Details

analyze1.2s (15.7%)

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
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample3.0s (40.2%)

Results

1.4s	2355×	body	1024	valid
759.0ms	4088×	body	128	valid
473.0ms	1180×	body	512	valid
178.0ms	627×	body	256	valid
29.0ms	183×	body	128	invalid
6.0ms	6×	body	2048	valid
1.0ms	2×	body	1024	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

105×	`fma-def_binary64`
66×	`fma-neg_binary64`
27×	`cancel-sign-sub-inv_binary64`
19×	`sub-neg_binary64`
11×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))

Compiler

Compiled 73 to 53 computations (27.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
✓	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 x (tan.f64 B))

series88.0ms (1.2%)

Counts

3 → 52

Calls

3 calls:

41.0ms	(/.f64 x (tan.f64 B))
41.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
6.0ms	(/.f64 1 (sin.f64 B))

rewrite125.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

785×	`prod-diff_binary64`
276×	`fma-def_binary64`
257×	`egg-rr`
223×	`fma-neg_binary64`
184×	`expm1-udef_binary64`

Counts

3 → 257

Calls

3 calls:

116.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
116.0ms	(/.f64 1 (sin.f64 B))
116.0ms	(/.f64 x (tan.f64 B))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	199	26
2	2714	26
3	4965	26
4	4966	26
0	0	0
1	0	0

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

610×	`+-commutative_binary64`
500×	`sub-neg_binary64`
422×	`associate--l+_binary64`
420×	`fma-def_binary64`
331×	`associate-+l+_binary64`

Counts

309 → 283

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	63	830
1	177	817
2	528	799
3	1983	797
4	4141	793
5	4721	793
6	4945	793

prune327.0ms (4.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	275	8	283
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	277	8	285

Error

Counts

285 → 8

Alt Table

Status	Error	Program
	27.4b	(*.f64 (-.f64 (pow.f64 (sin.f64 B) -2) (pow.f64 (/.f64 x (tan.f64 B)) 2)) (/.f64 1 (+.f64 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B)))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	15.6b	(-.f64 (cbrt.f64 (pow.f64 (sin.f64 B) -3)) (/.f64 x (tan.f64 B)))
	10.5b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
	10.6b	(/.f64 1 (/.f64 (.f64 (tan.f64 B) (sin.f64 B)) (-.f64 (tan.f64 B) (.f64 x (sin.f64 B)))))
	32.7b	(*.f64 (-.f64 (pow.f64 (sin.f64 B) -3) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (/.f64 1 (fma.f64 (/.f64 x (tan.f64 B)) (+.f64 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B))) (pow.f64 (sin.f64 B) -2))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))

Compiler

Compiled 8136 to 3095 computations (62% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
✓	0.1b	(*.f64 x (cos.f64 B))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

series54.0ms (0.7%)

Counts

3 → 35

Calls

3 calls:

26.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
21.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
7.0ms	(*.f64 x (cos.f64 B))

rewrite143.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

911×	`prod-diff_binary64`
331×	`egg-rr`
198×	`log1p-udef_binary64`
111×	`add-sqr-sqrt_binary64`
104×	`log1p-expm1-u_binary64`

Counts

3 → 331

Calls

3 calls:

130.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
130.0ms	(*.f64 x (cos.f64 B))
130.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	218	26
2	3043	26
3	5202	26
0	0	0
1	0	0

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

504×	`fma-neg_binary64`
445×	`associate--l+_binary64`
428×	`fma-def_binary64`
320×	`associate-+l+_binary64`
257×	`distribute-rgt-neg-in_binary64`

Counts

366 → 358

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	76	526
1	217	514
2	656	492
3	2541	488
4	4791	484
5	5040	484

prune366.0ms (5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	387	1	388
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	388	8	396

Error

Counts

396 → 8

Alt Table

Status	Error	Program
	11.3b	(.f64 (-.f64 (sin.f64 B) (.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))) (pow.f64 (sin.f64 B) -2))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	15.6b	(-.f64 (cbrt.f64 (pow.f64 (sin.f64 B) -3)) (/.f64 x (tan.f64 B)))
	10.5b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
	10.6b	(/.f64 1 (/.f64 (.f64 (tan.f64 B) (sin.f64 B)) (-.f64 (tan.f64 B) (.f64 x (sin.f64 B)))))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	32.7b	(*.f64 (-.f64 (pow.f64 (sin.f64 B) -3) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (/.f64 1 (fma.f64 (/.f64 x (tan.f64 B)) (+.f64 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B))) (pow.f64 (sin.f64 B) -2))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))

Compiler

Compiled 13305 to 4992 computations (62.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 1 (tan.f64 B))
✓	0.3b	(*.f64 x (/.f64 1 (tan.f64 B)))

series122.0ms (1.7%)

Counts

3 → 60

Calls

3 calls:

63.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
43.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
16.0ms	(/.f64 1 (tan.f64 B))

rewrite123.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

846×	`prod-diff_binary64`
689×	`fma-udef_binary64`
192×	`expm1-udef_binary64`
192×	`log1p-udef_binary64`
144×	`fma-neg_binary64`

Counts

3 → 125

Calls

3 calls:

