Details

analyze78.0ms (2.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 30 to 20 computations (33.3% saved)

sample29.0ms (0.9%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 57 to 38 computations (33.3% saved)

simplify63.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
510×	`distribute-rgt-in_binary64`
489×	`distribute-lft-in_binary64`
463×	`fma-neg_binary64`
415×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	40	26
2	185	17
3	915	13
4	2340	13
5	4455	13
6	4958	13
7	5077	13

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	46.4b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))

Compiler

Compiled 107 to 73 computations (31.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 4 (/.f64 1 (*.f64 i i)))
✓	0.4b	(/.f64 1 (*.f64 i i))
✓	0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
49×	`times-frac_binary64`
34×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`

Counts

3 → 134

Calls

3 calls:

7.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))
4.0ms	(/.f64 1 (*.f64 i i))

series18.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

7.0ms	(/.f64 1 (*.f64 i i))
6.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))

simplify189.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-neg_binary64`
446×	`unswap-sqr_binary64`
409×	`associate-l_binary64`
361×	`fma-def_binary64`
294×	`associate-r_binary64`

Counts

170 → 323

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	203	2573
1	382	2324
2	977	2089
3	3418	2089
4	4641	2081
5	4949	2081
6	4780	2081

prune143.0ms (4.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	320	3	323
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	322	3	325

Error

Counts

325 → 3

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 1/4 (+.f64 4 (*.f64 (neg.f64 (/.f64 1 i)) (/.f64 1 i))))
	28.3b	(/.f64 1/4 (/.f64 (-.f64 64 (/.f64 1 (pow.f64 i 6))) (+.f64 16 (+.f64 (/.f64 1 (pow.f64 i 4)) (/.f64 4 (*.f64 i i))))))
	30.5b	(*.f64 -1/4 (pow.f64 i 2))

Compiler

Compiled 3696 to 2744 computations (25.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 4 (*.f64 (neg.f64 (/.f64 1 i)) (/.f64 1 i)))
✓	0.3b	(*.f64 (neg.f64 (/.f64 1 i)) (/.f64 1 i))
✓	0.4b	(/.f64 1/4 (+.f64 4 (*.f64 (neg.f64 (/.f64 1 i)) (/.f64 1 i))))

rewrite26.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
30×	`associate-l_binary64`

Counts

3 → 116

Calls

3 calls:

13.0ms	(*.f64 (neg.f64 (/.f64 1 i)) (/.f64 1 i))
3.0ms	(/.f64 1/4 (+.f64 4 (*.f64 (neg.f64 (/.f64 1 i)) (/.f64 1 i))))
2.0ms	(+.f64 4 (*.f64 (neg.f64 (/.f64 1 i)) (/.f64 1 i)))

series17.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

9.0ms	(*.f64 (neg.f64 (/.f64 1 i)) (/.f64 1 i))
5.0ms	(+.f64 4 (*.f64 (neg.f64 (/.f64 1 i)) (/.f64 1 i)))
3.0ms	(/.f64 1/4 (+.f64 4 (*.f64 (neg.f64 (/.f64 1 i)) (/.f64 1 i))))

simplify174.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

651×	`fma-neg_binary64`
469×	`div-sub_binary64`
340×	`associate-l_binary64`
274×	`fma-def_binary64`
270×	`associate-r_binary64`

Counts

152 → 287

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	181	1972
1	421	1808
2	1016	1782
3	3098	1764
4	4379	1764
5	4959	1764
6	4840	1764

prune157.0ms (4.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	287	0	287
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	287	3	290

Error

Counts

290 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 1/4 (+.f64 4 (*.f64 (neg.f64 (/.f64 1 i)) (/.f64 1 i))))
▶	28.3b	(/.f64 1/4 (/.f64 (-.f64 64 (/.f64 1 (pow.f64 i 6))) (+.f64 16 (+.f64 (/.f64 1 (pow.f64 i 4)) (/.f64 4 (*.f64 i i))))))
	30.5b	(*.f64 -1/4 (pow.f64 i 2))

Compiler

Compiled 4044 to 3200 computations (20.9% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (pow.f64 i 6))
✓	0.4b	(/.f64 4 (*.f64 i i))
✓	0.4b	(/.f64 1/4 (/.f64 (-.f64 64 (/.f64 1 (pow.f64 i 6))) (+.f64 16 (+.f64 (/.f64 1 (pow.f64 i 4)) (/.f64 4 (*.f64 i i))))))
✓	28.2b	(/.f64 (-.f64 64 (/.f64 1 (pow.f64 i 6))) (+.f64 16 (+.f64 (/.f64 1 (pow.f64 i 4)) (/.f64 4 (*.f64 i i)))))

rewrite136.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Rules

810×	`*-un-lft-identity_binary64`
804×	`times-frac_binary64`
662×	`add-sqr-sqrt_binary64`
305×	`distribute-lft-out_binary64`
217×	`difference-of-squares_binary64`

