Details

analyze1.6s (14.7%)

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
12.5%	87.3%	0.2%	9
18.7%	81.1%	0.2%	10
21.8%	67.1%	11.1%	11
21.8%	67.1%	11.1%	12
32.7%	56.1%	11.1%	13
35.1%	53%	11.9%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample5.4s (48.6%)

Results

1.4s	1779×	body	1024	valid
1.3s	1974×	body	1024	invalid
753.0ms	4468×	body	128	valid
571.0ms	1247×	body	512	valid
453.0ms	2642×	body	128	invalid
408.0ms	993×	body	512	invalid
218.0ms	696×	body	256	valid
156.0ms	526×	body	256	invalid
74.0ms	66×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify41.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

485×	`rules-14-rev_binary64`
460×	`fma-neg_binary64`
315×	`rules-4_binary64`
245×	`rules-6-rev_binary64`
235×	`rules-6_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	29	22
2	64	22
3	154	22
4	635	22
5	2846	22
6	5130	22

prune6.0ms (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

17.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.2b	(+.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 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	0.0b	(exp.f64 (neg.f64 l))
✓	0.0b	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
✓	5.8b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series49.0ms (0.4%)

Counts

4 → 76

Calls

4 calls:

37.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
8.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
1.0ms	(exp.f64 (neg.f64 l))

rewrite125.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

710×	`prod-diff_binary64`
334×	`egg-rr`
135×	`add-sqr-sqrt_binary64`
126×	`log1p-expm1-u_binary64`
126×	`expm1-log1p-u_binary64`

Counts

4 → 334

Calls

4 calls:

116.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
116.0ms	(exp.f64 (neg.f64 l))
116.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
116.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	37
1	304	37
2	3919	37
3	5265	37
0	0	0
1	0	0

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-neg_binary64`
583×	`rules-11_binary64`
569×	`rules-20_binary64`
338×	`rules-21_binary64`
310×	`fma-def_binary64`

Counts

410 → 379

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1739
1	424	1438
2	1968	1430
3	5182	1430

prune423.0ms (3.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	372	7	379
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	373	7	380

Error

Counts

380 → 7

Alt Table

Status	Error	Program
	32.8b	(+.f64 (.f64 (+.f64 (fma.f64 (sqrt.f64 (.f64 2 (sinh.f64 l))) (.f64 J (sqrt.f64 (.f64 2 (sinh.f64 l)))) (neg.f64 (.f64 0 J))) (fma.f64 0 J (.f64 0 J))) (cos.f64 (/.f64 K 2))) U)
	0.1b	(+.f64 (/.f64 (.f64 (.f64 2 (sinh.f64 l)) J) (/.f64 1 (cos.f64 (/.f64 K 2)))) U)
	37.3b	(+.f64 (.f64 (.f64 J (/.f64 (pow.f64 (.f64 2 (sinh.f64 l)) 3) (+.f64 (pow.f64 (.f64 2 (sinh.f64 l)) 2) (+.f64 0 (.f64 (.f64 2 (sinh.f64 l)) 0))))) (cos.f64 (/.f64 K 2))) U)
	0.1b	(+.f64 (.f64 (/.f64 J (/.f64 1 (.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2))) U)
	22.8b	(+.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 (sinh.f64 l)) (*.f64 (cos.f64 (/.f64 K 2)) J))) 2) U)
▶	0.0b	(+.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) U)
	0.1b	(+.f64 (fma.f64 (.f64 (.f64 2 (sinh.f64 l)) (*.f64 (cos.f64 (/.f64 K 2)) J)) 1 0) U)

Compiler

Compiled 12098 to 5853 computations (51.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series153.0ms (1.4%)

Counts

4 → 120

Calls

4 calls:

65.0ms	(+.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) U)
56.0ms	(.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)))
25.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
8.0ms	(sinh.f64 l)

rewrite113.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

771×	`prod-diff_binary64`
229×	`egg-rr`
138×	`add-sqr-sqrt_binary64`
131×	`log1p-expm1-u_binary64`
131×	`expm1-log1p-u_binary64`