118.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
118.0ms	(/.f64 1 (tan.f64 B))
118.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	219	26
2	2710	26
3	4992	26
4	4538	26
5	5104	26
0	0	0
1	0	0

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

470×	`cancel-sign-sub-inv_binary64`
461×	`sub-neg_binary64`
439×	`associate--l+_binary64`
433×	`fma-def_binary64`
389×	`fma-neg_binary64`

Counts

185 → 153

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	68	894
1	190	879
2	573	864
3	2110	863
4	4178	859
5	4760	859
6	5013	859

prune152.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	183	8	191

Error

Counts

191 → 8

Alt Table

Status	Error	Program
	11.3b	(.f64 (-.f64 (sin.f64 B) (.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))) (pow.f64 (sin.f64 B) -2))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	15.6b	(-.f64 (cbrt.f64 (pow.f64 (sin.f64 B) -3)) (/.f64 x (tan.f64 B)))
	10.5b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
	10.6b	(/.f64 1 (/.f64 (.f64 (tan.f64 B) (sin.f64 B)) (-.f64 (tan.f64 B) (.f64 x (sin.f64 B)))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	32.7b	(*.f64 (-.f64 (pow.f64 (sin.f64 B) -3) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (/.f64 1 (fma.f64 (/.f64 x (tan.f64 B)) (+.f64 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B))) (pow.f64 (sin.f64 B) -2))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))

Compiler

Compiled 3604 to 1836 computations (49.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 (tan.f64 B) x)
✓	0.3b	(pow.f64 (/.f64 (tan.f64 B) x) -1)

series180.0ms (2.4%)

Counts

3 → 72

Calls

3 calls:

86.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
47.0ms	(pow.f64 (/.f64 (tan.f64 B) x) -1)
46.0ms	(/.f64 (tan.f64 B) x)

rewrite133.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

662×	`prod-diff_binary64`
452×	`fma-udef_binary64`
293×	`fma-def_binary64`
214×	`fma-neg_binary64`
210×	`egg-rr`

Counts

3 → 210

Calls

3 calls:

127.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
127.0ms	(/.f64 (tan.f64 B) x)
127.0ms	(pow.f64 (/.f64 (tan.f64 B) x) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	236	26
2	2891	26
3	4813	26
4	4780	26
5	4926	26
0	0	0
1	0	0

simplify90.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

536×	`sub-neg_binary64`
418×	`associate--l+_binary64`
388×	`fma-def_binary64`
331×	`associate-+l+_binary64`
330×	`cancel-sign-sub-inv_binary64`

Counts

282 → 238

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	75	1077
1	203	1064
2	590	1046
3	2099	1044
4	4314	1040
5	4972	1040
6	5082	1040

prune199.0ms (2.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	268	8	276

Error

Counts

276 → 8

Alt Table

Status	Error	Program
	11.3b	(.f64 (-.f64 (sin.f64 B) (.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))) (pow.f64 (sin.f64 B) -2))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	15.6b	(-.f64 (cbrt.f64 (pow.f64 (sin.f64 B) -3)) (/.f64 x (tan.f64 B)))
	10.5b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
	10.6b	(/.f64 1 (/.f64 (.f64 (tan.f64 B) (sin.f64 B)) (-.f64 (tan.f64 B) (.f64 x (sin.f64 B)))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	32.7b	(*.f64 (-.f64 (pow.f64 (sin.f64 B) -3) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (/.f64 1 (fma.f64 (/.f64 x (tan.f64 B)) (+.f64 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B))) (pow.f64 (sin.f64 B) -2))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))

Compiler

Compiled 5881 to 2508 computations (57.4% saved)

regimes667.0ms (9.1%)

Accuracy

Total 0.1b remaining (85.8%)

Threshold costs 0.1b (85.8%)

Counts

203 → 1

Compiler

Compiled 11320 to 7512 computations (33.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	17	17
2	21	17
3	24	17
4	25	17
5	24	17

end186.0ms (2.5%)

Compiler: Compiled 163 to 105 computations (35.6% saved)

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14

Details

analyze1.2s (15.7%)

sample3.0s (40.2%)

simplify14.0ms (0.2%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series88.0ms (1.2%)

rewrite125.0ms (1.7%)

simplify82.0ms (1.1%)

prune327.0ms (4.5%)

localize9.0ms (0.1%)

series54.0ms (0.7%)

rewrite143.0ms (1.9%)

simplify68.0ms (0.9%)

prune366.0ms (5%)

localize9.0ms (0.1%)

series122.0ms (1.7%)

rewrite123.0ms (1.7%)

simplify83.0ms (1.1%)

prune152.0ms (2.1%)

localize9.0ms (0.1%)

series180.0ms (2.4%)

rewrite133.0ms (1.8%)

simplify90.0ms (1.2%)

prune199.0ms (2.7%)

regimes667.0ms (9.1%)

simplify2.0ms (0%)

end186.0ms (2.5%)

Profiling

Iter	Nodes	Cost
0	11	19
1	24	14
2	48	14
3	81	14
4	122	14
5	168	14
6	187	14
7	229	14
8	226	14
9	244	14
10	241	14
11	216	14