Details

analyze1.1s (13.5%)

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 (35.7%)

Results

1.5s	2430×	body	1024	valid
748.0ms	4054×	body	128	valid
487.0ms	1219×	body	512	valid
162.0ms	542×	body	256	valid
28.0ms	167×	body	128	invalid
11.0ms	11×	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
▶	0.1b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.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))
✓	0.2b	(/.f64 x (tan.f64 B))

series83.0ms (1%)

Counts

3 → 52

Calls

3 calls:

38.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
37.0ms	(/.f64 x (tan.f64 B))
8.0ms	(/.f64 1 (sin.f64 B))

rewrite58.0ms (0.7%)

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:

14.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
2.0ms	(/.f64 x (tan.f64 B))
2.0ms	(/.f64 1 (sin.f64 B))

simplify401.0ms (4.8%)

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 (3.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	332	8	340
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	334	8	342

Error

0.0b

Counts

342 → 8

Alt Table

Status	Error	Program
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	16.5b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	37.8b	(/.f64 (-.f64 1 x) B)
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	22.3b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	34.4b	(fma.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B))) (neg.f64 (/.f64 x (tan.f64 B))))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	12.1b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))

Compiler

Compiled 12011 to 3756 computations (68.7% 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 1 (sin.f64 B))
✓	0.1b	(*.f64 x (cos.f64 B))
✓	0.2b	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

series58.0ms (0.7%)

Counts

3 → 35

Calls

3 calls:

25.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
25.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
7.0ms	(*.f64 x (cos.f64 B))

rewrite54.0ms (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:

10.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
3.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
3.0ms	(*.f64 x (cos.f64 B))

simplify211.0ms (2.5%)

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

prune198.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	258	2	260
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	261	7	268

Error

0.0b

Counts

268 → 7

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	16.5b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (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)))
	12.1b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	22.3b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	12.1b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))

Compiler

Compiled 8488 to 2537 computations (70.1% 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))

series18.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

18.0ms

(/.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))

simplify91.0ms (1.1%)

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

prune61.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	79	6	85

Error

0.0b

Counts

85 → 6

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	16.5b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	22.3b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	0.3b	(/.f64 1 (/.f64 (sin.f64 B) (-.f64 1 (*.f64 x (cos.f64 B)))))
	12.1b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))

Compiler

Compiled 1542 to 763 computations (50.5% 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 1 (/.f64 (tan.f64 B) x)))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.1b	(/.f64 (tan.f64 B) x)
✓	0.3b	(/.f64 1 (/.f64 (tan.f64 B) x))

series173.0ms (2.1%)

Counts

3 → 72

Calls

3 calls:

94.0ms	(/.f64 (tan.f64 B) x)
41.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
38.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))

rewrite198.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

1447×	`times-frac_binary64`
907×	`add-sqr-sqrt_binary64`
881×	`*-un-lft-identity_binary64`
860×	`add-cube-cbrt_binary64`
572×	`prod-diff_binary64`

Counts

3 → 773

Calls

3 calls:

36.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
4.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
2.0ms	(/.f64 (tan.f64 B) x)

simplify799.0ms (9.6%)

Algorithm

1×	egg-herbie

Rules

410×	`fma-neg_binary64`
391×	`cancel-sign-sub-inv_binary64`
275×	`associate-/l/_binary64`
265×	`distribute-rgt-out_binary64`
204×	`distribute-rgt-neg-in_binary64`

Counts

845 → 806

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	373	35425
1	857	21208
2	2522	15811
3	4410	15811
4	4636	15811
5	4963	15811
6	4630	15811

prune1.0s (12.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	848	0	848
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	848	6	854

Error

0.0b

Counts

854 → 6

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	16.5b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (sin.f64 B) (sin.f64 B)) (sin.f64 B)))) (/.f64 x (tan.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	22.3b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 6)) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	0.3b	(/.f64 1 (/.f64 (sin.f64 B) (-.f64 1 (*.f64 x (cos.f64 B)))))
	12.1b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))

Compiler

Compiled 43381 to 21400 computations (50.7% saved)

regimes395.0ms (4.7%)

Accuracy

Total 0.1b remaining (78.9%)

Threshold costs 0.1b (78.9%)

Counts

121 → 1

Compiler

Compiled 6871 to 4431 computations (35.5% saved)

simplify2.0ms (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	9	14
1	13	14
2	19	14
3	23	14
4	26	14
5	27	14
6	26	14

end98.0ms (1.2%)

Compiler: Compiled 123 to 83 computations (32.5% 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

analyze1.1s (13.5%)

sample3.0s (35.7%)

simplify14.0ms (0.2%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series83.0ms (1%)

rewrite58.0ms (0.7%)

simplify401.0ms (4.8%)

prune268.0ms (3.2%)

localize8.0ms (0.1%)

series58.0ms (0.7%)

rewrite54.0ms (0.6%)

simplify211.0ms (2.5%)

prune198.0ms (2.4%)

localize7.0ms (0.1%)

series18.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify91.0ms (1.1%)

prune61.0ms (0.7%)

localize9.0ms (0.1%)

series173.0ms (2.1%)

rewrite198.0ms (2.4%)

simplify799.0ms (9.6%)

prune1.0s (12.4%)

regimes395.0ms (4.7%)

simplify2.0ms (0%)

end98.0ms (1.2%)

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