Details

analyze1.2s (14.5%)

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)

sample3.1s (36.8%)

Results

1.6s	2331×	body	1024	valid
707.0ms	4156×	body	128	valid
501.0ms	1195×	body	512	valid
176.0ms	572×	body	256	valid
31.0ms	183×	body	128	invalid
2.0ms	2×	body	2048	valid
1.0ms	2×	body	1024	invalid
1.0ms	3×	body	512	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

prune4.0ms (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))
✓	0.1b	(/.f64 x (tan.f64 B))

series83.0ms (1%)

Counts

3 → 52

Calls

3 calls:

39.0ms	(/.f64 x (tan.f64 B))
38.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
6.0ms	(/.f64 1 (sin.f64 B))

rewrite59.0ms (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))

simplify296.0ms (3.6%)

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

prune353.0ms (4.2%)

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
	25.2b	(/.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))))
	30.7b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (sqrt.f64 x) (/.f64 (tan.f64 B) (sqrt.f64 x))))
	35.5b	(-.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 1 (/.f64 (tan.f64 B) x)))
	10.4b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (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)))
	15.7b	(-.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)))

Compiler

Compiled 12025 to 3768 computations (68.7% saved)

localize10.0ms (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))

series103.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

41.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
39.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
23.0ms	(/.f64 (tan.f64 B) x)

rewrite215.0ms (2.6%)

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:

38.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
12.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
3.0ms	(/.f64 (tan.f64 B) x)

simplify829.0ms (9.9%)

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

prune863.0ms (10.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	846	2	848
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	848	8	856

Error

0.0b

Counts

856 → 8

Alt Table

Status	Error	Program
	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 (/.f64 1 (tan.f64 B))) x))
	30.7b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (sqrt.f64 x) (/.f64 (tan.f64 B) (sqrt.f64 x))))
	8.1b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	35.5b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	34.7b	(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	15.7b	(-.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)))

Compiler

Compiled 43519 to 21495 computations (50.6% 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))

series60.0ms (0.7%)

Counts

3 → 52

Calls

3 calls:

24.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
20.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
15.0ms	(/.f64 x (sin.f64 B))

rewrite21.0ms (0.2%)

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))

simplify145.0ms (1.7%)

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

prune182.0ms (2.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	222	8	230

Error

0.0b

Counts

230 → 8

Alt Table

Status	Error	Program
	8.1b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	35.5b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	30.7b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (sqrt.f64 x) (/.f64 (tan.f64 B) (sqrt.f64 x))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	34.7b	(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	15.7b	(-.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 (*.f64 x (cos.f64 B))) (sin.f64 B))

Compiler

Compiled 4747 to 1749 computations (63.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series32.0ms (0.4%)

Counts

3 → 55

Calls

3 calls:

18.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
8.0ms	(*.f64 x (cos.f64 B))
6.0ms	(-.f64 1 (*.f64 x (cos.f64 B)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 72

Calls

3 calls:

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

simplify80.0ms (1%)

Algorithm

1×	egg-herbie

Rules

695×	`fma-def_binary64`
458×	`fma-neg_binary64`
343×	`associate-+l+_binary64`
244×	`cancel-sign-sub-inv_binary64`
241×	`associate-+r+_binary64`

Counts

127 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	1949
1	429	1830
2	1376	1785
3	4177	1783
4	4917	1783

prune170.0ms (2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	115	8	123

Error

0.0b

Counts

123 → 8

Alt Table

Status	Error	Program
	8.1b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	35.5b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	30.7b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (sqrt.f64 x) (/.f64 (tan.f64 B) (sqrt.f64 x))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	34.7b	(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sin.f64 B))) (sqrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	15.7b	(-.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 (*.f64 x (cos.f64 B))) (sin.f64 B))

Compiler

Compiled 2050 to 985 computations (52% saved)

regimes378.0ms (4.5%)

Accuracy

Total 0.1b remaining (79.7%)

Threshold costs 0.1b (79.7%)

Counts

115 → 1

Compiler

Compiled 5434 to 3846 computations (29.2% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	17	14
2	23	14
3	27	14
4	30	14
5	31	14
6	28	14

end111.0ms (1.3%)

Compiler: Compiled 145 to 99 computations (31.7% 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 (14.5%)

sample3.1s (36.8%)

simplify14.0ms (0.2%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series83.0ms (1%)

rewrite59.0ms (0.7%)

simplify296.0ms (3.6%)

prune353.0ms (4.2%)

localize10.0ms (0.1%)

series103.0ms (1.2%)

rewrite215.0ms (2.6%)

simplify829.0ms (9.9%)

prune863.0ms (10.3%)

localize9.0ms (0.1%)

series60.0ms (0.7%)

rewrite21.0ms (0.2%)

simplify145.0ms (1.7%)

prune182.0ms (2.2%)

localize10.0ms (0.1%)

series32.0ms (0.4%)

rewrite13.0ms (0.2%)

simplify80.0ms (1%)

prune170.0ms (2%)

regimes378.0ms (4.5%)

simplify11.0ms (0.1%)

end111.0ms (1.3%)

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