Details

analyze5.0s (24%)

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)

sample258.0ms (1.2%)

Algorithm

1×

intervals

Results

132.0ms	54×	body	1024	valid
42.0ms	42×	body	512	valid
40.0ms	148×	body	128	valid
8.0ms	12×	body	256	valid

Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify133.0ms (0.6%)

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

18.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	18.4b	(.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)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.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)
7.3b	(.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))))
9.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite355.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

18.3b

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))))
14.0ms	(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)))
9.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 2850 to 2286 computations (19.8% saved)

series697.0ms (3.4%)

Error

0.1b

Counts

4 → 59

Calls

4 calls:

240.0ms	(.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))))
191.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
106.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
77.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3860 to 3123 computations (19.1% saved)

simplify354.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

425×	`distribute-rgt-in_binary64`
411×	`associate-l_binary64`
293×	`associate-r_binary64`
190×	`*-commutative_binary64`
183×	`cancel-sign-sub-inv_binary64`

Counts

145 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	290	5119
1	689	4804
2	2707	4763
3	4713	4763
4	4974	4763
5	4944	4763

prune201.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	8	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	8	123

Error

3.5b

Counts

123 → 8

Alt Table

Status	Error	Program
	29.7b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
	27.0b	(/.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 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))))))
	50.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (/.f64 U (.f64 J (cos.f64 (.f64 K 1/2)))) -1/2))
	19.4b	(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))))) (cbrt.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))))) (cbrt.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))))
	18.5b	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
	47.0b	(cbrt.f64 (pow.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2))))) 3))
▶	18.4b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
	47.9b	(neg.f64 U)

Compiler

Compiled 2618 to 2045 computations (21.9% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
0.2b	(pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)
7.4b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
9.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))

rewrite325.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

Rules

31×	`add-exp-log_binary64`
23×	`pow1_binary64`
21×	`add-cbrt-cube_binary64`
14×	`prod-exp_binary64`
11×	`cbrt-unprod_binary64`

Counts

4 → 83

Calls

4 calls:

26.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
14.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
11.0ms	(pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)
8.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))

Compiler

Compiled 2739 to 2192 computations (20% saved)

series659.0ms (3.2%)

Error

3.5b

Counts

4 → 60

Calls

4 calls:

228.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
193.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
105.0ms	(pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)
47.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))

Compiler

Compiled 4066 to 3280 computations (19.3% saved)

simplify282.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

531×	`distribute-rgt-in_binary64`
464×	`associate-l_binary64`
435×	`associate-r_binary64`
241×	`*-commutative_binary64`
184×	`cancel-sign-sub-inv_binary64`

Counts

143 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	357	5133
1	829	4770
2	3088	4726
3	4945	4726

prune151.0ms (0.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	99	10	109

Error

3.5b

Counts

109 → 10

Alt Table

Status	Error	Program
	50.8b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (.f64 (/.f64 U (.f64 J (cos.f64 (.f64 K 1/2)))) -1/2)))
	29.7b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
	27.0b	(/.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 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))))))
	50.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (/.f64 U (.f64 J (cos.f64 (.f64 K 1/2)))) -1/2))
	19.4b	(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))))) (cbrt.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))))) (cbrt.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))))
▶	18.5b	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
	47.0b	(cbrt.f64 (pow.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2))))) 3))
✓	18.4b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
	47.9b	(neg.f64 U)
	23.7b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 J (+.f64 2 (.f64 (.f64 K K) -1/4)))) 2)))))

Compiler

Compiled 2091 to 1617 computations (22.7% saved)

localize58.0ms (0.3%)

Local error

Found 4 expressions with local error:

7.4b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
7.4b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))
9.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))

rewrite393.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

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:

17.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))
15.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
15.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
14.0ms	(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)

series1.1s (5.5%)

Error

3.5b

Counts

4 → 84

Calls

4 calls:

262.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
247.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))
221.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
217.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 9238 to 7566 computations (18.1% saved)

simplify480.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

731×	`distribute-rgt-in_binary64`
547×	`associate-l_binary64`
304×	`associate-r_binary64`
215×	`*-commutative_binary64`
208×	`cancel-sign-sub-inv_binary64`