Counts

4 → 519

Calls

4 calls:

34.0ms	(/.f64 1/4 (/.f64 (-.f64 64 (/.f64 1 (pow.f64 i 6))) (+.f64 16 (+.f64 (/.f64 1 (pow.f64 i 4)) (/.f64 4 (*.f64 i i))))))
30.0ms	(/.f64 (-.f64 64 (/.f64 1 (pow.f64 i 6))) (+.f64 16 (+.f64 (/.f64 1 (pow.f64 i 4)) (/.f64 4 (*.f64 i i)))))
3.0ms	(/.f64 1 (pow.f64 i 6))
3.0ms	(/.f64 4 (*.f64 i i))

series53.0ms (1.6%)

Counts

4 → 36

Calls

4 calls:

21.0ms	(/.f64 (-.f64 64 (/.f64 1 (pow.f64 i 6))) (+.f64 16 (+.f64 (/.f64 1 (pow.f64 i 4)) (/.f64 4 (*.f64 i i)))))
16.0ms	(/.f64 1 (pow.f64 i 6))
9.0ms	(/.f64 4 (*.f64 i i))
6.0ms	(/.f64 1/4 (/.f64 (-.f64 64 (/.f64 1 (pow.f64 i 6))) (+.f64 16 (+.f64 (/.f64 1 (pow.f64 i 4)) (/.f64 4 (*.f64 i i))))))

simplify593.0ms (17.8%)

Algorithm

1×	egg-herbie

Rules

877×	`fma-def_binary64`
829×	`times-frac_binary64`
282×	`associate-/r/_binary64`
196×	`*-commutative_binary64`
194×	`associate-*l/_binary64`

Counts

555 → 1040

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	448	24354
1	1000	23816
2	3319	22867
3	4680	22867
4	4881	22867

prune483.0ms (14.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	1040	0	1040
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	1040	3	1043

Error

Counts

1043 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 1/4 (+.f64 4 (*.f64 (neg.f64 (/.f64 1 i)) (/.f64 1 i))))
✓	28.3b	(/.f64 1/4 (/.f64 (-.f64 64 (/.f64 1 (pow.f64 i 6))) (+.f64 16 (+.f64 (/.f64 1 (pow.f64 i 4)) (/.f64 4 (*.f64 i i))))))
▶	30.5b	(*.f64 -1/4 (pow.f64 i 2))

Compiler

Compiled 19383 to 15505 computations (20% saved)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune3.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Error

Counts

3 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 1/4 (+.f64 4 (*.f64 (neg.f64 (/.f64 1 i)) (/.f64 1 i))))
✓	28.3b	(/.f64 1/4 (/.f64 (-.f64 64 (/.f64 1 (pow.f64 i 6))) (+.f64 16 (+.f64 (/.f64 1 (pow.f64 i 4)) (/.f64 4 (*.f64 i i))))))
✓	30.5b	(*.f64 -1/4 (pow.f64 i 2))

Compiler

Compiled 43 to 36 computations (16.3% saved)

regimes131.0ms (3.9%)

Accuracy

Total 0.3b remaining (98.3%)

Threshold costs 0.3b (98.3%)

Compiler

Compiled 2034 to 1657 computations (18.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	11	13
2	11	13

end1.0ms (0%)

Compiler: Compiled 10 to 9 computations (10% saved)

sample965.0ms (29%)

Algorithm

1×

intervals

Results

539.0ms	8000×	body	128	valid
105.0ms	8000×	pre	128	true

Compiler

Compiled 84 to 66 computations (21.4% saved)

Details

analyze78.0ms (2.3%)

sample29.0ms (0.9%)

simplify63.0ms (1.9%)

prune5.0ms (0.1%)

localize6.0ms (0.2%)

rewrite23.0ms (0.7%)

series18.0ms (0.5%)

simplify189.0ms (5.7%)

prune143.0ms (4.3%)

localize6.0ms (0.2%)

rewrite26.0ms (0.8%)

series17.0ms (0.5%)

simplify174.0ms (5.2%)

prune157.0ms (4.7%)

localize13.0ms (0.4%)

rewrite136.0ms (4.1%)

series53.0ms (1.6%)

simplify593.0ms (17.8%)

prune483.0ms (14.5%)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify8.0ms (0.3%)

prune3.0ms (0.1%)

regimes131.0ms (3.9%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample965.0ms (29%)

Profiling