Details

analyze1.1s (16.1%)

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 (42.3%)

Results

1.5s	2403×	body	1024	valid
688.0ms	4160×	body	128	valid
449.0ms	1102×	body	512	valid
258.0ms	587×	body	256	valid
26.0ms	169×	body	128	invalid
4.0ms	4×	body	2048	valid
2.0ms	3×	body	1024	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify15.0ms (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)

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

series99.0ms (1.4%)

Counts

3 → 52

Calls

3 calls:

54.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
39.0ms	(/.f64 x (tan.f64 B))
6.0ms	(/.f64 1 (sin.f64 B))

rewrite174.0ms (2.4%)

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:

20.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
5.0ms	(/.f64 1 (sin.f64 B))
5.0ms	(/.f64 x (tan.f64 B))

simplify305.0ms (4.3%)

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

prune279.0ms (3.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	333	7	340
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	335	7	342

Error

0.0b

Counts

342 → 7

Alt Table

Status	Error	Program
	14.3b	(-.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)))
	32.4b	(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 (tan.f64 B)))) (/.f64 x (sqrt.f64 (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)))
	30.9b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))
	8.8b	(/.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 (cos.f64 B)) (sin.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))

Compiler

Compiled 11997 to 3742 computations (68.8% 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 (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))

series51.0ms (0.7%)

Counts

3 → 35

Calls

3 calls:

24.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
19.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
7.0ms	(*.f64 x (cos.f64 B))

rewrite36.0ms (0.5%)

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))

simplify210.0ms (2.9%)

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

prune207.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	258	2	260
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	259	8	267

Error

Counts

267 → 8

Alt Table

Status	Error	Program
	14.3b	(-.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)))
	23.1b	(/.f64 (-.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (pow.f64 (cbrt.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B))) 6)) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B))))
	32.4b	(+.f64 (/.f64 1 (sin.f64 B)) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 (tan.f64 B)))) (/.f64 x (sqrt.f64 (tan.f64 B)))))
	8.8b	(/.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 (cos.f64 B)) (sin.f64 B)))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	8.7b	(/.f64 (-.f64 (.f64 1 (sin.f64 B)) (.f64 (sin.f64 B) (.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)))

Compiler

Compiled 8550 to 2570 computations (69.9% 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))))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 1 (tan.f64 B))
✓	0.3b	(*.f64 x (/.f64 1 (tan.f64 B)))

series89.0ms (1.2%)

Counts

3 → 60

Calls

3 calls:

37.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
37.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
15.0ms	(/.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:

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

simplify115.0ms (1.6%)

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

prune206.0ms (2.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	229	2	231
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	231	8	239

Error

Counts

239 → 8

Alt Table

Status	Error	Program
	14.3b	(-.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)))
	23.1b	(/.f64 (-.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (pow.f64 (cbrt.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B))) 6)) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B))))
▶	0.3b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 x (/.f64 1 (sin.f64 B))) (cos.f64 B)))
	32.4b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sqrt.f64 (tan.f64 B))) (/.f64 1 (sqrt.f64 (tan.f64 B)))))
	8.8b	(/.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 (cos.f64 B)) (sin.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)))

Compiler

Compiled 4472 to 2488 computations (44.4% 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 (/.f64 1 (sin.f64 B))) (cos.f64 B)))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(.f64 (.f64 x (/.f64 1 (sin.f64 B))) (cos.f64 B))
✓	0.3b	(*.f64 x (/.f64 1 (sin.f64 B)))

series59.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

25.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 x (/.f64 1 (sin.f64 B))) (cos.f64 B)))
20.0ms	(.f64 (.f64 x (/.f64 1 (sin.f64 B))) (cos.f64 B))
14.0ms	(*.f64 x (/.f64 1 (sin.f64 B)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
29×	`times-frac_binary64`
27×	`*-un-lft-identity_binary64`
27×	`add-exp-log_binary64`
26×	`add-cube-cbrt_binary64`

Counts

3 → 108

Calls

3 calls:

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

simplify120.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

873×	`fma-def_binary64`
372×	`fma-neg_binary64`
308×	`associate-*l/_binary64`
238×	`times-frac_binary64`
206×	`cancel-sign-sub-inv_binary64`

Counts

180 → 186

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	188	2995
1	470	2737
2	1516	2443
3	4293	2410
4	4973	2410
5	4999	2410

prune227.0ms (3.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	270	8	278

Error

Counts

278 → 8

Alt Table

Status	Error	Program
	14.3b	(-.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)))
	23.1b	(/.f64 (-.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (pow.f64 (cbrt.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B))) 6)) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B))))
✓	0.3b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 x (/.f64 1 (sin.f64 B))) (cos.f64 B)))
	32.4b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sqrt.f64 (tan.f64 B))) (/.f64 1 (sqrt.f64 (tan.f64 B)))))
	8.8b	(/.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 (cos.f64 B)) (sin.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)))

Compiler

Compiled 5863 to 2987 computations (49.1% saved)

regimes566.0ms (7.9%)

Accuracy

Total 0.1b remaining (85.1%)

Threshold costs 0.1b (85.1%)

Counts

168 → 1

Compiler

Compiled 8191 to 5811 computations (29.1% 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	11	14
1	15	14
2	20	14
3	24	14
4	27	14
5	28	14
6	26	14

end123.0ms (1.7%)

Compiler: Compiled 174 to 112 computations (35.6% 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

analyze1.1s (16.1%)

sample3.0s (42.3%)

simplify15.0ms (0.2%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series99.0ms (1.4%)

rewrite174.0ms (2.4%)

simplify305.0ms (4.3%)

prune279.0ms (3.9%)

localize9.0ms (0.1%)

series51.0ms (0.7%)

rewrite36.0ms (0.5%)

simplify210.0ms (2.9%)

prune207.0ms (2.9%)

localize8.0ms (0.1%)

series89.0ms (1.2%)

rewrite21.0ms (0.3%)

simplify115.0ms (1.6%)

prune206.0ms (2.9%)

localize9.0ms (0.1%)

series59.0ms (0.8%)

rewrite27.0ms (0.4%)

simplify120.0ms (1.7%)

prune227.0ms (3.2%)

regimes566.0ms (7.9%)

simplify2.0ms (0%)

end123.0ms (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