Details

analyze51.0ms (1.4%)

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
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)

sample1.0s (29.1%)

Results

737.0ms	8255×	body	128	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify272.0ms (7.6%)

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%)

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)

localize5.0ms (0.1%)

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:

19.0ms

(/.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)))

simplify87.0ms (2.4%)

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

prune88.0ms (2.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	106	4	110

Error

Counts

110 → 4

Alt Table

Status	Error	Program
	39.6b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))
▶	25.5b	(-.f64 (.f64 (+.f64 (/.f64 x (-.f64 2 y)) 1) (/.f64 x (-.f64 2 y))) (+.f64 (/.f64 y (-.f64 2 y)) (.f64 (/.f64 y (pow.f64 (-.f64 2 y) 2)) (+.f64 x (/.f64 (*.f64 x x) (-.f64 2 y))))))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
	25.6b	(-.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 (-.f64 2 x) 3)) x (.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 x (-.f64 2 x)))) (*.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 y (-.f64 2 x))))

Compiler

Compiled 2742 to 1437 computations (47.6% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.0b	(-.f64 (.f64 (+.f64 (/.f64 x (-.f64 2 y)) 1) (/.f64 x (-.f64 2 y))) (+.f64 (/.f64 y (-.f64 2 y)) (.f64 (/.f64 y (pow.f64 (-.f64 2 y) 2)) (+.f64 x (/.f64 (*.f64 x x) (-.f64 2 y))))))
✓	4.2b	(/.f64 (*.f64 x x) (-.f64 2 y))
✓	5.5b	(.f64 (/.f64 y (pow.f64 (-.f64 2 y) 2)) (+.f64 x (/.f64 (.f64 x x) (-.f64 2 y))))
✓	14.0b	(/.f64 y (pow.f64 (-.f64 2 y) 2))

series107.0ms (3%)

Counts

4 → 84

Calls

4 calls:

49.0ms	(-.f64 (.f64 (+.f64 (/.f64 x (-.f64 2 y)) 1) (/.f64 x (-.f64 2 y))) (+.f64 (/.f64 y (-.f64 2 y)) (.f64 (/.f64 y (pow.f64 (-.f64 2 y) 2)) (+.f64 x (/.f64 (*.f64 x x) (-.f64 2 y))))))
39.0ms	(.f64 (/.f64 y (pow.f64 (-.f64 2 y) 2)) (+.f64 x (/.f64 (.f64 x x) (-.f64 2 y))))
16.0ms	(/.f64 (*.f64 x x) (-.f64 2 y))
3.0ms	(/.f64 y (pow.f64 (-.f64 2 y) 2))

rewrite79.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
69×	`times-frac_binary64`
65×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
36×	`unpow-prod-down_binary64`

Counts

4 → 212

Calls

4 calls:

27.0ms	(-.f64 (.f64 (+.f64 (/.f64 x (-.f64 2 y)) 1) (/.f64 x (-.f64 2 y))) (+.f64 (/.f64 y (-.f64 2 y)) (.f64 (/.f64 y (pow.f64 (-.f64 2 y) 2)) (+.f64 x (/.f64 (*.f64 x x) (-.f64 2 y))))))
13.0ms	(.f64 (/.f64 y (pow.f64 (-.f64 2 y) 2)) (+.f64 x (/.f64 (.f64 x x) (-.f64 2 y))))
5.0ms	(/.f64 y (pow.f64 (-.f64 2 y) 2))
5.0ms	(/.f64 (*.f64 x x) (-.f64 2 y))

simplify218.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

639×	`distribute-rgt-in_binary64`
634×	`fma-def_binary64`
239×	`*-commutative_binary64`
173×	`times-frac_binary64`
172×	`fma-neg_binary64`

Counts

296 → 370

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	639	14434
1	2348	13449
2	5236	13449

prune467.0ms (13.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	370	0	370
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	370	4	374

Error

Counts

374 → 4

Alt Table

Status	Error	Program
	39.6b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))
✓	25.5b	(-.f64 (.f64 (+.f64 (/.f64 x (-.f64 2 y)) 1) (/.f64 x (-.f64 2 y))) (+.f64 (/.f64 y (-.f64 2 y)) (.f64 (/.f64 y (pow.f64 (-.f64 2 y) 2)) (+.f64 x (/.f64 (*.f64 x x) (-.f64 2 y))))))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
▶	25.6b	(-.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 (-.f64 2 x) 3)) x (.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 x (-.f64 2 x)))) (*.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 y (-.f64 2 x))))

Compiler

Compiled 24143 to 15766 computations (34.7% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 y (-.f64 2 x)))
✓	2.6b	(fma.f64 (/.f64 (.f64 y y) (pow.f64 (-.f64 2 x) 3)) x (.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 x (-.f64 2 x))))
✓	4.3b	(-.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 (-.f64 2 x) 3)) x (.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 x (-.f64 2 x)))) (*.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 y (-.f64 2 x))))
✓	8.2b	(/.f64 (*.f64 y y) (pow.f64 (-.f64 2 x) 3))

series141.0ms (4%)