Counts

4 → 229

Calls

4 calls:

108.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
108.0ms	(sinh.f64 l)
108.0ms	(+.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) U)
108.0ms	(.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	47
1	311	47
2	3993	47
3	5498	47
0	0	0
1	0	0

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-neg_binary64`
639×	`rules-20_binary64`
462×	`rules-21_binary64`
362×	`rules-14-rev_binary64`
348×	`fma-def_binary64`

Counts

349 → 289

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	163	3016
1	513	2866
2	2449	2866
3	5202	2866

prune358.0ms (3.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	288	1	289
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	290	6	296

Error

Counts

296 → 6

Alt Table

Status	Error	Program
	32.8b	(+.f64 (.f64 (+.f64 (fma.f64 (sqrt.f64 (.f64 2 (sinh.f64 l))) (.f64 J (sqrt.f64 (.f64 2 (sinh.f64 l)))) (neg.f64 (.f64 0 J))) (fma.f64 0 J (.f64 0 J))) (cos.f64 (/.f64 K 2))) U)
	0.1b	(+.f64 (/.f64 (.f64 (.f64 2 (sinh.f64 l)) J) (/.f64 1 (cos.f64 (/.f64 K 2)))) U)
	0.1b	(+.f64 (.f64 (/.f64 J (/.f64 1 (.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2))) U)
	22.8b	(+.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 (sinh.f64 l)) (*.f64 (cos.f64 (/.f64 K 2)) J))) 2) U)
	3.8b	(.f64 U (+.f64 1 (/.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) U)))
▶	0.1b	(+.f64 (fma.f64 (.f64 (.f64 2 (sinh.f64 l)) (*.f64 (cos.f64 (/.f64 K 2)) J)) 1 0) U)

Compiler

Compiled 7915 to 5194 computations (34.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sinh.f64 l)
✓	0.0b	(+.f64 (fma.f64 (.f64 (.f64 2 (sinh.f64 l)) (*.f64 (cos.f64 (/.f64 K 2)) J)) 1 0) U)
✓	0.1b	(*.f64 (cos.f64 (/.f64 K 2)) J)
✓	0.1b	(.f64 (.f64 2 (sinh.f64 l)) (*.f64 (cos.f64 (/.f64 K 2)) J))

series140.0ms (1.3%)

Counts

3 → 108

Calls

3 calls:

75.0ms	(+.f64 (fma.f64 (.f64 (.f64 2 (sinh.f64 l)) (*.f64 (cos.f64 (/.f64 K 2)) J)) 1 0) U)
55.0ms	(.f64 (.f64 2 (sinh.f64 l)) (*.f64 (cos.f64 (/.f64 K 2)) J))
9.0ms	(*.f64 (cos.f64 (/.f64 K 2)) J)

rewrite103.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

859×	`prod-diff_binary64`
193×	`egg-rr`
142×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`

Counts

3 → 193

Calls

3 calls:

97.0ms	(+.f64 (fma.f64 (.f64 (.f64 2 (sinh.f64 l)) (*.f64 (cos.f64 (/.f64 K 2)) J)) 1 0) U)
97.0ms	(*.f64 (cos.f64 (/.f64 K 2)) J)
96.0ms	(.f64 (.f64 2 (sinh.f64 l)) (*.f64 (cos.f64 (/.f64 K 2)) J))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	46
1	343	44
2	4077	44
3	5756	44
0	0	0
1	0	0

simplify124.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

993×	`fma-neg_binary64`
596×	`rules-20_binary64`
368×	`rules-21_binary64`
301×	`rules-14-rev_binary64`
279×	`rules-15-rev_binary64`

Counts

301 → 245

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	143	2760
1	464	2620
2	2255	2620
3	4954	2620
4	5045	2620

prune374.0ms (3.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	284	2	286
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	287	5	292

