Details

analyze1.0s (10.8%)

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)

sample226.0ms (2.4%)

Algorithm

1×

intervals

Results

120.0ms	65×	body	1024	valid
13.0ms	138×	body	128	valid
9.0ms	36×	body	512	valid
3.0ms	16×	body	256	valid
1.0ms	1×	body	2048	valid
0.0ms	2×	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

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)

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

series82.0ms (0.9%)

Counts

3 → 52

Calls

3 calls:

39.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
38.0ms	(/.f64 x (tan.f64 B))
5.0ms	(/.f64 1 (sin.f64 B))

rewrite61.0ms (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:

16.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
2.0ms	(/.f64 1 (sin.f64 B))
2.0ms	(/.f64 x (tan.f64 B))

simplify325.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

908×	`fma-def_binary64`
454×	`times-frac_binary64`
255×	`fma-neg_binary64`
182×	`associate-/l/_binary64`
153×	`cancel-sign-sub-inv_binary64`

Counts

347 → 336

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

prune531.0ms (5.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	328	8	336
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	330	8	338

Error

0.0b

Counts

338 → 8

Alt Table

Status	Error	Program
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	19.3b	(-.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)))
	14.3b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	0.7b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (tan.f64 B)) (cbrt.f64 (tan.f64 B)))) (/.f64 (cbrt.f64 x) (cbrt.f64 (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)))
	33.3b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (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)))) (cbrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 11935 to 3727 computations (68.8% 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 (/.f64 x (sin.f64 B)) (cos.f64 B)))
✓	0.1b	(/.f64 x (sin.f64 B))
	0.2b	(/.f64 1 (sin.f64 B))
✓	0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

series63.0ms (0.7%)

Counts

3 → 52

Calls

3 calls:

26.0ms	(-.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))
17.0ms	(/.f64 x (sin.f64 B))

rewrite23.0ms (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:

9.0ms	(-.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))

simplify146.0ms (1.6%)

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

prune235.0ms (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	217	5	222
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	221	9	230

Error

Counts

230 → 9

Alt Table

Status	Error	Program
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	19.3b	(-.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)))
	34.2b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (fma.f64 (cos.f64 B) (.f64 (/.f64 x (sin.f64 B)) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B)))) (/.f64 1 (*.f64 (sin.f64 B) (sin.f64 B)))))
	14.3b	(/.f64 (.f64 (sin.f64 B) (-.f64 1 (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (sin.f64 B)))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (*.f64 (/.f64 x (cbrt.f64 (sin.f64 B))) (cos.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)))
	1.0b	(+.f64 (-.f64 (pow.f64 (/.f64 1 (cbrt.f64 (sin.f64 B))) 3) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))) 0)
	28.1b	(/.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))))

Compiler

Compiled 4924 to 1837 computations (62.7% 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 1 (/.f64 (tan.f64 B) x)))
✓	0.1b	(/.f64 (tan.f64 B) x)
	0.2b	(/.f64 1 (sin.f64 B))
✓	0.4b	(/.f64 1 (/.f64 (tan.f64 B) x))

series169.0ms (1.8%)

Counts

3 → 72

Calls

3 calls:

74.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
72.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
23.0ms	(/.f64 (tan.f64 B) x)

rewrite292.0ms (3.1%)

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)))
5.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
3.0ms	(/.f64 (tan.f64 B) x)

simplify900.0ms (9.7%)

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

prune1.1s (12.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	847	1	848
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	848	9	857

Error

Counts

857 → 9

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	19.3b	(-.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)))
	34.2b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (fma.f64 (cos.f64 B) (.f64 (/.f64 x (sin.f64 B)) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B)))) (/.f64 1 (*.f64 (sin.f64 B) (sin.f64 B)))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (sin.f64 B) (*.f64 x (cos.f64 B)))))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (*.f64 (/.f64 x (cbrt.f64 (sin.f64 B))) (cos.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)))
	1.0b	(+.f64 (-.f64 (pow.f64 (/.f64 1 (cbrt.f64 (sin.f64 B))) 3) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))) 0)
	28.1b	(/.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))))

Compiler

Compiled 43661 to 21560 computations (50.6% 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 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)))

series703.0ms (7.6%)

Counts

3 → 60

Calls

3 calls:

648.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
40.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
15.0ms	(/.f64 1 (tan.f64 B))

rewrite23.0ms (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))

simplify118.0ms (1.3%)

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

prune249.0ms (2.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	231	9	240

Error

Counts

240 → 9

Alt Table

Status	Error	Program
	1.0b	(+.f64 (-.f64 (pow.f64 (/.f64 1 (cbrt.f64 (sin.f64 B))) 3) (/.f64 x (tan.f64 B))) 0)
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (sin.f64 B)) (cbrt.f64 (sin.f64 B)))) (*.f64 (/.f64 x (cbrt.f64 (sin.f64 B))) (cos.f64 B))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	19.3b	(-.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)))
	34.2b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (fma.f64 (cos.f64 B) (.f64 (/.f64 x (sin.f64 B)) (fma.f64 x (/.f64 (cos.f64 B) (sin.f64 B)) (/.f64 1 (sin.f64 B)))) (/.f64 1 (*.f64 (sin.f64 B) (sin.f64 B)))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (sin.f64 B) (*.f64 x (cos.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)))
	28.1b	(/.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))))

Compiler

Compiled 4396 to 2437 computations (44.6% saved)

regimes726.0ms (7.8%)

Accuracy

Total 0.1b remaining (84.7%)

Threshold costs 0.1b (84.7%)

Counts

207 → 1

Compiler

Compiled 12496 to 8286 computations (33.7% 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

end1.0ms (0%)

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

sample2.2s (23.7%)

Algorithm

1×

intervals

Results

998.0ms	2341×	body	1024	valid
384.0ms	3969×	body	128	valid
296.0ms	1115×	body	512	valid
104.0ms	568×	body	256	valid
17.0ms	179×	body	128	invalid
6.0ms	7×	body	2048	valid
1.0ms	2×	body	1024	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 229 to 144 computations (37.1% 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

analyze1.0s (10.8%)

sample226.0ms (2.4%)

simplify14.0ms (0.2%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series82.0ms (0.9%)

rewrite61.0ms (0.7%)

simplify325.0ms (3.5%)

prune531.0ms (5.7%)

localize10.0ms (0.1%)

series63.0ms (0.7%)

rewrite23.0ms (0.3%)

simplify146.0ms (1.6%)

prune235.0ms (2.5%)

localize8.0ms (0.1%)

series169.0ms (1.8%)

rewrite292.0ms (3.1%)

simplify900.0ms (9.7%)

prune1.1s (12.3%)

localize10.0ms (0.1%)

series703.0ms (7.6%)

rewrite23.0ms (0.3%)

simplify118.0ms (1.3%)

prune249.0ms (2.7%)

regimes726.0ms (7.8%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.2s (23.7%)

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