Details

analyze1.1s (16.9%)

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 (44.1%)

Results

1.3s	2337×	body	1024	valid
724.0ms	4081×	body	128	valid
460.0ms	1202×	body	512	valid
177.0ms	631×	body	256	valid
29.0ms	192×	body	128	invalid
5.0ms	5×	body	2048	valid
0.0ms	1×	body	512	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify13.0ms (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
▶	0.1b	(-.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))

series81.0ms (1.3%)

Counts

3 → 52

Calls

3 calls:

38.0ms	(/.f64 x (tan.f64 B))
37.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
6.0ms	(/.f64 1 (sin.f64 B))

rewrite120.0ms (1.9%)

Algorithm

1×	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:

113.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
113.0ms	(/.f64 1 (sin.f64 B))
113.0ms	(/.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

simplify79.0ms (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

prune217.0ms (3.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	274	7	281
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	276	7	283

Error

Counts

283 → 7

Alt Table

Status	Error	Program
	8.9b	(/.f64 (-.f64 (/.f64 (tan.f64 B) x) (sin.f64 B)) (*.f64 (sin.f64 B) (/.f64 (tan.f64 B) x)))
	23.5b	(/.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))))
	11.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (tan.f64 B) (sin.f64 B)))
	12.3b	(.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (/.f64 1 (*.f64 (tan.f64 B) (sin.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
	28.5b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))) 3))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))

Compiler

Compiled 8054 to 3047 computations (62.2% 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 (/.f64 x (sin.f64 B)) (cos.f64 B)))
✓	0.1b	(/.f64 x (sin.f64 B))
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

series57.0ms (0.9%)

Counts

3 → 52

Calls

3 calls:

24.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
19.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
14.0ms	(/.f64 x (sin.f64 B))

rewrite175.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

810×	`prod-diff_binary64`
242×	`egg-rr`
194×	`expm1-udef_binary64`
194×	`log1p-udef_binary64`
110×	`add-sqr-sqrt_binary64`

Counts

3 → 242

Calls

3 calls:

168.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
168.0ms	(/.f64 x (sin.f64 B))
168.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	216	31
2	2807	31
3	4966	31

simplify81.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

619×	`+-commutative_binary64`
496×	`sub-neg_binary64`
474×	`fma-def_binary64`
418×	`associate--l+_binary64`
394×	`associate-l_binary64`

Counts

294 → 267

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	67	844
1	190	829
2	574	811
3	2123	809
4	4366	805
5	4965	805
6	5066	805

prune239.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	296	1	297
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	297	7	304

Error

Counts

304 → 7

Alt Table

Status	Error	Program
	28.5b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))) 3))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (cos.f64 B) (/.f64 (sin.f64 B) x)))
	23.5b	(/.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))))
	11.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (tan.f64 B) (sin.f64 B)))
	12.3b	(.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (/.f64 1 (*.f64 (tan.f64 B) (sin.f64 B))))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))

Compiler

Compiled 9683 to 3026 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 (cos.f64 B) (/.f64 (sin.f64 B) x)))
✓	0.1b	(/.f64 (sin.f64 B) x)
	0.1b	(/.f64 1 (sin.f64 B))
✓	0.2b	(/.f64 (cos.f64 B) (/.f64 (sin.f64 B) x))

series55.0ms (0.9%)

Counts

3 → 52

Calls

3 calls:

27.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (cos.f64 B) (/.f64 (sin.f64 B) x)))
20.0ms	(/.f64 (cos.f64 B) (/.f64 (sin.f64 B) x))
8.0ms	(/.f64 (sin.f64 B) x)

rewrite84.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

339×	`fma-def_binary64`
216×	`log-div_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`
204×	`egg-rr`

Counts

3 → 204

Calls

3 calls:

79.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (cos.f64 B) (/.f64 (sin.f64 B) x)))
79.0ms	(/.f64 (sin.f64 B) x)
79.0ms	(/.f64 (cos.f64 B) (/.f64 (sin.f64 B) x))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	224	36
2	3190	32
3	5114	32

simplify86.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

440×	`associate--l+_binary64`
396×	`fma-def_binary64`
383×	`cancel-sign-sub-inv_binary64`
340×	`associate-l_binary64`
317×	`associate-+l+_binary64`

Counts

256 → 231

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	75	861
1	211	846
2	622	828
3	2229	826
4	4450	822
5	4780	822
6	5198	822

prune216.0ms (3.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	261	7	268

Error

Counts

268 → 7

Alt Table

Status	Error	Program
	28.5b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))) 3))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (cos.f64 B) (/.f64 (sin.f64 B) x)))
	23.5b	(/.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))))
	11.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (tan.f64 B) (sin.f64 B)))
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (cos.f64 B) (pow.f64 (/.f64 x (sin.f64 B)) -1)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))

Compiler

Compiled 5871 to 3120 computations (46.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series78.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

57.0ms	(pow.f64 (/.f64 x (sin.f64 B)) -1)
21.0ms	(/.f64 (cos.f64 B) (pow.f64 (/.f64 x (sin.f64 B)) -1))

rewrite58.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

910×	`log1p-expm1-u_binary64`
910×	`expm1-log1p-u_binary64`
96×	`add-sqr-sqrt_binary64`
88×	`add-cbrt-cube_binary64`
88×	`add-log-exp_binary64`

Counts

2 → 77

Calls

2 calls:

57.0ms	(pow.f64 (/.f64 x (sin.f64 B)) -1)
57.0ms	(/.f64 (cos.f64 B) (pow.f64 (/.f64 x (sin.f64 B)) -1))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	190	17
2	2345	17
3	5706	17

simplify108.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

622×	`distribute-rgt-neg-in_binary64`
546×	`fma-def_binary64`
527×	`distribute-lft-neg-in_binary64`
374×	`cancel-sign-sub-inv_binary64`
359×	`neg-mul-1_binary64`

Counts

125 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	499
1	124	493
2	335	482
3	938	478
4	2914	478
5	4533	478
6	4995	478
7	4986	478
8	5268	478

prune130.0ms (2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	164	7	171

Error

Counts

171 → 7

Alt Table

Status	Error	Program
	28.5b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))) 3))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (cos.f64 B) (/.f64 (sin.f64 B) x)))
	23.5b	(/.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))))
	11.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 x (sin.f64 B))) (.f64 (tan.f64 B) (sin.f64 B)))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (cos.f64 B) (pow.f64 (/.f64 x (sin.f64 B)) -1)))
	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (pow.f64 (/.f64 (tan.f64 B) x) -1))
✓	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))

Compiler

Compiled 3134 to 1476 computations (52.9% saved)

regimes488.0ms (7.6%)

Accuracy

Total 0.1b remaining (83.6%)

Threshold costs 0.1b (83.6%)

Counts

143 → 1

Compiler

Compiled 6820 to 4893 computations (28.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`
3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	22	19
2	32	19
3	35	19
4	36	19
5	34	19

end107.0ms (1.7%)

Compiler: Compiled 137 to 94 computations (31.4% 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 (16.9%)

sample2.8s (44.1%)

simplify13.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series81.0ms (1.3%)

rewrite120.0ms (1.9%)

simplify79.0ms (1.2%)

prune217.0ms (3.4%)

localize8.0ms (0.1%)

series57.0ms (0.9%)

rewrite175.0ms (2.7%)

simplify81.0ms (1.3%)

prune239.0ms (3.7%)

localize8.0ms (0.1%)

series55.0ms (0.9%)

rewrite84.0ms (1.3%)

simplify86.0ms (1.3%)

prune216.0ms (3.4%)

localize10.0ms (0.2%)

series78.0ms (1.2%)

rewrite58.0ms (0.9%)

simplify108.0ms (1.7%)

prune130.0ms (2%)

regimes488.0ms (7.6%)

simplify2.0ms (0%)

end107.0ms (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