Details

analyze1.1s (12%)

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 (31.6%)

Results

1.6s	2362×	body	1024	valid
688.0ms	4099×	body	128	valid
488.0ms	1195×	body	512	valid
176.0ms	597×	body	256	valid
24.0ms	153×	body	128	invalid
3.0ms	3×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify14.0ms (0.1%)

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)

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))

series88.0ms (0.9%)

Counts

3 → 52

Calls

3 calls:

41.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
40.0ms	(/.f64 x (tan.f64 B))
7.0ms	(/.f64 1 (sin.f64 B))

rewrite62.0ms (0.6%)

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

simplify381.0ms (4%)

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

prune320.0ms (3.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	329	11	340
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	331	11	342

Error

0.0b

Counts

342 → 11

Alt Table

Status	Error	Program
	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 (cbrt.f64 x) (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)))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (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))))
	25.6b	(/.f64 (-.f64 (.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B)))) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	35.6b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))
	12.2b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (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)))
	27.0b	(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 12175 to 3838 computations (68.5% 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 x (/.f64 1 (tan.f64 B))))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.1b	(/.f64 1 (tan.f64 B))
✓	0.3b	(*.f64 x (/.f64 1 (tan.f64 B)))

series109.0ms (1.1%)

Counts

3 → 60

Calls

3 calls:

49.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
42.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
17.0ms	(/.f64 1 (tan.f64 B))

rewrite22.0ms (0.2%)

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 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 (1.2%)

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

prune298.0ms (3.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	231	11	242

Error

0.0b

Counts

242 → 11

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)))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (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))))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	25.6b	(/.f64 (-.f64 (.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B)))) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	0.9b	(+.f64 (-.f64 (pow.f64 (/.f64 1 (cbrt.f64 (sin.f64 B))) 3) (/.f64 x (tan.f64 B))) 0)
	35.6b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))
	12.2b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (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)))
	27.0b	(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 4594 to 2557 computations (44.3% 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 (*.f64 x (cos.f64 B)) (sin.f64 B)))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(*.f64 x (cos.f64 B))
✓	0.2b	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

series57.0ms (0.6%)

Counts

3 → 35

Calls

3 calls:

27.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
22.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
7.0ms	(*.f64 x (cos.f64 B))

rewrite40.0ms (0.4%)

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))

simplify226.0ms (2.4%)

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

prune248.0ms (2.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	261	10	271

Error

Counts

271 → 10

Alt Table

Status	Error	Program
	32.8b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (+.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (.f64 (sin.f64 B) (sin.f64 B))) (+.f64 (.f64 x (cos.f64 B)) 1))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.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)))
▶	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (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))))
	25.6b	(/.f64 (-.f64 (.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B)))) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	35.6b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))
	12.2b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	27.0b	(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 8651 to 2614 computations (69.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 x (tan.f64 B))
✓	0.4b	(.f64 (.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B))))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B))))
✓	0.6b	(cbrt.f64 (/.f64 x (tan.f64 B)))

series2.2s (22.8%)

Counts

3 → 72

Calls

3 calls:

1.5s

(*.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B))))

653.0ms

(cbrt.f64 (/.f64 x (tan.f64 B)))

56.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B))))

rewrite48.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`cbrt-prod_binary64`
78×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
50×	`*-un-lft-identity_binary64`
50×	`add-cube-cbrt_binary64`

Counts

3 → 165

Calls

3 calls:

15.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B))))

13.0ms

(*.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B))))

2.0ms

(cbrt.f64 (/.f64 x (tan.f64 B)))

simplify180.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

373×	`fma-def_binary64`
261×	`associate-/l*_binary64`
243×	`fma-neg_binary64`
231×	`associate-*l/_binary64`
228×	`associate-l_binary64`

Counts

237 → 256

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	5221
1	582	4992
2	1727	4574
3	4594	4574
4	4981	4574

prune424.0ms (4.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	467	0	467
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	467	10	477

Error

Counts

477 → 10

Alt Table

Status	Error	Program
	32.8b	(/.f64 (-.f64 (/.f64 1 (pow.f64 (sin.f64 B) 3)) (pow.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) 3)) (+.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (.f64 (sin.f64 B) (sin.f64 B))) (+.f64 (.f64 x (cos.f64 B)) 1))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.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)))
✓	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) (cbrt.f64 (/.f64 x (tan.f64 B)))) (cbrt.f64 (/.f64 x (tan.f64 B)))))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (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))))
	25.6b	(/.f64 (-.f64 (.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (sin.f64 B))) (.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B)))) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	35.6b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 (/.f64 x (tan.f64 B))) (sqrt.f64 (/.f64 x (tan.f64 B)))))
	12.2b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (sin.f64 B) (tan.f64 B)))
	27.0b	(-.f64 (log1p.f64 (expm1.f64 (/.f64 1 (sin.f64 B)))) (/.f64 x (tan.f64 B)))

Compiler

Compiled 14022 to 3920 computations (72% saved)

regimes370.0ms (3.9%)

Accuracy

Total 0.1b remaining (80.1%)

Threshold costs 0.1b (80.1%)

Counts

115 → 1

Compiler

Compiled 5938 to 3987 computations (32.9% saved)

simplify3.0ms (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	27	14

end167.0ms (1.7%)

Compiler: Compiled 236 to 140 computations (40.7% 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 (12%)

sample3.0s (31.6%)

simplify14.0ms (0.1%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series88.0ms (0.9%)

rewrite62.0ms (0.6%)

simplify381.0ms (4%)

prune320.0ms (3.3%)

localize9.0ms (0.1%)

series109.0ms (1.1%)

rewrite22.0ms (0.2%)

simplify118.0ms (1.2%)

prune298.0ms (3.1%)

localize8.0ms (0.1%)

series57.0ms (0.6%)

rewrite40.0ms (0.4%)

simplify226.0ms (2.4%)

prune248.0ms (2.6%)

localize12.0ms (0.1%)

series2.2s (22.8%)

rewrite48.0ms (0.5%)

simplify180.0ms (1.9%)

prune424.0ms (4.4%)

regimes370.0ms (3.9%)

simplify3.0ms (0%)

end167.0ms (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