Details

analyze56.0ms (1.5%)

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)

sample1.2s (31.6%)

Results

855.0ms	8254×	body	128	valid
1.0ms	2×	body	1024	valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify270.0ms (7.4%)

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)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series18.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

18.0ms

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

rewrite13.0ms (0.4%)

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)))

simplify103.0ms (2.8%)

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

prune92.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	105	5	110

Error

Counts

110 → 5

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
	32.4b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (*.f64 (-.f64 2 (+.f64 x y)) (+.f64 x y)))
	25.8b	(-.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))))
▶	0.1b	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)))
	40.2b	(-.f64 (+.f64 (/.f64 2 y) (+.f64 1 (fma.f64 2 (.f64 (/.f64 x y) (/.f64 x y)) (/.f64 4 (.f64 y y))))) (*.f64 (/.f64 x y) (+.f64 2 (/.f64 6 y))))

Compiler

Compiled 2768 to 1443 computations (47.9% saved)

localize9.0ms (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)))

series37.0ms (1%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)))
13.0ms	(/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y))

rewrite62.0ms (1.7%)

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:

13.0ms	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)))
8.0ms	(/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y))

simplify213.0ms (5.8%)

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

prune247.0ms (6.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	299	1	300
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	301	4	305

Error

Counts

305 → 4

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)))
	40.2b	(-.f64 (+.f64 (/.f64 2 y) (+.f64 1 (fma.f64 2 (.f64 (/.f64 x y) (/.f64 x y)) (/.f64 4 (.f64 y y))))) (*.f64 (/.f64 x y) (+.f64 2 (/.f64 6 y))))
▶	30.9b	(/.f64 1 (-.f64 (fma.f64 2 (/.f64 x y) 1) (/.f64 2 y)))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

Compiler

Compiled 7798 to 4042 computations (48.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (/.f64 x y) 1)
✓	0.0b	(-.f64 (fma.f64 2 (/.f64 x y) 1) (/.f64 2 y))
✓	0.5b	(/.f64 1 (-.f64 (fma.f64 2 (/.f64 x y) 1) (/.f64 2 y)))

series35.0ms (1%)

Counts

3 → 72

Calls

3 calls:

19.0ms	(/.f64 1 (-.f64 (fma.f64 2 (/.f64 x y) 1) (/.f64 2 y)))
10.0ms	(-.f64 (fma.f64 2 (/.f64 x y) 1) (/.f64 2 y))
5.0ms	(fma.f64 2 (/.f64 x y) 1)

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-sqr-sqrt_binary64`
66×	`*-un-lft-identity_binary64`
59×	`times-frac_binary64`
56×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`

Counts

3 → 129

Calls

3 calls:

7.0ms	(-.f64 (fma.f64 2 (/.f64 x y) 1) (/.f64 2 y))
6.0ms	(/.f64 1 (-.f64 (fma.f64 2 (/.f64 x y) 1) (/.f64 2 y)))
0.0ms	(fma.f64 2 (/.f64 x y) 1)

simplify137.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

844×	`times-frac_binary64`
435×	`fma-neg_binary64`
285×	`cancel-sign-sub-inv_binary64`
187×	`fma-def_binary64`
173×	`sub-neg_binary64`

Counts

201 → 200

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	328	4483
1	829	3817
2	2583	3532
3	4808	3532
4	4860	3532

prune205.0ms (5.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	200	4	204

Error

Counts

204 → 4

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)))
▶	40.2b	(-.f64 (+.f64 (/.f64 2 y) (+.f64 1 (fma.f64 2 (.f64 (/.f64 x y) (/.f64 x y)) (/.f64 4 (.f64 y y))))) (*.f64 (/.f64 x y) (+.f64 2 (/.f64 6 y))))
✓	30.9b	(/.f64 1 (-.f64 (fma.f64 2 (/.f64 x y) 1) (/.f64 2 y)))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

