Details

analyze10.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.9s (35.5%)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify53.0ms (1%)

Algorithm

1×	egg-herbie

Rules

396×	`fma-neg_binary64`
375×	`fma-def_binary64`
260×	`div-sub_binary64`
123×	`times-frac_binary64`
116×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	57	17
5	73	17
6	102	17
7	158	17
8	240	17
9	299	17
10	391	17
11	536	17
12	777	17
13	826	17
14	799	17
15	722	17

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))

Compiler

Compiled 36 to 30 computations (16.7% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
✓	0.0b	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
✓	0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))

series17.0ms (0.3%)

Counts

3 → 24

Calls

3 calls:

10.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
4.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
3.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

rewrite242.0ms (4.5%)

Algorithm

2×	batch-egg-rewrite

Rules

913×	`log1p-expm1-u_binary64`
913×	`expm1-log1p-u_binary64`
311×	`prod-diff_binary64`
161×	`egg-rr`
85×	`add-sqr-sqrt_binary64`

Counts

3 → 161

Calls

3 calls:

233.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
233.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
233.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	36
1	174	36
2	2291	36
3	6247	36
0	0	0
1	0	0

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-def_binary64`
653×	`fma-neg_binary64`
443×	`cancel-sign-sub-inv_binary64`
264×	`associate-/l/_binary64`
194×	`sub-neg_binary64`

Counts

185 → 187

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	61	494
1	188	468
2	590	456
3	1925	394
4	4421	390
5	4962	390

prune386.0ms (7.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	186	2	188

Error

Counts

188 → 2

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 2 (atan.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3)))
	0.0b	(.f64 2 (atan.f64 (sqrt.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))))))

Compiler

Compiled 6155 to 4588 computations (25.5% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3)
✓	0.0b	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2)
✓	0.0b	(atan.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3))
	0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))

series36.0ms (0.7%)

Counts

3 → 24

Calls

3 calls:

25.0ms	(pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3)
6.0ms	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2)
5.0ms	(atan.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3))

rewrite114.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

501×	`log-prod_binary64`
311×	`prod-diff_binary64`
194×	`expm1-udef_binary64`
193×	`log1p-udef_binary64`
184×	`fma-def_binary64`

Counts

3 → 73

Calls

3 calls:

111.0ms	(pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3)
111.0ms	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2)
111.0ms	(atan.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	41
1	247	39
2	2867	39
3	5473	39
0	0	0
1	0	0

simplify98.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-neg_binary64`
366×	`neg-mul-1_binary64`
315×	`sub-neg_binary64`
233×	`distribute-rgt-neg-in_binary64`
226×	`distribute-neg-frac_binary64`

Counts

97 → 98

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	569
1	190	533
2	659	483
3	2636	450
4	4777	450
5	5156	450

prune450.0ms (8.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	224	0	224
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	224	2	226

Error

Counts

226 → 2

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 2 (atan.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3)))
▶	0.0b	(.f64 2 (atan.f64 (sqrt.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))))))

Compiler

Compiled 7329 to 5635 computations (23.1% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
✓	0.0b	(atan.f64 (sqrt.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))))))
✓	0.0b	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))
✓	0.0b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))))

series44.0ms (0.8%)

Counts

4 → 32

Calls

4 calls:

20.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))
16.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
4.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))))
3.0ms	(atan.f64 (sqrt.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))))))

rewrite209.0ms (3.9%)

Algorithm

2×	batch-egg-rewrite

Rules

340×	`prod-diff_binary64`
262×	`egg-rr`
217×	`fma-def_binary64`
198×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`

Counts

4 → 262

Calls

4 calls:

195.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
195.0ms	(atan.f64 (sqrt.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))))))
195.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))
195.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	45
1	240	43
2	3102	43
3	4928	43
0	0	0
1	0	0

simplify103.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

676×	`fma-def_binary64`
500×	`distribute-rgt-neg-in_binary64`
491×	`cancel-sign-sub-inv_binary64`
395×	`fma-neg_binary64`
387×	`sub-neg_binary64`

Counts

294 → 289

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	406
1	160	392
2	413	376
3	1128	358
4	3682	358
5	4601	358
6	4968	358

prune722.0ms (13.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	289	2	291

Error

Counts

291 → 2

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 2 (atan.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2) 1/3)))
✓	0.0b	(.f64 2 (atan.f64 (sqrt.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))))))

Compiler

Compiled 10144 to 7986 computations (21.3% saved)

regimes697.0ms (12.9%)

Accuracy

Total 0.0b remaining (43.2%)

Threshold costs 0.0b (43.2%)

Counts

75 → 1

Compiler

Compiled 6500 to 5573 computations (14.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	27
1	22	27
2	26	27
3	28	27
4	29	27
5	28	27

end170.0ms (3.1%)

Compiler: Compiled 73 to 64 computations (12.3% saved)

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	57	17
5	73	17
6	102	17
7	158	17
8	240	17
9	299	17
10	391	17
11	536	17
12	777	17
13	826	17
14	799	17
15	722	17

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	57	17
5	73	17
6	102	17
7	158	17
8	240	17
9	299	17
10	391	17
11	536	17
12	777	17
13	826	17
14	799	17
15	722	17

Details

analyze10.0ms (0.2%)

sample1.9s (35.5%)

simplify53.0ms (1%)

prune3.0ms (0.1%)

localize14.0ms (0.3%)

series17.0ms (0.3%)

rewrite242.0ms (4.5%)

simplify69.0ms (1.3%)

prune386.0ms (7.2%)

localize20.0ms (0.4%)

series36.0ms (0.7%)

rewrite114.0ms (2.1%)

simplify98.0ms (1.8%)

prune450.0ms (8.3%)

localize20.0ms (0.4%)

series44.0ms (0.8%)

rewrite209.0ms (3.9%)

simplify103.0ms (1.9%)

prune722.0ms (13.4%)

regimes697.0ms (12.9%)

simplify5.0ms (0.1%)

end170.0ms (3.1%)

Profiling

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	57	17
5	73	17
6	102	17
7	158	17
8	240	17
9	299	17
10	391	17
11	536	17
12	777	17
13	826	17
14	799	17
15	722	17