Details

analyze66.0ms (0.6%)

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
37.5%	62.4%	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 (12%)

Results

831.0ms	8255×	body	128	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify386.0ms (3.8%)

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)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series29.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

25.0ms	(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
3.0ms	(-.f64 2 (+.f64 x y))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
21×	`distribute-lft-out--_binary64`

Counts

2 → 97

Calls

2 calls:

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

simplify191.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

518×	`times-frac_binary64`
407×	`distribute-rgt-in_binary64`
283×	`cancel-sign-sub-inv_binary64`
236×	`sub-neg_binary64`
138×	`distribute-neg-in_binary64`

Counts

145 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	272	3067
1	714	2924
2	2485	2754
3	5075	2754

prune316.0ms (3.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	159	4	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	4	164

Error

Counts

164 → 4

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
	39.7b	(-.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))))
	40.6b	(-.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))))))
	7.7b	(cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))) (/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))))

Compiler

Compiled 3751 to 1809 computations (51.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series104.0ms (1%)

Counts

3 → 72

Calls

3 calls:

41.0ms	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
35.0ms	(/.f64 y (-.f64 2 (+.f64 x y)))
28.0ms	(/.f64 x (-.f64 2 (+.f64 x y)))

rewrite390.0ms (3.8%)

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:

79.0ms	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
12.0ms	(/.f64 x (-.f64 2 (+.f64 x y)))
11.0ms	(/.f64 y (-.f64 2 (+.f64 x y)))

simplify1.4s (13.9%)

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 → 719

Iterations

Useful iterations: 2 (0.0ms)

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

prune886.0ms (8.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	826	1	827
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	828	3	831

Error

Counts

831 → 3

Alt Table

Status	Error	Program
	40.6b	(-.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))))))
✓	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
▶	7.3b	(-.f64 (log.f64 (exp.f64 (/.f64 x (-.f64 2 (+.f64 x y))))) (/.f64 y (-.f64 2 (+.f64 x y))))

Compiler

Compiled 41962 to 21478 computations (48.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (-.f64 2 (+.f64 x y)))
	0.0b	(/.f64 y (-.f64 2 (+.f64 x y)))
✓	0.0b	(-.f64 (log.f64 (exp.f64 (/.f64 x (-.f64 2 (+.f64 x y))))) (/.f64 y (-.f64 2 (+.f64 x y))))
✓	2.6b	(log.f64 (exp.f64 (/.f64 x (-.f64 2 (+.f64 x y)))))

series44.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

26.0ms	(-.f64 (log.f64 (exp.f64 (/.f64 x (-.f64 2 (+.f64 x y))))) (/.f64 y (-.f64 2 (+.f64 x y))))
17.0ms	(log.f64 (exp.f64 (/.f64 x (-.f64 2 (+.f64 x y)))))

rewrite374.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

1407×	`*-un-lft-identity_binary64`
991×	`times-frac_binary64`
914×	`add-sqr-sqrt_binary64`
672×	`prod-diff_binary64`
651×	`log-pow_binary64`

Counts

2 → 782

Calls

2 calls:

55.0ms	(-.f64 (log.f64 (exp.f64 (/.f64 x (-.f64 2 (+.f64 x y))))) (/.f64 y (-.f64 2 (+.f64 x y))))
7.0ms	(log.f64 (exp.f64 (/.f64 x (-.f64 2 (+.f64 x y)))))

simplify1.7s (16.3%)

Algorithm

1×	egg-herbie

Rules

406×	`fma-udef_binary64`
287×	`unsub-neg_binary64`
259×	`associate-+r-_binary64`
223×	`associate-+r+_binary64`
220×	`fma-neg_binary64`

Counts

830 → 644

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	777	68343
1	1816	41080
2	4586	40184
3	4964	40184
4	4996	40184
5	4967	40184

prune1.3s (12.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	826	0	826
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	826	3	829

Error

Counts

829 → 3

Alt Table

Status	Error	Program
▶	40.6b	(-.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))))))
✓	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
✓	7.3b	(-.f64 (log.f64 (exp.f64 (/.f64 x (-.f64 2 (+.f64 x y))))) (/.f64 y (-.f64 2 (+.f64 x y))))

Compiler

Compiled 46590 to 24811 computations (46.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (/.f64 y x) (+.f64 2 (/.f64 6 x)))
✓	0.2b	(*.f64 (/.f64 y x) (/.f64 y x))
✓	0.6b	(/.f64 4 (*.f64 x x))
✓	7.5b	(-.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))))))

series83.0ms (0.8%)

Counts

4 → 84

Calls

4 calls:

39.0ms	(-.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))))))
28.0ms	(*.f64 (/.f64 y x) (/.f64 y x))
13.0ms	(*.f64 (/.f64 y x) (+.f64 2 (/.f64 6 x)))
2.0ms	(/.f64 4 (*.f64 x x))

rewrite51.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 156

Calls

4 calls:

10.0ms	(-.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))))))
9.0ms	(*.f64 (/.f64 y x) (+.f64 2 (/.f64 6 x)))
8.0ms	(*.f64 (/.f64 y x) (/.f64 y x))
3.0ms	(/.f64 4 (*.f64 x x))

simplify283.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

683×	`times-frac_binary64`
561×	`fma-neg_binary64`
259×	`associate-l_binary64`
236×	`associate-r_binary64`
222×	`associate-*l/_binary64`

Counts

240 → 249

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	292	5030
1	859	4343
2	2872	4005
3	4791	4005
4	4951	4005

prune394.0ms (3.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	249	3	252

Error

Counts

252 → 3

Alt Table

Status	Error	Program
✓	40.6b	(-.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))))))
✓	0.0b	(-.f64 (/.f64 x (-.f64 2 (+.f64 x y))) (/.f64 y (-.f64 2 (+.f64 x y))))
✓	7.3b	(-.f64 (log.f64 (exp.f64 (/.f64 x (-.f64 2 (+.f64 x y))))) (/.f64 y (-.f64 2 (+.f64 x y))))

Compiler

Compiled 9685 to 5013 computations (48.2% saved)

regimes792.0ms (7.7%)

Accuracy

Total 0.0b remaining (22.1%)

Threshold costs 0.0b (22.1%)

Counts

153 → 1

Compiler

Compiled 9126 to 5888 computations (35.5% saved)

simplify6.0ms (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

end134.0ms (1.3%)

Compiler: Compiled 102 to 62 computations (39.2% saved)

Details

analyze66.0ms (0.6%)

sample1.2s (12%)

simplify386.0ms (3.8%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series29.0ms (0.3%)

rewrite26.0ms (0.3%)

simplify191.0ms (1.9%)

prune316.0ms (3.1%)

localize13.0ms (0.1%)

series104.0ms (1%)

rewrite390.0ms (3.8%)

simplify1.4s (13.9%)

prune886.0ms (8.7%)

localize13.0ms (0.1%)

series44.0ms (0.4%)

rewrite374.0ms (3.6%)

simplify1.7s (16.3%)

prune1.3s (12.7%)

localize14.0ms (0.1%)

series83.0ms (0.8%)

rewrite51.0ms (0.5%)

simplify283.0ms (2.8%)

prune394.0ms (3.9%)

regimes792.0ms (7.7%)

simplify6.0ms (0.1%)

end134.0ms (1.3%)

Profiling