Details

analyze44.0ms (0.3%)

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)

sample316.0ms (1.9%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 25 to 17 computations (32% saved)

simplify275.0ms (1.7%)

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%)

Local error

Found 1 expressions with local error:

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

series16.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

16.0ms

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

rewrite17.0ms (0.1%)

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:

12.0ms

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

simplify86.0ms (0.5%)

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

prune121.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	5	110

Error

Counts

110 → 5

Alt Table

Status	Error	Program
	38.8b	(-.f64 (.f64 (/.f64 y x) (+.f64 2 (/.f64 6 x))) (fma.f64 2 (.f64 (/.f64 y x) (/.f64 y x)) (+.f64 1 (+.f64 (/.f64 2 x) (/.f64 4 (*.f64 x x))))))
	0.1b	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) (-.f64 x y)))
▶	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
	39.5b	(fma.f64 (/.f64 x y) -2 (+.f64 1 (/.f64 2 y)))
	28.8b	(-.f64 (+.f64 (/.f64 x (-.f64 2 x)) (+.f64 (/.f64 (.f64 y x) (pow.f64 (-.f64 2 x) 2)) (/.f64 (.f64 (pow.f64 y 2) x) (pow.f64 (-.f64 2 x) 3)))) (+.f64 (/.f64 y (-.f64 2 x)) (/.f64 (pow.f64 y 2) (pow.f64 (-.f64 2 x) 2))))

Compiler

Compiled 2787 to 1464 computations (47.5% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

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

series59.0ms (0.4%)

Counts

3 → 72

Calls

3 calls:

27.0ms	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
16.0ms	(/.f64 y (-.f64 2 (+.f64 x y)))
15.0ms	(/.f64 x (-.f64 2 (+.f64 x y)))

rewrite239.0ms (1.5%)

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:

43.0ms	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
8.0ms	(/.f64 y (-.f64 2 (+.f64 x y)))
5.0ms	(/.f64 x (-.f64 2 (+.f64 x y)))

simplify1.0s (6.3%)

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 → 645

Iterations

Useful iterations: 2 (0.0ms)

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

prune721.0ms (4.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	641	4	645
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	646	4	650

Error

Counts

650 → 4

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) x)) (/.f64 y (-.f64 2 (+.f64 x y))))
	32.7b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (*.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) (-.f64 2 (+.f64 x y)))))
	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) y)))
	6.8b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y)))) 3))

Compiler

Compiled 37535 to 19421 computations (48.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 y (-.f64 2 (+.f64 x y)))
✓	0.0b	(-.f64 (/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) x)) (/.f64 y (-.f64 2 (+.f64 x y))))
✓	0.0b	(/.f64 (-.f64 2 (+.f64 x y)) x)
✓	0.2b	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) x))

series49.0ms (0.3%)

Counts

3 → 72

Calls

3 calls:

24.0ms	(-.f64 (/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) x)) (/.f64 y (-.f64 2 (+.f64 x y))))
15.0ms	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) x))
10.0ms	(/.f64 (-.f64 2 (+.f64 x y)) x)

rewrite929.0ms (5.6%)

Algorithm

1×	rewrite-expression-head

Rules

4475×	`times-frac_binary64`
4429×	`*-un-lft-identity_binary64`
3069×	`add-sqr-sqrt_binary64`
2122×	`add-cube-cbrt_binary64`
1704×	`prod-diff_binary64`

Counts

3 → 1986

Calls

3 calls:

109.0ms	(-.f64 (/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) x)) (/.f64 y (-.f64 2 (+.f64 x y))))
9.0ms	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) x))
7.0ms	(/.f64 (-.f64 2 (+.f64 x y)) x)

simplify2.9s (17.4%)

Algorithm

1×	egg-herbie

Rules

358×	`fma-neg_binary64`
323×	`fma-udef_binary64`
256×	`unsub-neg_binary64`
206×	`associate-*r/_binary64`
205×	`fma-def_binary64`

