Details

analyze46.0ms (1%)

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)

sample302.0ms (6.3%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 25 to 17 computations (32% saved)

simplify272.0ms (5.7%)

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)))

series18.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

18.0ms

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

rewrite13.0ms (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:

8.0ms

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

simplify93.0ms (1.9%)

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

prune93.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	4	110

Error

Counts

110 → 4

Alt Table

Status	Error	Program
	0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
	6.6b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x))) 3))
▶	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
	29.4b	(-.f64 (fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 (-.f64 2 x) 4)) x (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 (/.f64 y (-.f64 2 x)) 1) (/.f64 y (-.f64 2 x))) (pow.f64 (/.f64 y (-.f64 2 x)) 3)))

Compiler

Compiled 2755 to 1444 computations (47.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series90.0ms (1.9%)

Counts

3 → 72

Calls

3 calls:

59.0ms	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
16.0ms	(/.f64 x (-.f64 2 (+.f64 x y)))
15.0ms	(/.f64 y (-.f64 2 (+.f64 x y)))

rewrite242.0ms (5%)

Algorithm

1×	rewrite-expression-head

Rules

1377×	`*-un-lft-identity_binary64`
964×	`times-frac_binary64`
859×	`add-sqr-sqrt_binary64`
576×	`prod-diff_binary64`
527×	`add-cube-cbrt_binary64`

Counts

3 → 745

Calls

3 calls:

42.0ms	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
6.0ms	(/.f64 x (-.f64 2 (+.f64 x y)))
5.0ms	(/.f64 y (-.f64 2 (+.f64 x y)))

simplify966.0ms (20.2%)

Algorithm

1×	egg-herbie

Rules

353×	`fma-udef_binary64`
257×	`unsub-neg_binary64`
249×	`fma-def_binary64`
232×	`fma-neg_binary64`
213×	`associate-*r/_binary64`

Counts

817 → 662

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	769	69746
1	1968	39458
2	4382	38404
3	4995	38404
4	5000	38404

prune926.0ms (19.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	661	1	662
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	662	4	666

Error

Counts

666 → 4

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
	6.6b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x))) 3))
✓	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
	29.2b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (+.f64 (/.f64 y (-.f64 2 x)) (/.f64 (pow.f64 y 2) (pow.f64 (-.f64 2 x) 2))))

Compiler

Compiled 37941 to 19595 computations (48.4% saved)

localize9.0ms (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))))

series32.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

18.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
14.0ms	(/.f64 1 (-.f64 2 (+.f64 x y)))

rewrite51.0ms (1.1%)

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:

39.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
6.0ms	(/.f64 1 (-.f64 2 (+.f64 x y)))

simplify111.0ms (2.3%)

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

prune134.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	192	4	196

Error

Counts

196 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
▶	6.6b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x))) 3))
✓	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
	26.6b	(*.f64 (-.f64 x y) (+.f64 (/.f64 1 (-.f64 2 x)) (/.f64 y (pow.f64 (-.f64 2 x) 2))))

Compiler

Compiled 4700 to 2726 computations (42% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x)))
✓	0.1b	(pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x))) 3)
✓	6.6b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x))) 3))

series97.0ms (2%)

Counts

3 → 72

Calls

3 calls:

47.0ms	(pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x))) 3)
32.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x))) 3))
18.0ms	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x)))

rewrite80.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

258×	`*-un-lft-identity_binary64`
180×	`add-sqr-sqrt_binary64`
150×	`times-frac_binary64`
83×	`distribute-lft-out--_binary64`
78×	`cbrt-prod_binary64`

Counts

3 → 244

Calls

3 calls:

16.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x))) 3))
10.0ms	(pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x))) 3)
8.0ms	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x)))

simplify161.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

324×	`fma-def_binary64`
275×	`times-frac_binary64`
264×	`associate-/l*_binary64`
235×	`associate-/r*_binary64`
183×	`associate-*r/_binary64`

Counts

316 → 219

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	510	10185
1	1618	9749
2	5011	9749

prune164.0ms (3.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	219	4	223

Error

Counts

223 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 2 (+.f64 x y))))
✓	6.6b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x))) 3))
✓	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
	26.6b	(*.f64 (-.f64 x y) (+.f64 (/.f64 1 (-.f64 2 x)) (/.f64 y (pow.f64 (-.f64 2 x) 2))))

Compiler

Compiled 6669 to 3914 computations (41.3% saved)

regimes294.0ms (6.1%)

Accuracy

Total 0.0b remaining (48.1%)

Threshold costs 0.0b (48.1%)

Counts

73 → 1

Compiler

Compiled 4292 to 2806 computations (34.6% 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

end0.0ms (0%)

Compiler: Compiled 17 to 10 computations (41.2% saved)

sample574.0ms (12%)

Algorithm

1×

intervals

Results

305.0ms	7999×	body	128	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 94 to 63 computations (33% saved)

Details

analyze46.0ms (1%)

sample302.0ms (6.3%)

simplify272.0ms (5.7%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series18.0ms (0.4%)

rewrite13.0ms (0.3%)

simplify93.0ms (1.9%)

prune93.0ms (1.9%)

localize9.0ms (0.2%)

series90.0ms (1.9%)

rewrite242.0ms (5%)

simplify966.0ms (20.2%)

prune926.0ms (19.3%)

localize9.0ms (0.2%)

series32.0ms (0.7%)

rewrite51.0ms (1.1%)

simplify111.0ms (2.3%)

prune134.0ms (2.8%)

localize8.0ms (0.2%)

series97.0ms (2%)

rewrite80.0ms (1.7%)

simplify161.0ms (3.4%)

prune164.0ms (3.4%)

regimes294.0ms (6.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample574.0ms (12%)

Profiling