Details

analyze49.0ms (1.3%)

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
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
56.2%	43.7%	0.1%	5
65.6%	34.3%	0.1%	6
79.6%	20.3%	0.1%	7
83.5%	16.4%	0.1%	8
90.1%	9.8%	0.1%	9
91.9%	8%	0.1%	10
95.1%	4.8%	0.1%	11
96%	4%	0.1%	12
97.5%	2.4%	0.1%	13
97.9%	2%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.1s (29.7%)

Results

784.0ms	8255×	body	128	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify266.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

1222×	`fma-neg_binary64`
983×	`fma-def_binary64`
688×	`div-sub_binary64`
423×	`sub-neg_binary64`
412×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	35	13
3	74	13
4	151	13
5	245	13
6	641	13
7	1125	13
8	2158	13
9	2729	13
10	3037	13
11	2995	13
12	3049	13
13	3063	13
14	3569	13
15	3559	13
16	3559	13
17	3559	13
18	3559	13
19	3559	13
20	3655	13
21	3703	13
22	3785	13
23	3593	13

prune2.0ms (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 (-.f64 x y) (-.f64 2 (+.f64 x y)))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

series19.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

18.0ms

(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
19×	`distribute-lft-out--_binary64`
14×	`add-cube-cbrt_binary64`

Counts

1 → 60

Calls

1 calls:

7.0ms

(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

simplify96.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

702×	`fma-def_binary64`
518×	`times-frac_binary64`
339×	`fma-neg_binary64`
291×	`distribute-rgt-in_binary64`
228×	`cancel-sign-sub-inv_binary64`

Counts

84 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	2433
1	635	2369
2	2115	2256
3	4853	2256
4	5045	2256

prune77.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	3	110

Error

Counts

110 → 3

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)))
	30.5b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 (-.f64 2 y) 2)) (/.f64 x (-.f64 2 y))) (+.f64 (/.f64 (.f64 y x) (pow.f64 (-.f64 2 y) 2)) (+.f64 (/.f64 y (-.f64 2 y)) (/.f64 (.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3)))))
	0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))

Compiler

Compiled 2691 to 1404 computations (47.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y))
✓	0.1b	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)))

series31.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

16.0ms	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)))
15.0ms	(/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y))

rewrite56.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

292×	`*-un-lft-identity_binary64`
258×	`times-frac_binary64`
214×	`add-sqr-sqrt_binary64`
100×	`add-cube-cbrt_binary64`
83×	`distribute-lft-out--_binary64`

Counts

2 → 230

Calls

2 calls:

16.0ms	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)))
8.0ms	(/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y))

simplify199.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

814×	`times-frac_binary64`
253×	`fma-neg_binary64`
207×	`fma-def_binary64`
179×	`+-commutative_binary64`
143×	`associate--r+_binary64`

Counts

278 → 300

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	338	7906
1	968	7346
2	3444	7309
3	4998	7309
4	4964	7309

prune203.0ms (5.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	300	0	300
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	300	3	303

Error

Counts

303 → 3

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)))
	30.5b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 (-.f64 2 y) 2)) (/.f64 x (-.f64 2 y))) (+.f64 (/.f64 (.f64 y x) (pow.f64 (-.f64 2 y) 2)) (+.f64 (/.f64 y (-.f64 2 y)) (/.f64 (.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3)))))
▶	0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))

Compiler

Compiled 7811 to 4057 computations (48.1% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 2 (+.f64 x y)))
✓	0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))

series29.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
12.0ms	(/.f64 1 (-.f64 2 (+.f64 x y)))

rewrite28.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`*-un-lft-identity_binary64`
47×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
24×	`associate-r_binary64`
24×	`add-cube-cbrt_binary64`

Counts

2 → 102

Calls

2 calls:

12.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
9.0ms	(/.f64 1 (-.f64 2 (+.f64 x y)))

simplify110.0ms (3%)

Algorithm

1×	egg-herbie

Rules

654×	`times-frac_binary64`
403×	`fma-neg_binary64`
325×	`sub-neg_binary64`
288×	`cancel-sign-sub-inv_binary64`
188×	`+-commutative_binary64`

