Details

analyze1.1s (16.4%)

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)

sample2.8s (43.1%)

Results

1.3s	2348×	body	1024	valid
621.0ms	4151×	body	128	valid
534.0ms	1177×	body	512	valid
159.0ms	574×	body	256	valid
27.0ms	170×	body	128	invalid
6.0ms	6×	body	2048	valid
1.0ms	1×	body	1024	invalid

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

prune3.0ms (0.1%)

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 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))
▶	0.1b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.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))

series84.0ms (1.3%)

Counts

3 → 52

Calls

3 calls:

38.0ms	(/.f64 x (tan.f64 B))
38.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
8.0ms	(/.f64 1 (sin.f64 B))

rewrite122.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

785×	`prod-diff_binary64`
276×	`fma-def_binary64`
254×	`egg-rr`
223×	`fma-neg_binary64`
184×	`expm1-udef_binary64`

Counts

3 → 254

Calls

3 calls:

114.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
114.0ms	(/.f64 1 (sin.f64 B))
114.0ms	(/.f64 x (tan.f64 B))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	199	26
2	2714	26
3	4965	26
4	4966	26
0	0	0
1	0	0

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

610×	`+-commutative_binary64`
500×	`sub-neg_binary64`
422×	`associate--l+_binary64`
420×	`fma-def_binary64`
331×	`associate-+l+_binary64`

Counts

306 → 281

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	63	830
1	177	817
2	528	799
3	1983	797
4	4141	793
5	4721	793
6	4945	793

prune222.0ms (3.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	273	8	281
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	275	8	283

Error

0.0b

Counts

283 → 8

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 -1 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	26.7b	(/.f64 (-.f64 (pow.f64 (sin.f64 B) -2) (pow.f64 (/.f64 x (tan.f64 B)) 2)) (+.f64 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B))))
	35.2b	(/.f64 (-.f64 1 x) B)
	0.7b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 B)) 2)) (/.f64 x (cbrt.f64 (tan.f64 B)))))
	12.8b	(fma.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (/.f64 1 (.f64 (tan.f64 B) (sin.f64 B))) (fma.f64 (neg.f64 (/.f64 1 (tan.f64 B))) x (/.f64 x (tan.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 3))

Compiler

Compiled 8088 to 3083 computations (61.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 -1 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B)))
	0.1b	(/.f64 1 (sin.f64 B))
	0.1b	(/.f64 x (tan.f64 B))

series40.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

40.0ms

(fma.f64 -1 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B)))

rewrite44.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

884×	`log1p-expm1-u_binary64`
884×	`expm1-log1p-u_binary64`
121×	`prod-diff_binary64`
98×	`add-sqr-sqrt_binary64`
90×	`add-cbrt-cube_binary64`

Counts

1 → 23

Calls

1 calls:

43.0ms

(fma.f64 -1 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	198	15
2	2288	15
3	5661	15
0	0	0
1	0	0

simplify57.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

591×	`+-commutative_binary64`
412×	`cancel-sign-sub-inv_binary64`
402×	`associate--l+_binary64`
357×	`sub-neg_binary64`
353×	`fma-neg_binary64`

Counts

47 → 35

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	53	482
1	138	473
2	400	466
3	1549	464
4	2834	458
5	4905	458
6	5038	458

prune95.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	106	8	114

Error

0.0b

Counts

114 → 8

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 -1 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B)))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	26.7b	(/.f64 (-.f64 (pow.f64 (sin.f64 B) -2) (pow.f64 (/.f64 x (tan.f64 B)) 2)) (+.f64 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B))))
	35.2b	(/.f64 (-.f64 1 x) B)
	0.7b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 B)) 2)) (/.f64 x (cbrt.f64 (tan.f64 B)))))
	12.8b	(fma.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (/.f64 1 (.f64 (tan.f64 B) (sin.f64 B))) (fma.f64 (neg.f64 (/.f64 1 (tan.f64 B))) x (/.f64 x (tan.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 3))

Compiler

Compiled 1886 to 1014 computations (46.2% 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))
✓	0.1b	(/.f64 1 (tan.f64 B))
✓	0.2b	(*.f64 x (/.f64 1 (tan.f64 B)))

series181.0ms (2.8%)

Counts

3 → 60

Calls

3 calls:

129.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))
37.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
15.0ms	(/.f64 1 (tan.f64 B))

rewrite124.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

846×	`prod-diff_binary64`
689×	`fma-udef_binary64`
192×	`expm1-udef_binary64`
192×	`log1p-udef_binary64`
144×	`fma-neg_binary64`

Counts

3 → 123

Calls

3 calls:

121.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
121.0ms	(/.f64 1 (tan.f64 B))
121.0ms	(*.f64 x (/.f64 1 (tan.f64 B)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	219	26
2	2710	26
3	4992	26
4	4538	26
5	5104	26
0	0	0
1	0	0

simplify92.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

470×	`cancel-sign-sub-inv_binary64`
461×	`sub-neg_binary64`
439×	`associate--l+_binary64`
433×	`fma-def_binary64`
389×	`fma-neg_binary64`

Counts

183 → 151

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	68	894
1	190	879
2	573	864
3	2110	863
4	4178	859
5	4760	859
6	5013	859

prune155.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	181	8	189

Error

0.0b

Counts

189 → 8

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 -1 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	26.7b	(/.f64 (-.f64 (pow.f64 (sin.f64 B) -2) (pow.f64 (/.f64 x (tan.f64 B)) 2)) (+.f64 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B))))
	35.2b	(/.f64 (-.f64 1 x) B)
	0.7b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 B)) 2)) (/.f64 x (cbrt.f64 (tan.f64 B)))))
	12.8b	(fma.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (/.f64 1 (.f64 (tan.f64 B) (sin.f64 B))) (fma.f64 (neg.f64 (/.f64 1 (tan.f64 B))) x (/.f64 x (tan.f64 B))))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (cbrt.f64 (/.f64 x (tan.f64 B))) 3))

Compiler

Compiled 3572 to 1833 computations (48.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.1b	(/.f64 (tan.f64 B) x)
✓	0.3b	(pow.f64 (/.f64 (tan.f64 B) x) -1)

series110.0ms (1.7%)

Counts

3 → 72

Calls

3 calls:

45.0ms	(pow.f64 (/.f64 (tan.f64 B) x) -1)
43.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
22.0ms	(/.f64 (tan.f64 B) x)

rewrite133.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

662×	`prod-diff_binary64`
452×	`fma-udef_binary64`
293×	`fma-def_binary64`
214×	`fma-neg_binary64`
208×	`egg-rr`

Counts

3 → 208

Calls

3 calls:

128.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
128.0ms	(/.f64 (tan.f64 B) x)
128.0ms	(pow.f64 (/.f64 (tan.f64 B) x) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	236	26
2	2891	26
3	4813	26
4	4780	26
5	4926	26
0	0	0
1	0	0

simplify84.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

536×	`sub-neg_binary64`
418×	`associate--l+_binary64`
388×	`fma-def_binary64`
331×	`associate-+l+_binary64`
330×	`cancel-sign-sub-inv_binary64`

Counts

280 → 236

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	75	1077
1	203	1064
2	590	1046
3	2099	1044
4	4314	1040
5	4972	1040
6	5082	1040

prune224.0ms (3.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	264	2	266
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	267	7	274

Error

0.0b

Counts

274 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 -1 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 1 (tan.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (*.f64 (tan.f64 B) (/.f64 1 x)) -1))
	26.7b	(/.f64 (-.f64 (pow.f64 (sin.f64 B) -2) (pow.f64 (/.f64 x (tan.f64 B)) 2)) (+.f64 (/.f64 x (tan.f64 B)) (/.f64 1 (sin.f64 B))))
	35.2b	(/.f64 (-.f64 1 x) B)
	12.8b	(fma.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (/.f64 1 (.f64 (tan.f64 B) (sin.f64 B))) (fma.f64 (neg.f64 (/.f64 1 (tan.f64 B))) x (/.f64 x (tan.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (sin.f64 B) (*.f64 x (cos.f64 B))) -1))

Compiler

Compiled 5838 to 2491 computations (57.3% saved)

regimes603.0ms (9.4%)

Accuracy

Total 0.1b remaining (81.1%)

Threshold costs 0.1b (81.1%)

Counts

165 → 1

Compiler

Compiled 8317 to 5988 computations (28% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	12	15
2	11	15

end101.0ms (1.6%)

Compiler: Compiled 138 to 94 computations (31.9% 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 (16.4%)

sample2.8s (43.1%)

simplify14.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series84.0ms (1.3%)

rewrite122.0ms (1.9%)

simplify80.0ms (1.2%)

prune222.0ms (3.5%)

localize9.0ms (0.1%)

series40.0ms (0.6%)

rewrite44.0ms (0.7%)

simplify57.0ms (0.9%)

prune95.0ms (1.5%)

localize8.0ms (0.1%)

series181.0ms (2.8%)

rewrite124.0ms (1.9%)

simplify92.0ms (1.4%)

prune155.0ms (2.4%)

localize8.0ms (0.1%)

series110.0ms (1.7%)

rewrite133.0ms (2.1%)

simplify84.0ms (1.3%)

prune224.0ms (3.5%)

regimes603.0ms (9.4%)

simplify2.0ms (0%)

end101.0ms (1.6%)

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