Details

analyze1.5s (21.9%)

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
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)

sample2.9s (42.9%)

Results

1.5s	2295×	body	1024	valid
656.0ms	4142×	body	128	valid
470.0ms	1216×	body	512	valid
167.0ms	598×	body	256	valid
24.0ms	156×	body	128	invalid
5.0ms	5×	body	2048	valid

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

prune4.0ms (0.1%)

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)))
▶	0.1b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))

Compiler

Compiled 73 to 53 computations (27.4% saved)

localize8.0ms (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))
✓	0.1b	(/.f64 x (tan.f64 B))

series91.0ms (1.3%)

Counts

3 → 52

Calls

3 calls:

42.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
42.0ms	(/.f64 x (tan.f64 B))
6.0ms	(/.f64 1 (sin.f64 B))

rewrite59.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64`
239×	`add-sqr-sqrt_binary64`
231×	`*-un-lft-identity_binary64`
222×	`add-cube-cbrt_binary64`
182×	`prod-diff_binary64`

Counts

3 → 295

Calls

3 calls:

16.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
3.0ms	(/.f64 x (tan.f64 B))
2.0ms	(/.f64 1 (sin.f64 B))

simplify317.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

908×	`fma-def_binary64`
453×	`times-frac_binary64`
255×	`fma-neg_binary64`
182×	`associate-/l/_binary64`
153×	`cancel-sign-sub-inv_binary64`

Counts

347 → 340

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	312	11199
1	749	7806
2	1775	6080
3	4356	6080
4	4828	6080
5	4996	6080
6	4788	6080

prune268.0ms (4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	331	9	340
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	333	9	342

Error

0.0b

Counts

342 → 9

Alt Table

Status	Error	Program
	34.6b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	34.9b	(/.f64 (-.f64 1 x) B)
	35.4b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	0.8b	(-.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (/.f64 1 (cbrt.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	34.7b	(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	18.7b	(-.f64 (cbrt.f64 (.f64 (.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))

Compiler

Compiled 12029 to 3774 computations (68.6% saved)

localize8.0ms (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 (0.8%)

Counts

3 → 35

Calls

3 calls:

26.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
20.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
8.0ms	(*.f64 x (cos.f64 B))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

120×	`times-frac_binary64`
100×	`add-sqr-sqrt_binary64`
98×	`*-un-lft-identity_binary64`
91×	`prod-diff_binary64`
91×	`add-cube-cbrt_binary64`

Counts

3 → 177

Calls

3 calls:

11.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
4.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
3.0ms	(*.f64 x (cos.f64 B))

simplify225.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

319×	`associate-/l/_binary64`
318×	`fma-neg_binary64`
292×	`associate-/r*_binary64`
287×	`cancel-sign-sub-inv_binary64`
231×	`distribute-rgt-neg-in_binary64`

Counts

212 → 218

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	6796
1	591	5509
2	2082	4195
3	4407	4192
4	4936	4192
5	4990	4192
6	4856	4192

prune200.0ms (3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	257	3	260
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	260	9	269

Error

0.0b

Counts

269 → 9

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	32.5b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (+.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (.f64 (sin.f64 B) (sin.f64 B))) (+.f64 (.f64 x (cos.f64 B)) 1))))
	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	12.8b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
	0.8b	(-.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (/.f64 1 (cbrt.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	34.7b	(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	34.6b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	18.7b	(-.f64 (cbrt.f64 (.f64 (.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 8604 to 2605 computations (69.7% 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 (sin.f64 B)) (cos.f64 B)))
✓	0.1b	(/.f64 x (sin.f64 B))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

series63.0ms (0.9%)

Counts

3 → 52

Calls

3 calls:

26.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
21.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
15.0ms	(/.f64 x (sin.f64 B))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
13×	`fma-neg_binary64`

Counts

3 → 105

Calls

3 calls:

6.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
5.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
2.0ms	(/.f64 x (sin.f64 B))

simplify149.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-def_binary64`
414×	`fma-neg_binary64`
372×	`associate-/l*_binary64`
342×	`times-frac_binary64`
338×	`associate-*l/_binary64`

Counts

157 → 180

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	2974
1	476	2749
2	1426	2544
3	4328	2511
4	4945	2511
5	4995	2511
6	4920	2511

prune180.0ms (2.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	221	10	231

Error

Counts

231 → 10

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	32.5b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (+.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (.f64 (sin.f64 B) (sin.f64 B))) (+.f64 (.f64 x (cos.f64 B)) 1))))
▶	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	12.8b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
	0.8b	(-.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (/.f64 1 (cbrt.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	0.9b	(+.f64 (-.f64 (pow.f64 (/.f64 1 (cbrt.f64 (sin.f64 B))) 3) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))) 0)
	34.7b	(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	34.6b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	18.7b	(-.f64 (cbrt.f64 (.f64 (.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 4906 to 1841 computations (62.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series19.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

19.0ms

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

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 32

Calls

1 calls:

4.0ms

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

simplify94.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

406×	`fma-def_binary64`
324×	`distribute-rgt-in_binary64`
312×	`distribute-lft-in_binary64`
299×	`associate-+l+_binary64`
245×	`fma-neg_binary64`

Counts

56 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	1158
1	272	1083
2	798	1076
3	2856	1072
4	4831	1072
5	4997	1072
6	4950	1072

prune66.0ms (1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	78	10	88

Error

Counts

88 → 10

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	32.5b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (+.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (.f64 (sin.f64 B) (sin.f64 B))) (+.f64 (.f64 x (cos.f64 B)) 1))))
✓	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	12.8b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
	0.8b	(-.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (/.f64 1 (cbrt.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	0.9b	(+.f64 (-.f64 (pow.f64 (/.f64 1 (cbrt.f64 (sin.f64 B))) 3) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))) 0)
	34.7b	(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	34.6b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	18.7b	(-.f64 (cbrt.f64 (.f64 (.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 1547 to 761 computations (50.8% saved)

regimes325.0ms (4.8%)

Accuracy

Total 0.1b remaining (88.6%)

Threshold costs 0.1b (88.6%)

Counts

106 → 1

Compiler

Compiled 5041 to 3504 computations (30.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	15	14
2	21	14
3	25	14
4	28	14
5	29	14
6	26	14

end137.0ms (2%)

Compiler: Compiled 218 to 140 computations (35.8% 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

analyze1.5s (21.9%)

sample2.9s (42.9%)

simplify14.0ms (0.2%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series91.0ms (1.3%)

rewrite59.0ms (0.9%)

simplify317.0ms (4.7%)

prune268.0ms (4%)

localize8.0ms (0.1%)

series54.0ms (0.8%)

rewrite37.0ms (0.6%)

simplify225.0ms (3.4%)

prune200.0ms (3%)

localize9.0ms (0.1%)

series63.0ms (0.9%)

rewrite20.0ms (0.3%)

simplify149.0ms (2.2%)

prune180.0ms (2.7%)

localize7.0ms (0.1%)

series19.0ms (0.3%)

rewrite6.0ms (0.1%)

simplify94.0ms (1.4%)

prune66.0ms (1%)

regimes325.0ms (4.8%)

simplify3.0ms (0%)

end137.0ms (2%)

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