Error

Counts

292 → 5

Alt Table

Status	Error	Program
	0.1b	(+.f64 (.f64 (/.f64 J (/.f64 1 (.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2))) U)
▶	0.1b	(fma.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 2 (sinh.f64 l)) J) U)
	22.8b	(+.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 (sinh.f64 l)) (*.f64 (cos.f64 (/.f64 K 2)) J))) 2) U)
	0.1b	(fma.f64 (.f64 2 (sinh.f64 l)) (.f64 (cos.f64 (/.f64 K 2)) J) U)
	0.1b	(+.f64 (/.f64 (.f64 (.f64 2 (sinh.f64 l)) J) (/.f64 1 (cos.f64 (/.f64 K 2)))) U)

Compiler

Compiled 8270 to 5696 computations (31.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series82.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

57.0ms	(fma.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 2 (sinh.f64 l)) J) U)
24.0ms	(.f64 (.f64 2 (sinh.f64 l)) J)

rewrite79.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

948×	`fma-neg_binary64`
362×	`prod-diff_binary64`
221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`
156×	`egg-rr`

Counts

2 → 156

Calls

2 calls:

76.0ms	(.f64 (.f64 2 (sinh.f64 l)) J)
76.0ms	(fma.f64 (cos.f64 (/.f64 K 2)) (.f64 (.f64 2 (sinh.f64 l)) J) U)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	276	27
2	3416	27
3	5696	27
0	0	0
1	0	0

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

493×	`rules-20_binary64`
420×	`rules-11_binary64`
381×	`fma-neg_binary64`
328×	`rules-21_binary64`
260×	`rules-14-rev_binary64`

Counts

228 → 191

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1837
1	395	1763
2	1776	1740
3	5163	1740

prune226.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	233	4	237

Error

Counts

237 → 4

Alt Table

Status	Error	Program
	0.1b	(+.f64 (.f64 (/.f64 J (/.f64 1 (.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2))) U)
	0.1b	(fma.f64 (.f64 2 (sinh.f64 l)) (.f64 (cos.f64 (/.f64 K 2)) J) U)
	0.1b	(+.f64 (/.f64 (.f64 (.f64 2 (sinh.f64 l)) J) (/.f64 1 (cos.f64 (/.f64 K 2)))) U)
	0.1b	(fma.f64 (cos.f64 (/.f64 K 2)) (/.f64 (*.f64 2 (sinh.f64 l)) (/.f64 1 J)) U)

Compiler

Compiled 5157 to 3275 computations (36.5% saved)

regimes1.4s (12.4%)

Accuracy

Total 0.0b remaining (51.2%)

Threshold costs 0.0b (51.2%)

Counts

128 → 1

Compiler

Compiled 26958 to 20702 computations (23.2% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	13	20

end74.0ms (0.7%)

Compiler: Compiled 106 to 82 computations (22.6% saved)

Details

analyze1.6s (14.7%)

sample5.4s (48.6%)

simplify41.0ms (0.4%)

prune6.0ms (0%)

localize11.0ms (0.1%)

series49.0ms (0.4%)

rewrite125.0ms (1.1%)

simplify64.0ms (0.6%)

prune423.0ms (3.8%)

localize10.0ms (0.1%)

series153.0ms (1.4%)

rewrite113.0ms (1%)

simplify79.0ms (0.7%)

prune358.0ms (3.2%)

localize12.0ms (0.1%)

series140.0ms (1.3%)

rewrite103.0ms (0.9%)

simplify124.0ms (1.1%)

prune374.0ms (3.3%)

localize10.0ms (0.1%)

series82.0ms (0.7%)

rewrite79.0ms (0.7%)

simplify68.0ms (0.6%)

prune226.0ms (2%)

regimes1.4s (12.4%)

simplify1.0ms (0%)

end74.0ms (0.7%)

Profiling