Details

analyze1.3s (16.5%)

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)

sample71.0ms (0.9%)

Algorithm

1×

intervals

Results

36.0ms	82×	body	1024	valid
11.0ms	119×	body	128	valid
10.0ms	38×	body	512	valid
3.0ms	17×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 31 to 25 computations (19.4% 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)

localize10.0ms (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))

series90.0ms (1.1%)

Counts

3 → 52

Calls

3 calls:

42.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
41.0ms	(/.f64 x (tan.f64 B))
6.0ms	(/.f64 1 (sin.f64 B))

rewrite75.0ms (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:

17.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
3.0ms	(/.f64 1 (sin.f64 B))
3.0ms	(/.f64 x (tan.f64 B))

simplify302.0ms (3.7%)

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

prune304.0ms (3.8%)

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
	14.0b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	26.8b	(-.f64 (log1p.f64 (expm1.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)))
	31.0b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))
	0.9b	(-.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)))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	17.4b	(-.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)))
	26.8b	(/.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))))

Compiler

Compiled 12069 to 3790 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 (sin.f64 B)) (cos.f64 B)))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.1b	(/.f64 x (sin.f64 B))
✓	0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

series66.0ms (0.8%)

Counts

3 → 52

Calls

3 calls:

26.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
22.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
17.0ms	(/.f64 x (sin.f64 B))

rewrite41.0ms (0.5%)

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:

26.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
7.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
2.0ms	(/.f64 x (sin.f64 B))

simplify145.0ms (1.8%)

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

prune309.0ms (3.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	219	3	222
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	223	8	231

Error

Counts

231 → 8

Alt Table

Status	Error	Program
	26.8b	(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	13.9b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
▶	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	14.0b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	17.4b	(-.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)))
	31.1b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (.f64 (/.f64 x (sqrt.f64 (sin.f64 B))) (cos.f64 B))))
	26.8b	(/.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))))

Compiler

Compiled 4806 to 1782 computations (62.9% saved)

localize8.0ms (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))

series28.0ms (0.3%)

Counts

2 → 40

Calls

2 calls:

19.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
8.0ms	(*.f64 x (cos.f64 B))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

2 → 52

Calls

2 calls:

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

simplify92.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

600×	`div-sub_binary64`
557×	`fma-def_binary64`
511×	`fma-neg_binary64`
391×	`associate-l_binary64`
329×	`associate-r_binary64`

Counts

92 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	1498
1	372	1396
2	1170	1379
3	3882	1377
4	4657	1377
5	5719	1377

prune82.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	78	8	86

Error

Counts

86 → 8

Alt Table

Status	Error	Program
	26.8b	(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	13.9b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
✓	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	14.0b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	17.4b	(-.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)))
	31.1b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (.f64 (/.f64 x (sqrt.f64 (sin.f64 B))) (cos.f64 B))))
	26.8b	(/.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))))

Compiler

Compiled 1617 to 810 computations (49.9% 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))

series117.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

48.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
45.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
24.0ms	(/.f64 (tan.f64 B) x)

rewrite262.0ms (3.2%)

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:

39.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
5.0ms	(/.f64 (tan.f64 B) x)
4.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))

simplify890.0ms (11%)

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

prune937.0ms (11.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	847	1	848
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	849	7	856

Error

Counts

856 → 7

Alt Table

Status	Error	Program
	26.8b	(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	13.9b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
✓	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	10.9b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
	17.4b	(-.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)))
	31.1b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (.f64 (/.f64 x (sqrt.f64 (sin.f64 B))) (cos.f64 B))))
	26.8b	(/.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))))

Compiler

Compiled 43408 to 21413 computations (50.7% saved)

regimes563.0ms (7%)

Accuracy

Total 0.1b remaining (82.8%)

Threshold costs 0.1b (82.8%)

Counts

158 → 1

Compiler

Compiled 7762 to 5517 computations (28.9% 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	10	14
1	14	14
2	20	14
3	24	14
4	27	14
5	28	14
6	26	14

end1.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample2.3s (28.5%)

Algorithm

1×

intervals

Results

1.0s	2247×	body	1024	valid
405.0ms	4026×	body	128	valid
313.0ms	1144×	body	512	valid
142.0ms	578×	body	256	valid
19.0ms	190×	body	128	invalid
5.0ms	5×	body	2048	valid

Compiler

Compiled 156 to 102 computations (34.6% 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

analyze1.3s (16.5%)

sample71.0ms (0.9%)

simplify14.0ms (0.2%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series90.0ms (1.1%)

rewrite75.0ms (0.9%)

simplify302.0ms (3.7%)

prune304.0ms (3.8%)

localize8.0ms (0.1%)

series66.0ms (0.8%)

rewrite41.0ms (0.5%)

simplify145.0ms (1.8%)

prune309.0ms (3.8%)

localize8.0ms (0.1%)

series28.0ms (0.3%)

rewrite10.0ms (0.1%)

simplify92.0ms (1.1%)

prune82.0ms (1%)

localize9.0ms (0.1%)

series117.0ms (1.5%)

rewrite262.0ms (3.2%)

simplify890.0ms (11%)

prune937.0ms (11.6%)

regimes563.0ms (7%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.3s (28.5%)

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