Details

analyze1.2s (15%)

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)

sample82.0ms (1%)

Algorithm

1×

intervals

Results

43.0ms	65×	body	1024	valid
14.0ms	139×	body	128	valid
9.0ms	36×	body	512	valid
3.0ms	15×	body	256	valid
2.0ms	3×	body	128	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 31 to 25 computations (19.4% 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

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))

series95.0ms (1.2%)

Counts

3 → 52

Calls

3 calls:

44.0ms	(/.f64 x (tan.f64 B))
43.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
8.0ms	(/.f64 1 (sin.f64 B))

rewrite64.0ms (0.8%)

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))

simplify353.0ms (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

prune278.0ms (3.6%)

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

Counts

342 → 8

Alt Table

Status	Error	Program
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	33.9b	(/.f64 (-.f64 1 x) 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)))
	24.8b	(/.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))))
	18.3b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	1.3b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B)))) (cbrt.f64 (/.f64 1 (sin.f64 B))) (neg.f64 (.f64 (/.f64 (cbrt.f64 x) (tan.f64 B)) (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 x) (tan.f64 B))) (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (.f64 (/.f64 (cbrt.f64 x) (tan.f64 B)) (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1))))
	12.9b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))

Compiler

Compiled 12079 to 3784 computations (68.7% 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 (/.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))

series176.0ms (2.2%)

Counts

3 → 52

Calls

3 calls:

124.0ms	(/.f64 x (sin.f64 B))
29.0ms	(-.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))

rewrite22.0ms (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))
3.0ms	(/.f64 x (sin.f64 B))

simplify169.0ms (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

prune167.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	220	2	222
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	224	6	230

Error

Counts

230 → 6

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	13.0b	(/.f64 (-.f64 (.f64 1 (sin.f64 B)) (.f64 (sin.f64 B) (.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))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	18.3b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	12.9b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))

Compiler

Compiled 4688 to 1707 computations (63.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series27.0ms (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))

simplify89.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

600×	`div-sub_binary64`
557×	`fma-def_binary64`
511×	`fma-neg_binary64`
388×	`associate-l_binary64`
327×	`associate-r_binary64`

Counts

92 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	1498
1	373	1396
2	1170	1379
3	3882	1377
4	4657	1377
5	5719	1377

prune74.0ms (0.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	104	6	110

Error

Counts

110 → 6

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	13.0b	(/.f64 (-.f64 (.f64 1 (sin.f64 B)) (.f64 (sin.f64 B) (.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))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	18.3b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	12.9b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))

Compiler

Compiled 1953 to 913 computations (53.3% 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))

series110.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

42.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
42.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
25.0ms	(/.f64 (tan.f64 B) x)

rewrite221.0ms (2.8%)

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)))
4.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
3.0ms	(/.f64 (tan.f64 B) x)

simplify853.0ms (10.9%)

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

prune890.0ms (11.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	848	0	848
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	848	6	854

Error

Counts

854 → 6

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
	13.0b	(/.f64 (-.f64 (.f64 1 (sin.f64 B)) (.f64 (sin.f64 B) (.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))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	18.3b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	12.9b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))

Compiler

Compiled 43367 to 21390 computations (50.7% saved)

regimes470.0ms (6%)

Accuracy

Total 0.1b remaining (80.6%)

Threshold costs 0.1b (80.6%)

Counts

123 → 1

Compiler

Compiled 8398 to 5052 computations (39.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-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	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)

sample2.4s (31.3%)

Algorithm

1×

intervals

Results

1.1s	2338×	body	1024	valid
439.0ms	3929×	body	128	valid
317.0ms	1142×	body	512	valid
132.0ms	581×	body	256	valid
16.0ms	169×	body	128	invalid
10.0ms	10×	body	2048	valid
0.0ms	1×	body	512	invalid

Compiler

Compiled 115 to 79 computations (31.3% 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

analyze1.2s (15%)

sample82.0ms (1%)

simplify15.0ms (0.2%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series95.0ms (1.2%)

rewrite64.0ms (0.8%)

simplify353.0ms (4.5%)

prune278.0ms (3.6%)

localize8.0ms (0.1%)

series176.0ms (2.2%)

rewrite22.0ms (0.3%)

simplify169.0ms (2.2%)

prune167.0ms (2.1%)

localize7.0ms (0.1%)

series27.0ms (0.3%)

rewrite10.0ms (0.1%)

simplify89.0ms (1.1%)

prune74.0ms (0.9%)

localize9.0ms (0.1%)

series110.0ms (1.4%)

rewrite221.0ms (2.8%)

simplify853.0ms (10.9%)

prune890.0ms (11.4%)

regimes470.0ms (6%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.4s (31.3%)

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