Details

analyze2.5s (19.9%)

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)

sample205.0ms (1.6%)

Algorithm

1×

intervals

Results

51.0ms	61×	body	1024	valid
25.0ms	147×	body	128	valid
13.0ms	26×	body	512	valid
7.0ms	22×	body	256	valid

Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify81.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1043×	`associate-*l/_binary64`
692×	`associate-/l/_binary64`
651×	`associate-/r/_binary64`
474×	`associate-/l*_binary64`
398×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	37	32
2	83	32
3	208	32
4	742	32
5	2273	32
6	2474	32
7	2875	32
8	3015	32
9	3126	32
10	3234	32
11	4835	32
12	4953	32
13	4880	32

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

8.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.2b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Compiler

Compiled 96 to 76 computations (20.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
✓	0.1b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
✓	0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
✓	7.6b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series210.0ms (1.7%)

Counts

4 → 120

Calls

4 calls:

142.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
46.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
11.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
10.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64`
32×	`add-exp-log_binary64`
23×	`pow1_binary64`
15×	`cbrt-unprod_binary64`
15×	`prod-exp_binary64`

Counts

4 → 88

Calls

4 calls:

10.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
5.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
5.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
4.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify173.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-def_binary64`
375×	`associate-l_binary64`
303×	`fma-neg_binary64`
300×	`associate-r_binary64`
204×	`*-commutative_binary64`

Counts

208 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	323	5501
1	854	4903
2	3368	4868
3	4900	4868
4	4981	4868
5	4956	4868

prune210.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	184	6	190
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	184	7	191

Error

0.0b

Counts

191 → 7

Alt Table

Status	Error	Program
	36.6b	(.f64 (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))))
	46.2b	(neg.f64 U)
	20.3b	(.f64 (.f64 (.f64 (.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
▶	8.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	8.2b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	40.9b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 -2 J)) (.f64 -2 J)) (.f64 (.f64 (cos.f64 (/.f64 K 2)) (cos.f64 (/.f64 K 2))) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	47.5b	(fma.f64 2 (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) U) U)

Compiler

Compiled 6644 to 4978 computations (25.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
✓	0.3b	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
✓	0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
✓	7.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series713.0ms (5.6%)

Counts

4 → 84

Calls

4 calls:

344.0ms	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
188.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
169.0ms	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
12.0ms	(.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2))))

rewrite43.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`pow1_binary64`
49×	`add-exp-log_binary64`
34×	`pow-prod-down_binary64`
33×	`cbrt-unprod_binary64`
33×	`prod-exp_binary64`

Counts

4 → 119

Calls

4 calls:

13.0ms	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
11.0ms	(.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
5.0ms	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

simplify162.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

852×	`fma-def_binary64`
491×	`associate-l_binary64`
370×	`associate-r_binary64`
270×	`fma-neg_binary64`
205×	`*-commutative_binary64`

Counts

203 → 214

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	336	5881
1	836	5091
2	3332	4908
3	4961	4908
4	4995	4908

prune465.0ms (3.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	260	2	262
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	260	9	269

Error

0.0b

Counts

269 → 9

Alt Table

Status	Error	Program
	36.6b	(.f64 (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))))
	46.2b	(neg.f64 U)
	20.4b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 (/.f64 K 2)))) (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	20.3b	(.f64 (.f64 (.f64 (.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
▶	8.7b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	40.9b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 -2 J)) (.f64 -2 J)) (.f64 (.f64 (cos.f64 (/.f64 K 2)) (cos.f64 (/.f64 K 2))) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	8.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	8.2b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	47.5b	(fma.f64 2 (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) U) U)

Compiler

Compiled 11497 to 9065 computations (21.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))
✓	0.3b	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
	0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
✓	7.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series582.0ms (4.6%)

Counts

3 → 60

Calls

3 calls:

255.0ms

(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))

188.0ms

(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))

139.0ms

(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (*.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

rewrite58.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-exp-log_binary64`
69×	`pow1_binary64`
54×	`cbrt-unprod_binary64`
54×	`prod-exp_binary64`
54×	`pow-prod-down_binary64`

Counts

3 → 77

Calls

3 calls:

28.0ms

(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (*.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

3.0ms

(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))

1.0ms

(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))

simplify202.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

802×	`fma-def_binary64`
572×	`associate-l_binary64`
471×	`associate-r_binary64`
248×	`unswap-sqr_binary64`
224×	`*-commutative_binary64`

