Details

analyze1.1s (14%)

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)

sample2.9s (35.8%)

Results

1.5s	2428×	body	1024	valid
636.0ms	4046×	body	128	valid
461.0ms	1192×	body	512	valid
165.0ms	584×	body	256	valid
28.0ms	184×	body	128	invalid
6.0ms	6×	body	2048	valid

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

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
▶	0.2b	(-.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))
✓	0.2b	(/.f64 x (tan.f64 B))

series84.0ms (1%)

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))
8.0ms	(/.f64 1 (sin.f64 B))

rewrite57.0ms (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:

15.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
2.0ms	(/.f64 x (tan.f64 B))
2.0ms	(/.f64 1 (sin.f64 B))

simplify286.0ms (3.5%)

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

prune341.0ms (4.2%)

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
	31.2b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	31.8b	(-.f64 (exp.f64 (neg.f64 (log.f64 (sin.f64 B)))) (/.f64 x (tan.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	12.7b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	31.8b	(-.f64 (expm1.f64 (log1p.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 1 (/.f64 (tan.f64 B) x)))
	33.7b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.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))))
	17.7b	(-.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)))

Compiler

Compiled 12055 to 3788 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 1 (/.f64 (tan.f64 B) x)))
✓	0.1b	(/.f64 (tan.f64 B) x)
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.3b	(/.f64 1 (/.f64 (tan.f64 B) x))

series138.0ms (1.7%)

Counts

3 → 72

Calls

3 calls:

75.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
40.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
23.0ms	(/.f64 (tan.f64 B) x)

rewrite203.0ms (2.5%)

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:

42.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
4.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
2.0ms	(/.f64 (tan.f64 B) x)

simplify796.0ms (9.8%)

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

prune880.0ms (10.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	847	1	848
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	848	10	858

Error

0.0b

Counts

858 → 10

Alt Table

Status	Error	Program
	33.7b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))
	10.8b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
	31.2b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	12.7b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	31.8b	(-.f64 (expm1.f64 (log1p.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 1 (/.f64 (tan.f64 B) x)))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	17.7b	(-.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)))

Compiler

Compiled 43581 to 21523 computations (50.6% 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 (sin.f64 B)) (cos.f64 B)))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 x (sin.f64 B))
✓	0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

series63.0ms (0.8%)

Counts

3 → 52

Calls

3 calls:

27.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
21.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
15.0ms	(/.f64 x (sin.f64 B))

rewrite20.0ms (0.2%)

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:

6.0ms	(-.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))

simplify137.0ms (1.7%)

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

prune251.0ms (3.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	220	2	222
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	222	10	232

Error

0.0b

Counts

232 → 10

Alt Table

Status	Error	Program
	33.7b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))
	10.8b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
	17.7b	(-.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)))
	1.0b	(+.f64 (-.f64 (pow.f64 (/.f64 1 (cbrt.f64 (sin.f64 B))) 3) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))) 0)
	31.2b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	12.7b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
▶	0.2b	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.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)))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))

Compiler

Compiled 4821 to 1789 computations (62.9% saved)

localize7.0ms (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))

series26.0ms (0.3%)

Counts

2 → 40

Calls

2 calls:

18.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
8.0ms	(*.f64 x (cos.f64 B))

rewrite9.0ms (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))

simplify86.0ms (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

prune119.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	7	7
Picked	1	0	1
Done	1	1	2
Total	79	9	88

Error

0.0b

Counts

88 → 9

Alt Table

Status	Error	Program
	33.7b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))
	10.8b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
	17.7b	(-.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)))
	1.0b	(+.f64 (-.f64 (pow.f64 (/.f64 1 (cbrt.f64 (sin.f64 B))) 3) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))) 0)
	31.2b	(-.f64 (/.f64 (/.f64 1 (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
	12.7b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	13.7b	(/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 x (cos.f64 B)) (.f64 x (cos.f64 B)))) (*.f64 (sin.f64 B) (fma.f64 x (cos.f64 B) 1)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))

Compiler

Compiled 1509 to 738 computations (51.1% saved)

regimes387.0ms (4.8%)

Accuracy

Total 0.1b remaining (84.8%)

Threshold costs 0.1b (84.8%)

Counts

124 → 1

Compiler

Compiled 5731 to 4062 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	10	14
1	14	14
2	20	14
3	24	14
4	27	14
5	28	14
6	26	14

end136.0ms (1.7%)

Compiler: Compiled 181 to 116 computations (35.9% 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 (14%)

sample2.9s (35.8%)

simplify14.0ms (0.2%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series84.0ms (1%)

rewrite57.0ms (0.7%)

simplify286.0ms (3.5%)

prune341.0ms (4.2%)

localize8.0ms (0.1%)

series138.0ms (1.7%)

rewrite203.0ms (2.5%)

simplify796.0ms (9.8%)

prune880.0ms (10.8%)

localize9.0ms (0.1%)

series63.0ms (0.8%)

rewrite20.0ms (0.2%)

simplify137.0ms (1.7%)

prune251.0ms (3.1%)

localize7.0ms (0.1%)

series26.0ms (0.3%)

rewrite9.0ms (0.1%)

simplify86.0ms (1.1%)

prune119.0ms (1.5%)

regimes387.0ms (4.8%)

simplify2.0ms (0%)

end136.0ms (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