Compiler

Compiled 5866 to 4143 computations (29.4% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (/.f64 x y) (+.f64 2 (/.f64 6 y)))
✓	0.2b	(*.f64 (/.f64 x y) (/.f64 x y))
✓	0.4b	(/.f64 4 (*.f64 y y))
✓	7.0b	(-.f64 (+.f64 (/.f64 2 y) (+.f64 1 (fma.f64 2 (.f64 (/.f64 x y) (/.f64 x y)) (/.f64 4 (.f64 y y))))) (*.f64 (/.f64 x y) (+.f64 2 (/.f64 6 y))))

series96.0ms (2.6%)

Counts

4 → 84

Calls

4 calls:

42.0ms	(-.f64 (+.f64 (/.f64 2 y) (+.f64 1 (fma.f64 2 (.f64 (/.f64 x y) (/.f64 x y)) (/.f64 4 (.f64 y y))))) (*.f64 (/.f64 x y) (+.f64 2 (/.f64 6 y))))
29.0ms	(*.f64 (/.f64 x y) (/.f64 x y))
23.0ms	(*.f64 (/.f64 x y) (+.f64 2 (/.f64 6 y)))
2.0ms	(/.f64 4 (*.f64 y y))

rewrite50.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-sqr-sqrt_binary64`
56×	`*-un-lft-identity_binary64`
53×	`times-frac_binary64`
44×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`

Counts

4 → 182

Calls

4 calls:

14.0ms	(-.f64 (+.f64 (/.f64 2 y) (+.f64 1 (fma.f64 2 (.f64 (/.f64 x y) (/.f64 x y)) (/.f64 4 (.f64 y y))))) (*.f64 (/.f64 x y) (+.f64 2 (/.f64 6 y))))
8.0ms	(*.f64 (/.f64 x y) (+.f64 2 (/.f64 6 y)))
7.0ms	(*.f64 (/.f64 x y) (/.f64 x y))
3.0ms	(/.f64 4 (*.f64 y y))

simplify241.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

442×	`distribute-rgt-in_binary64`
423×	`distribute-lft-in_binary64`
249×	`associate-*r/_binary64`
240×	`associate-*l/_binary64`
202×	`fma-def_binary64`

Counts

266 → 295

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	402	9030
1	1385	8302
2	4656	8251
3	4981	8251
4	4974	8251

prune307.0ms (8.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	295	0	295
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	295	4	299

Error

Counts

299 → 4

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)))
✓	40.2b	(-.f64 (+.f64 (/.f64 2 y) (+.f64 1 (fma.f64 2 (.f64 (/.f64 x y) (/.f64 x y)) (/.f64 4 (.f64 y y))))) (*.f64 (/.f64 x y) (+.f64 2 (/.f64 6 y))))
✓	30.9b	(/.f64 1 (-.f64 (fma.f64 2 (/.f64 x y) 1) (/.f64 2 y)))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

Compiler

Compiled 15650 to 7984 computations (49% saved)

regimes177.0ms (4.8%)

Accuracy

Total 0.0b remaining (48.8%)

Threshold costs 0.0b (48.8%)

Counts

59 → 1

Compiler

Compiled 3322 to 2272 computations (31.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	13	13
2	24	13
3	32	13
4	36	13
5	37	13
6	37	13

end73.0ms (2%)

Compiler: Compiled 92 to 61 computations (33.7% saved)

Details

analyze56.0ms (1.5%)

sample1.2s (31.6%)

simplify270.0ms (7.4%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series18.0ms (0.5%)

rewrite13.0ms (0.4%)

simplify103.0ms (2.8%)

prune92.0ms (2.5%)

localize9.0ms (0.2%)

series37.0ms (1%)

rewrite62.0ms (1.7%)

simplify213.0ms (5.8%)

prune247.0ms (6.7%)

localize8.0ms (0.2%)

series35.0ms (1%)

rewrite31.0ms (0.9%)

simplify137.0ms (3.7%)

prune205.0ms (5.6%)

localize17.0ms (0.5%)

series96.0ms (2.6%)

rewrite50.0ms (1.4%)

simplify241.0ms (6.6%)

prune307.0ms (8.4%)

regimes177.0ms (4.8%)

simplify2.0ms (0.1%)

end73.0ms (2%)

Profiling