Counts

137 → 139

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	358	9312
1	827	7477
2	3470	4286
3	4637	4276
4	4904	4276
5	4936	4276

prune841.0ms (6.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	357	1	358
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	358	9	367

Error

0.0b

Counts

367 → 9

Alt Table

Status	Error	Program
	36.6b	(.f64 (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))))
	46.2b	(neg.f64 U)
	20.4b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 (/.f64 K 2)))) (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
▶	20.3b	(.f64 (.f64 (.f64 (.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
✓	8.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	8.2b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	8.7b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	47.5b	(fma.f64 2 (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) U) U)
	43.8b	(cbrt.f64 (pow.f64 (.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 2 J))))) 3))

Compiler

Compiled 24649 to 20105 computations (18.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
✓	0.1b	(.f64 (.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2))))
	0.1b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
✓	6.2b	(.f64 (.f64 (.f64 (.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))

series149.0ms (1.2%)

Counts

2 → 60

Calls

2 calls:

138.0ms

(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

12.0ms

(*.f64 (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2))))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-cbrt-cube_binary64`
25×	`add-exp-log_binary64`
25×	`pow1_binary64`
16×	`cbrt-unprod_binary64`
16×	`prod-exp_binary64`

Counts

2 → 52

Calls

2 calls:

9.0ms

(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

8.0ms

(*.f64 (*.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2))))

simplify142.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-def_binary64`
408×	`associate-l_binary64`
321×	`fma-neg_binary64`
278×	`associate-r_binary64`
267×	`cancel-sign-sub-inv_binary64`

Counts

112 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	262	4014
1	695	3530
2	2794	3500
3	4850	3492
4	4983	3492
5	4964	3492

prune271.0ms (2.1%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	1	4	5
Picked	0	1	1
Done	0	3	3
Total	200	9	209

Error

0.0b

Counts

209 → 9

Alt Table

Status	Error	Program
	36.6b	(.f64 (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))))
	46.2b	(neg.f64 U)
✓	8.7b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	20.3b	(.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))))) (sqrt.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	20.3b	(.f64 (.f64 (.f64 (.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
✓	8.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	8.2b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	47.5b	(fma.f64 2 (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) U) U)
	43.8b	(cbrt.f64 (pow.f64 (.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 2 J))))) 3))

Compiler

Compiled 7957 to 6094 computations (23.4% saved)

regimes1.3s (10.6%)

Accuracy

Total 8.4b remaining (99.6%)

Threshold costs 0b (0%)

Counts

110 → 5

Compiler

Compiled 24062 to 19668 computations (18.3% saved)

bsearch238.0ms (1.9%)

Steps

Iters	Range		Point
6	2.418116980686494e-249	1.0986246421124474e-248	2.7554685803717827e-249
8	2.8151970346909866e-284	4.486245601613879e-281	2.3963648443487414e-281
9	-2.5368727035995616e-257	-1.9554844594352556e-264	-2.0731189763801308e-263
8	-1.285610142136025e-231	-2.4069637682403594e-236	-3.678515660926543e-236

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
1×	`+-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	38	135
1	50	135
2	52	135
3	53	135
4	52	135

end2.0ms (0%)

Compiler: Compiled 93 to 67 computations (28% saved)

sample3.9s (31%)

Algorithm

1×

intervals

Results

1.9s	2019×	body	1024	valid
688.0ms	4503×	body	128	valid
542.0ms	973×	body	512	valid
197.0ms	503×	body	256	valid
3.0ms	2×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 418 to 330 computations (21.1% saved)

Details

analyze2.5s (19.9%)

sample205.0ms (1.6%)

simplify81.0ms (0.6%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series210.0ms (1.7%)

rewrite29.0ms (0.2%)

simplify173.0ms (1.4%)

prune210.0ms (1.7%)

localize15.0ms (0.1%)

series713.0ms (5.6%)

rewrite43.0ms (0.3%)

simplify162.0ms (1.3%)

prune465.0ms (3.7%)

localize22.0ms (0.2%)

series582.0ms (4.6%)

rewrite58.0ms (0.5%)

simplify202.0ms (1.6%)

prune841.0ms (6.6%)

localize13.0ms (0.1%)

series149.0ms (1.2%)

rewrite22.0ms (0.2%)

simplify142.0ms (1.1%)

prune271.0ms (2.1%)

regimes1.3s (10.6%)

bsearch238.0ms (1.9%)

simplify6.0ms (0%)

end2.0ms (0%)

sample3.9s (31%)

Profiling