Counts

160 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	358	9066
1	784	8974
2	2748	8736
3	4536	8700
4	4963	8700

prune266.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	131	10	141

Error

3.5b

Counts

141 → 10

Alt Table

Status	Error	Program
	50.8b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (.f64 (/.f64 U (.f64 J (cos.f64 (.f64 K 1/2)))) -1/2)))
	29.7b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
	50.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (/.f64 U (.f64 J (cos.f64 (.f64 K 1/2)))) -1/2))
	19.4b	(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))))) (cbrt.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))))) (cbrt.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))))
✓	18.4b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
	47.9b	(neg.f64 U)
	23.7b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 J (+.f64 2 (.f64 (.f64 K K) -1/4)))) 2)))))
	47.0b	(cbrt.f64 (pow.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2))))) 3))
▶	18.5b	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))) (pow.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/4))
	18.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))))) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))

Compiler

Compiled 3670 to 2927 computations (20.2% saved)

localize57.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)
7.4b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))
9.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
17.5b	(pow.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/4)

rewrite388.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

Rules

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

Counts

4 → 81

Calls

4 calls:

17.0ms	(pow.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/4)
16.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
15.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))
14.0ms	(pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)

Compiler

Compiled 3913 to 3194 computations (18.4% saved)

series1.0s (5%)

Error

3.5b

Counts

4 → 69

Calls

4 calls:

315.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))
243.0ms	(pow.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/4)
211.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
121.0ms	(pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)

Compiler

Compiled 7793 to 6419 computations (17.6% saved)

simplify318.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

816×	`distribute-rgt-in_binary64`
525×	`associate-l_binary64`
348×	`associate-r_binary64`
250×	`*-commutative_binary64`
210×	`cancel-sign-sub-inv_binary64`

Counts

150 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	387	7807
1	829	7694
2	3329	7409
3	5290	7409

prune244.0ms (1.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	126	10	136

Error

3.5b

Counts

136 → 10

Alt Table

Status	Error	Program
	50.8b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (.f64 (/.f64 U (.f64 J (cos.f64 (.f64 K 1/2)))) -1/2)))
	29.7b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
	50.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (/.f64 U (.f64 J (cos.f64 (.f64 K 1/2)))) -1/2))
	19.4b	(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))))) (cbrt.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))))) (cbrt.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))))
✓	18.4b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
	47.9b	(neg.f64 U)
	23.7b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 J (+.f64 2 (.f64 (.f64 K K) -1/4)))) 2)))))
	47.0b	(cbrt.f64 (pow.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 -2 J) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2))))) 3))
✓	18.5b	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))) (pow.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/4))
	18.5b	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2))))) (.f64 (pow.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)) 1/8) (pow.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)) 1/8)))

Compiler

Compiled 3367 to 2685 computations (20.3% saved)

regimes2.4s (11.8%)

Accuracy

Total 5.5b remaining (59%)

Threshold costs 0b (0%)

Compiler

Compiled 21618 to 17626 computations (18.5% saved)

bsearch13.0ms (0.1%)

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

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	125
1	37	125
2	39	125
3	40	125
4	39	125

end4.0ms (0%)

Compiler: Compiled 84 to 67 computations (20.2% saved)

sample5.4s (26.2%)

Algorithm

1×

intervals

Results

2.6s	1939×	body	1024	valid
996.0ms	4482×	body	128	valid
824.0ms	1050×	body	512	valid
266.0ms	526×	body	256	valid
7.0ms	3×	body	2048	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 447 to 362 computations (19% saved)

Details

analyze5.0s (24%)

sample258.0ms (1.2%)

simplify133.0ms (0.6%)

prune6.0ms (0%)

localize32.0ms (0.2%)

rewrite355.0ms (1.7%)

series697.0ms (3.4%)

simplify354.0ms (1.7%)

prune201.0ms (1%)

localize32.0ms (0.2%)

rewrite325.0ms (1.6%)

series659.0ms (3.2%)

simplify282.0ms (1.4%)

prune151.0ms (0.7%)

localize58.0ms (0.3%)

rewrite393.0ms (1.9%)

series1.1s (5.5%)

simplify480.0ms (2.3%)

prune266.0ms (1.3%)

localize57.0ms (0.3%)

rewrite388.0ms (1.9%)

series1.0s (5%)

simplify318.0ms (1.5%)

prune244.0ms (1.2%)

regimes2.4s (11.8%)

bsearch13.0ms (0.1%)

simplify12.0ms (0.1%)

end4.0ms (0%)

sample5.4s (26.2%)

Profiling