Details

analyze2.2s (10.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	94.3%	5.7%	11
0%	94.3%	5.7%	12
0%	94.3%	5.7%	13
0%	94%	6%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample14.3s (66.7%)

Results

9.7s	4015×	body	8192	exit
1.4s	1721×	body	1024	valid
895.0ms	4593×	body	128	valid
661.0ms	1012×	body	1024	invalid
635.0ms	1201×	body	512	valid
255.0ms	1326×	body	128	invalid
240.0ms	533×	body	512	invalid
221.0ms	666×	body	256	valid
88.0ms	269×	body	256	invalid
87.0ms	75×	body	2048	valid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify67.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-def_binary64`
657×	`div-sub_binary64`
464×	`fma-neg_binary64`
424×	`times-frac_binary64`
411×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	29	22
2	53	22
3	105	22
4	233	22
5	540	22
6	1242	22
7	2242	22
8	3501	22
9	4490	22
10	4976	22

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

20.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.0b	(+.f64 (.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2))) U)

Compiler

Compiled 71 to 46 computations (35.2% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	0.0b	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
✓	4.9b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series40.0ms (0.2%)

Counts

3 → 68

Calls

3 calls:

28.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
10.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
27×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 104

Calls

3 calls:

7.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
7.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
4.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

simplify118.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

454×	`fma-neg_binary64`
355×	`associate-l_binary64`
346×	`times-frac_binary64`
328×	`associate-r_binary64`
277×	`cancel-sign-sub-inv_binary64`

Counts

172 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	266	3954
1	584	3250
2	2168	2993
3	4724	2991
4	4931	2991

prune161.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	173	3	176
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	174	3	177

Error

0.0b

Counts

177 → 3

Alt Table

Status	Error	Program
	20.0b	(+.f64 (.f64 (.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (*.f64 1/2 K))) J) U)
▶	0.1b	(+.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) U)
	0.2b	(+.f64 (+.f64 (.f64 1/60 (.f64 (pow.f64 l 5) (.f64 J (cos.f64 (.f64 1/2 K))))) (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 J (cos.f64 (.f64 1/2 K))))) (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))))) U)

Compiler

Compiled 5005 to 1999 computations (60.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) U)
✓	0.0b	(sinh.f64 l)
✓	0.0b	(.f64 J (.f64 2 (sinh.f64 l)))
✓	0.1b	(.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)))

series163.0ms (0.8%)

Counts

4 → 120

Calls

4 calls:

68.0ms	(+.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) U)
60.0ms	(.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)))
27.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
8.0ms	(sinh.f64 l)

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
18×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

4 → 69

Calls

4 calls:

6.0ms	(.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)))
6.0ms	(+.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) U)
6.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
1.0ms	(sinh.f64 l)

simplify133.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-neg_binary64`
373×	`associate--l+_binary64`
372×	`cancel-sign-sub-inv_binary64`
278×	`associate-l_binary64`
252×	`associate-r_binary64`

Counts

189 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	260	4367
1	663	4209
2	2256	3738
3	4692	3737
4	5092	3737

prune160.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	134	6	140
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	136	7	143

Error

Counts

143 → 7

Alt Table

Status	Error	Program
	33.4b	(+.f64 (.f64 (.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2))) U)
	0.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))))) U)
	27.1b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))))) U)
	12.9b	(+.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (.f64 J (.f64 2 (sinh.f64 l)))) (.f64 J (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2))) U)
	0.2b	(+.f64 (+.f64 (.f64 1/60 (.f64 (pow.f64 l 5) (.f64 J (cos.f64 (.f64 1/2 K))))) (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 J (cos.f64 (.f64 1/2 K))))) (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))))) U)
	0.2b	(+.f64 (.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) U)
▶	0.1b	(+.f64 (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) U)

Compiler

Compiled 3738 to 2316 computations (38% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) U)
	0.0b	(sinh.f64 l)
✓	0.1b	(.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))
✓	0.1b	(.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))

series154.0ms (0.7%)

Counts

3 → 108

Calls

3 calls:

65.0ms	(+.f64 (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) U)
57.0ms	(.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))
32.0ms	(.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

3 → 59

Calls

3 calls:

9.0ms	(.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))
6.0ms	(+.f64 (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) U)
4.0ms	(.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))

simplify129.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

416×	`cancel-sign-sub-inv_binary64`
274×	`associate-r_binary64`
257×	`associate-l_binary64`
249×	`fma-neg_binary64`
221×	`fma-def_binary64`

Counts

167 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	4541
1	713	4341
2	2453	3858
3	4512	3857
4	4996	3857

prune206.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	151	7	158

Error

Counts

158 → 7

Alt Table

Status	Error	Program
	33.4b	(+.f64 (.f64 (.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2))) U)
	0.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))))) U)
	27.1b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))))) U)
	12.9b	(+.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (.f64 J (.f64 2 (sinh.f64 l)))) (.f64 J (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2))) U)
	0.2b	(+.f64 (+.f64 (.f64 1/60 (.f64 (pow.f64 l 5) (.f64 J (cos.f64 (.f64 1/2 K))))) (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 J (cos.f64 (.f64 1/2 K))))) (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))))) U)
▶	0.2b	(+.f64 (.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) U)
✓	0.1b	(+.f64 (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) U)

Compiler

Compiled 4102 to 2543 computations (38% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 J (.f64 2 (sinh.f64 l))) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
✓	0.1b	(.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
✓	0.2b	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
✓	0.2b	(cbrt.f64 (cos.f64 (/.f64 K 2)))

series1.5s (6.9%)

Counts

4 → 96

Calls

4 calls:

990.0ms	(.f64 (.f64 J (.f64 2 (sinh.f64 l))) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
248.0ms	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
180.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
63.0ms	(.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2))))

rewrite52.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`pow1_binary64`
56×	`add-exp-log_binary64`
39×	`pow-prod-down_binary64`
38×	`cbrt-unprod_binary64`
38×	`prod-exp_binary64`

Counts

4 → 125

Calls

4 calls:

14.0ms	(.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
11.0ms	(.f64 (.f64 J (.f64 2 (sinh.f64 l))) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
10.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
5.0ms	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))

simplify162.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

496×	`associate-l_binary64`
473×	`associate-r_binary64`
362×	`cancel-sign-sub-inv_binary64`
232×	`fma-neg_binary64`
218×	`*-commutative_binary64`

Counts

221 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	299	5802
1	765	5045
2	2883	4723
3	4554	4696
4	4974	4696

prune410.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	259	6	265

Error

Counts

265 → 6

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) U)
	0.1b	(+.f64 (.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (pow.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2) 1/3)) (cbrt.f64 (cos.f64 (/.f64 K 2)))) U)
	33.4b	(+.f64 (.f64 (.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2))) U)
	12.9b	(+.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (.f64 J (.f64 2 (sinh.f64 l)))) (.f64 J (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2))) U)
	0.2b	(+.f64 (+.f64 (.f64 1/60 (.f64 (pow.f64 l 5) (.f64 J (cos.f64 (.f64 1/2 K))))) (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 J (cos.f64 (.f64 1/2 K))))) (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))))) U)
✓	0.1b	(+.f64 (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) U)

Compiler

Compiled 8734 to 6307 computations (27.8% saved)

regimes1.2s (5.6%)

Accuracy

Total 0.0b remaining (73%)

Threshold costs 0.0b (73%)

Counts

114 → 1

Compiler

Compiled 26417 to 19874 computations (24.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	14	18
2	14	18

end126.0ms (0.6%)

Compiler: Compiled 201 to 152 computations (24.4% saved)

Details

analyze2.2s (10.5%)

sample14.3s (66.7%)

simplify67.0ms (0.3%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series40.0ms (0.2%)

rewrite27.0ms (0.1%)

simplify118.0ms (0.5%)

prune161.0ms (0.8%)

localize12.0ms (0.1%)

series163.0ms (0.8%)

rewrite22.0ms (0.1%)

simplify133.0ms (0.6%)

prune160.0ms (0.7%)

localize10.0ms (0%)

series154.0ms (0.7%)

rewrite22.0ms (0.1%)

simplify129.0ms (0.6%)

prune206.0ms (1%)

localize13.0ms (0.1%)

series1.5s (6.9%)

rewrite52.0ms (0.2%)

simplify162.0ms (0.8%)

prune410.0ms (1.9%)

regimes1.2s (5.6%)

simplify3.0ms (0%)

end126.0ms (0.6%)

Profiling