms (0.3%)

Local error

Found 4 expressions with local error:

8.3b	(.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))))
8.3b	(.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 2 J))) 2))))
8.3b	(.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 2 J))) 2))))
8.3b	(.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 2 J))) 2))))

rewrite475.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

40×	`add-cbrt-cube_binary64`
40×	`add-exp-log_binary64`
40×	`pow1_binary64`
28×	`associate-r_binary64`
24×	`cbrt-unprod_binary64`

Counts

4 → 108

Calls

4 calls:

20.0ms	(.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 2 J))) 2))))
16.0ms	(.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 2 J))) 2))))
16.0ms	(.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 2 J))) 2))))
16.0ms	(.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))))

Compiler

Compiled 13351 to 10802 computations (19.1% saved)

series1.2s (8.8%)

Error

0.0b

Counts

4 → 80

Calls

4 calls:

256.0ms	(.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 2 J))) 2))))
254.0ms	(.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))))
252.0ms	(.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 2 J))) 2))))
251.0ms	(.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 2 J))) 2))))

Compiler

Compiled 23663 to 19204 computations (18.8% saved)

simplify250.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

474×	`times-frac_binary64`
342×	`associate-/l*_binary64`
265×	`associate-l_binary64`
263×	`associate-*l/_binary64`
258×	`associate-/r*_binary64`

Counts

188 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	7860
1	441	7076
2	1610	6892
3	4700	6892
4	4983	6892
5	5074	6892

prune301.0ms (2.2%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	127	10	137

Error

0.0b

Counts

137 → 10

Alt Table

Status	Error	Program
	14.8b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 2 J))) 2))))) (cbrt.f64 (.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 2 J))) 2)))))) (cbrt.f64 (.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 2 J))) 2))))))) (cbrt.f64 (.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)))))) (cbrt.f64 (.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))))))
	35.6b	(.f64 (sqrt.f64 (.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))))) (sqrt.f64 (.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))))))
	14.8b	(.f64 (.f64 (cbrt.f64 (.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))))) (cbrt.f64 (.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)))))) (cbrt.f64 (.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))))))
	51.4b	(+.f64 U (.f64 2 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) (.f64 J J)) U)))
	48.8b	(neg.f64 U)
	37.3b	(.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))))
	25.2b	(.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))))
	13.9b	(.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))))
	14.3b	(.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))))
	22.9b	(/.f64 (.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)))) 6)))) (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 10229 to 7978 computations (22% saved)

regimes2.3s (17%)

Accuracy

Total 9.5b remaining (99.5%)

Threshold costs 0b (0%)

Compiler

Compiled 42055 to 33958 computations (19.3% saved)

bsearch9.0ms (0.1%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`mul-1-neg_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	126
1	40	126
2	41	126
3	42	126
4	43	126
5	42	126

end3.0ms (0%)

Compiler: Compiled 84 to 68 computations (19% saved)

sample3.1s (23%)

Algorithm

1×

intervals

Results

1.2s	2003×	body	1024	valid
521.0ms	4482×	body	128	valid
437.0ms	1011×	body	512	valid
130.0ms	500×	body	256	valid
3.0ms	4×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 616 to 499 computations (19% saved)

Details

analyze2.0s (14.7%)

sample91.0ms (0.7%)

simplify114.0ms (0.8%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite263.0ms (1.9%)

series413.0ms (3.1%)

simplify143.0ms (1.1%)

prune123.0ms (0.9%)

localize21.0ms (0.2%)

rewrite252.0ms (1.9%)

series433.0ms (3.2%)

simplify149.0ms (1.1%)

prune148.0ms (1.1%)

localize32.0ms (0.2%)

rewrite363.0ms (2.7%)

series894.0ms (6.6%)

simplify152.0ms (1.1%)

prune254.0ms (1.9%)

localize46.0ms (0.3%)

rewrite475.0ms (3.5%)

series1.2s (8.8%)

simplify250.0ms (1.8%)

prune301.0ms (2.2%)

regimes2.3s (17%)

bsearch9.0ms (0.1%)

simplify7.0ms (0.1%)

end3.0ms (0%)

sample3.1s (23%)

Profiling