Counts

150 → 192

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	306	3603
1	851	3445
2	3068	3427
3	4942	3427
4	5145	3427

prune136.0ms (3.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	192	3	195

Error

Counts

195 → 3

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)))
▶	30.5b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 (-.f64 2 y) 2)) (/.f64 x (-.f64 2 y))) (+.f64 (/.f64 (.f64 y x) (pow.f64 (-.f64 2 y) 2)) (+.f64 (/.f64 y (-.f64 2 y)) (/.f64 (.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3)))))
✓	0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))

Compiler

Compiled 4720 to 2743 computations (41.9% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.4b	(*.f64 y (pow.f64 x 2))
✓	6.8b	(/.f64 (pow.f64 x 2) (pow.f64 (-.f64 2 y) 2))
✓	10.2b	(/.f64 (*.f64 y x) (pow.f64 (-.f64 2 y) 2))
✓	11.0b	(/.f64 (*.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3))

series150.0ms (4.1%)

Counts

4 → 44

Calls

4 calls:

55.0ms	(/.f64 (*.f64 y x) (pow.f64 (-.f64 2 y) 2))
43.0ms	(/.f64 (*.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3))
42.0ms	(/.f64 (pow.f64 x 2) (pow.f64 (-.f64 2 y) 2))
9.0ms	(*.f64 y (pow.f64 x 2))

rewrite43.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`times-frac_binary64`
102×	`unpow-prod-down_binary64`
93×	`add-sqr-sqrt_binary64`
87×	`*-un-lft-identity_binary64`
60×	`add-exp-log_binary64`

Counts

4 → 251

Calls

4 calls:

10.0ms	(/.f64 (pow.f64 x 2) (pow.f64 (-.f64 2 y) 2))
7.0ms	(/.f64 (*.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3))
6.0ms	(/.f64 (*.f64 y x) (pow.f64 (-.f64 2 y) 2))
4.0ms	(*.f64 y (pow.f64 x 2))

simplify164.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

944×	`fma-def_binary64`
409×	`times-frac_binary64`
319×	`associate-/l*_binary64`
311×	`associate-/r*_binary64`
180×	`associate-r_binary64`

Counts

295 → 372

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	401	6151
1	826	5249
2	3580	5180
3	4972	5180
4	5008	5180

prune453.0ms (12.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	372	0	372
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	372	3	375

Error

Counts

375 → 3

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)))
✓	30.5b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) (pow.f64 (-.f64 2 y) 2)) (/.f64 x (-.f64 2 y))) (+.f64 (/.f64 (.f64 y x) (pow.f64 (-.f64 2 y) 2)) (+.f64 (/.f64 y (-.f64 2 y)) (/.f64 (.f64 y (pow.f64 x 2)) (pow.f64 (-.f64 2 y) 3)))))
✓	0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))

Compiler

Compiled 19204 to 13314 computations (30.7% saved)

regimes340.0ms (9.3%)

Accuracy

Total 0.0b remaining (33.1%)

Threshold costs 0.0b (33.1%)

Counts

108 → 1

Compiler

Compiled 7929 to 5207 computations (34.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	28	13
3	36	13
4	40	13
5	41	13
6	40	13

end68.0ms (1.8%)

Compiler: Compiled 93 to 65 computations (30.1% saved)

Details

analyze49.0ms (1.3%)

sample1.1s (29.7%)

simplify266.0ms (7.3%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series19.0ms (0.5%)

rewrite12.0ms (0.3%)

simplify96.0ms (2.6%)

prune77.0ms (2.1%)

localize6.0ms (0.2%)

series31.0ms (0.9%)

rewrite56.0ms (1.5%)

simplify199.0ms (5.4%)

prune203.0ms (5.5%)

localize6.0ms (0.2%)

series29.0ms (0.8%)

rewrite28.0ms (0.8%)

simplify110.0ms (3%)

prune136.0ms (3.7%)

localize17.0ms (0.5%)

series150.0ms (4.1%)

rewrite43.0ms (1.2%)

simplify164.0ms (4.5%)

prune453.0ms (12.4%)

regimes340.0ms (9.3%)

simplify2.0ms (0.1%)

end68.0ms (1.8%)

Profiling