Details

analyze1.1s (16.8%)

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)

sample2.8s (43.7%)

Results

1.3s	2356×	body	1024	valid
620.0ms	4093×	body	128	valid
544.0ms	1227×	body	512	valid
158.0ms	576×	body	256	valid
24.0ms	170×	body	128	invalid
4.0ms	4×	body	2048	valid
0.0ms	1×	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

prune3.0ms (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
▶	0.1b	(-.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)

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)))
✓	0.2b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 x (tan.f64 B))

series83.0ms (1.3%)

Counts

3 → 52

Calls

3 calls:

37.0ms	(-.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))

rewrite56.0ms (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:

14.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
3.0ms	(/.f64 1 (sin.f64 B))
2.0ms	(/.f64 x (tan.f64 B))

simplify288.0ms (4.5%)

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

prune362.0ms (5.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	330	10	340
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	332	10	342

Error

0.0b

Counts

342 → 10

Alt Table

Status	Error	Program
	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	32.9b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	15.5b	(-.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)))
	38.0b	(/.f64 (-.f64 1 x) B)
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	25.8b	(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.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 (tan.f64 B) (cbrt.f64 x))))
▶	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))))

Compiler

Compiled 12077 to 3804 computations (68.5% 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)))
	0.2b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 x (sin.f64 B))
✓	0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

series94.0ms (1.5%)

Counts

3 → 52

Calls

3 calls:

59.0ms	(-.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))
14.0ms	(/.f64 x (sin.f64 B))

rewrite21.0ms (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:

7.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
6.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
2.0ms	(/.f64 x (sin.f64 B))

simplify141.0ms (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 (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	220	2	222
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	224	8	232

Error

0.0b

Counts

232 → 8

Alt Table

Status	Error	Program
	15.5b	(-.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)))
	24.8b	(/.f64 (-.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)))) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B))))
▶	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	25.8b	(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (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 (tan.f64 B) (cbrt.f64 x))))
✓	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 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 4818 to 1785 computations (63% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series33.0ms (0.5%)

Counts

4 → 59

Calls

4 calls:

18.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
7.0ms	(*.f64 x (cos.f64 B))
6.0ms	(-.f64 1 (*.f64 x (cos.f64 B)))
2.0ms	(cos.f64 B)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 81

Calls

4 calls:

4.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
3.0ms	(*.f64 x (cos.f64 B))
2.0ms	(-.f64 1 (*.f64 x (cos.f64 B)))
1.0ms	(cos.f64 B)

simplify84.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-def_binary64`
451×	`fma-neg_binary64`
348×	`associate-+l+_binary64`
292×	`cancel-sign-sub-inv_binary64`
247×	`associate-+r+_binary64`

Counts

140 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	193	2065
1	457	1932
2	1444	1882
3	4364	1880
4	5075	1880

prune169.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	131	8	139

Error

0.0b

Counts

139 → 8

Alt Table

Status	Error	Program
	0.2b	(/.f64 (-.f64 1 (*.f64 x (log.f64 (exp.f64 (cos.f64 B))))) (sin.f64 B))
	15.5b	(-.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)))
	24.8b	(/.f64 (-.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)))) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B))))
✓	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	25.8b	(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.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 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 2439 to 1213 computations (50.3% 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 x (/.f64 1 (tan.f64 B))))
	0.2b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 1 (tan.f64 B))
✓	0.2b	(*.f64 x (/.f64 1 (tan.f64 B)))

series93.0ms (1.5%)

Counts

3 → 60

Calls

3 calls:

38.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
38.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
16.0ms	(/.f64 1 (tan.f64 B))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`

Counts

3 → 115

Calls

3 calls:

7.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
6.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
3.0ms	(/.f64 1 (tan.f64 B))

simplify117.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-neg_binary64`
690×	`fma-def_binary64`
330×	`associate-+l+_binary64`
308×	`associate-l_binary64`
263×	`associate-r_binary64`

Counts

175 → 189

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	178	2673
1	426	2347
2	1219	2210
3	3953	2177
4	4671	2175
5	4892	2175

prune195.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	1	4	5
Picked	0	1	1
Done	1	1	2
Total	232	7	239

Error

0.0b

Counts

239 → 7

Alt Table

Status	Error	Program
	0.2b	(/.f64 (-.f64 1 (*.f64 x (log.f64 (exp.f64 (cos.f64 B))))) (sin.f64 B))
	15.5b	(-.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)))
	24.8b	(/.f64 (-.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)))) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B))))
✓	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
	25.8b	(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	11.0b	(/.f64 (-.f64 (.f64 1 (tan.f64 B)) (.f64 (sin.f64 B) (.f64 x 1))) (.f64 (sin.f64 B) (tan.f64 B)))

Compiler

Compiled 4323 to 2396 computations (44.6% saved)

regimes402.0ms (6.3%)

Accuracy

Total 0.1b remaining (83.4%)

Threshold costs 0.1b (83.4%)

Counts

133 → 1

Compiler

Compiled 7399 to 4968 computations (32.9% saved)

simplify3.0ms (0%)

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	10	14
1	15	14
2	21	14
3	25	14
4	28	14
5	29	14
6	28	14

end111.0ms (1.7%)

Compiler: Compiled 150 to 97 computations (35.3% 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 (16.8%)

sample2.8s (43.7%)

simplify14.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series83.0ms (1.3%)

rewrite56.0ms (0.9%)

simplify288.0ms (4.5%)

prune362.0ms (5.7%)

localize8.0ms (0.1%)

series94.0ms (1.5%)

rewrite21.0ms (0.3%)

simplify141.0ms (2.2%)

prune180.0ms (2.8%)

localize7.0ms (0.1%)

series33.0ms (0.5%)

rewrite13.0ms (0.2%)

simplify84.0ms (1.3%)

prune169.0ms (2.6%)

localize8.0ms (0.1%)

series93.0ms (1.5%)

rewrite21.0ms (0.3%)

simplify117.0ms (1.8%)

prune195.0ms (3.1%)

regimes402.0ms (6.3%)

simplify3.0ms (0%)

end111.0ms (1.7%)

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