Counts

4 → 96

Calls

4 calls:

44.0ms	(-.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 (-.f64 2 x) 3)) x (.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 x (-.f64 2 x)))) (*.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 y (-.f64 2 x))))
42.0ms	(/.f64 (*.f64 y y) (pow.f64 (-.f64 2 x) 3))
28.0ms	(fma.f64 (/.f64 (.f64 y y) (pow.f64 (-.f64 2 x) 3)) x (.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 x (-.f64 2 x))))
26.0ms	(*.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 y (-.f64 2 x)))

rewrite39.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
22×	`add-exp-log_binary64`

Counts

4 → 133

Calls

4 calls:

14.0ms	(*.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 y (-.f64 2 x)))
8.0ms	(-.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 (-.f64 2 x) 3)) x (.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 x (-.f64 2 x)))) (*.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 y (-.f64 2 x))))
6.0ms	(/.f64 (*.f64 y y) (pow.f64 (-.f64 2 x) 3))
0.0ms	(fma.f64 (/.f64 (.f64 y y) (pow.f64 (-.f64 2 x) 3)) x (.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 x (-.f64 2 x))))

simplify108.0ms (3%)

Algorithm

1×	egg-herbie

Rules

372×	`fma-def_binary64`
281×	`associate-+r+_binary64`
220×	`associate-r_binary64`
207×	`associate-l_binary64`
202×	`associate-+l+_binary64`

Counts

229 → 258

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	430	7282
1	1230	6541
2	4973	6541

prune286.0ms (8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	258	0	258
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	258	4	262

Error

Counts

262 → 4

Alt Table

Status	Error	Program
▶	39.6b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))
✓	25.5b	(-.f64 (.f64 (+.f64 (/.f64 x (-.f64 2 y)) 1) (/.f64 x (-.f64 2 y))) (+.f64 (/.f64 y (-.f64 2 y)) (.f64 (/.f64 y (pow.f64 (-.f64 2 y) 2)) (+.f64 x (/.f64 (*.f64 x x) (-.f64 2 y))))))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
✓	25.6b	(-.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 (-.f64 2 x) 3)) x (.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 x (-.f64 2 x)))) (*.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 y (-.f64 2 x))))

Compiler

Compiled 12685 to 8474 computations (33.2% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series16.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))
6.0ms	(fma.f64 2 (/.f64 y x) -1)

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`fma-def_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 28

Calls

2 calls:

4.0ms	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))
0.0ms	(fma.f64 2 (/.f64 y x) -1)

simplify64.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

463×	`times-frac_binary64`
439×	`associate-+l+_binary64`
325×	`associate-*l/_binary64`
257×	`associate-*r/_binary64`
214×	`fma-neg_binary64`

Counts

76 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	896
1	135	770
2	326	763
3	1375	761
4	4564	761
5	5204	761

prune37.0ms (1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	49	4	53

Error

Counts

53 → 4

Alt Table

Status	Error	Program
✓	39.6b	(+.f64 (fma.f64 2 (/.f64 y x) -1) (/.f64 -2 x))
✓	25.5b	(-.f64 (.f64 (+.f64 (/.f64 x (-.f64 2 y)) 1) (/.f64 x (-.f64 2 y))) (+.f64 (/.f64 y (-.f64 2 y)) (.f64 (/.f64 y (pow.f64 (-.f64 2 y) 2)) (+.f64 x (/.f64 (*.f64 x x) (-.f64 2 y))))))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
✓	25.6b	(-.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 (-.f64 2 x) 3)) x (.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 x (-.f64 2 x)))) (*.f64 (+.f64 (/.f64 y (-.f64 2 x)) 1) (/.f64 y (-.f64 2 x))))

Compiler

Compiled 862 to 585 computations (32.1% saved)

regimes311.0ms (8.7%)

Accuracy

Total 0.0b remaining (31.4%)

Threshold costs 0.0b (31.4%)

Counts

93 → 1

Compiler

Compiled 7393 to 5058 computations (31.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	14	22
2	27	22
3	37	22
4	43	22
5	45	22
6	45	22

end74.0ms (2.1%)

Compiler: Compiled 136 to 91 computations (33.1% saved)

Details

analyze51.0ms (1.4%)

sample1.0s (29.1%)

simplify272.0ms (7.6%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series19.0ms (0.5%)

rewrite12.0ms (0.3%)

simplify87.0ms (2.4%)

prune88.0ms (2.5%)

localize14.0ms (0.4%)

series107.0ms (3%)

rewrite79.0ms (2.2%)

simplify218.0ms (6.1%)

prune467.0ms (13.1%)

localize15.0ms (0.4%)

series141.0ms (4%)

rewrite39.0ms (1.1%)

simplify108.0ms (3%)

prune286.0ms (8%)

localize6.0ms (0.2%)

series16.0ms (0.4%)

rewrite6.0ms (0.2%)

simplify64.0ms (1.8%)

prune37.0ms (1%)

regimes311.0ms (8.7%)

simplify3.0ms (0.1%)

end74.0ms (2.1%)

Profiling