Counts

2058 → 1361

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	780	198878
1	1886	112896
2	4390	111420
3	5278	111420

prune1.9s (11.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	1432	0	1432
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	1432	4	1436

Error

Counts

1436 → 4

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) x)) (/.f64 y (-.f64 2 (+.f64 x y))))
	32.7b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (*.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) (-.f64 2 (+.f64 x y)))))
▶	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) y)))
	6.8b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y)))) 3))

Compiler

Compiled 97591 to 53353 computations (45.3% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) y)))
✓	0.0b	(/.f64 (-.f64 2 (+.f64 x y)) y)
	0.0b	(/.f64 x (-.f64 2 (+.f64 x y)))
✓	0.6b	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) y))

series347.0ms (2.1%)

Counts

3 → 72

Calls

3 calls:

319.0ms	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) y))
22.0ms	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) y)))
6.0ms	(/.f64 (-.f64 2 (+.f64 x y)) y)

rewrite849.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Rules

4475×	`times-frac_binary64`
4429×	`*-un-lft-identity_binary64`
3069×	`add-sqr-sqrt_binary64`
2122×	`add-cube-cbrt_binary64`
1704×	`prod-diff_binary64`

Counts

3 → 1986

Calls

3 calls:

105.0ms	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) y)))
8.0ms	(/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) y))
8.0ms	(/.f64 (-.f64 2 (+.f64 x y)) y)

simplify3.1s (18.8%)

Algorithm

1×	egg-herbie

Rules

324×	`fma-udef_binary64`
279×	`fma-neg_binary64`
238×	`unsub-neg_binary64`
214×	`fma-def_binary64`
180×	`associate-/l*_binary64`

Counts

2058 → 1535

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	789	206326
1	1850	137112
2	4830	137112
3	5041	137112

prune2.3s (14.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	1605	0	1605
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	1605	4	1609

Error

Counts

1609 → 4

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) x)) (/.f64 y (-.f64 2 (+.f64 x y))))
	32.7b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (*.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) (-.f64 2 (+.f64 x y)))))
✓	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 1 (/.f64 (-.f64 2 (+.f64 x y)) y)))
	6.8b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y)))) 3))

Compiler

Compiled 116866 to 69051 computations (40.9% saved)

regimes577.0ms (3.5%)

Accuracy

Total 0.0b remaining (51.4%)

Threshold costs 0.0b (51.4%)

Counts

177 → 1

Compiler

Compiled 11939 to 7672 computations (35.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`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	11	25
1	21	25
2	31	25
3	40	25
4	44	25
5	45	25
6	44	25

end1.0ms (0%)

Compiler: Compiled 19 to 12 computations (36.8% saved)

sample528.0ms (3.2%)

Algorithm

1×

intervals

Results

283.0ms

8000×

body

128

valid

Compiler

Compiled 112 to 71 computations (36.6% saved)

Details

analyze44.0ms (0.3%)

sample316.0ms (1.9%)

simplify275.0ms (1.7%)

prune2.0ms (0%)

localize5.0ms (0%)

series16.0ms (0.1%)

rewrite17.0ms (0.1%)

simplify86.0ms (0.5%)

prune121.0ms (0.7%)

localize6.0ms (0%)

series59.0ms (0.4%)

rewrite239.0ms (1.5%)

simplify1.0s (6.3%)

prune721.0ms (4.4%)

localize11.0ms (0.1%)

series49.0ms (0.3%)

rewrite929.0ms (5.6%)

simplify2.9s (17.4%)

prune1.9s (11.8%)

localize8.0ms (0%)

series347.0ms (2.1%)

rewrite849.0ms (5.2%)

simplify3.1s (18.8%)

prune2.3s (14.1%)

regimes577.0ms (3.5%)

simplify3.0ms (0%)

end1.0ms (0%)

sample528.0ms (3.2%)

Profiling