Details

analyze1.4s (32.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
3.1%	46.9%	50%	5
7.8%	42.2%	50%	6
10.2%	39.8%	50%	7
10.9%	39%	50%	8
11.3%	38.7%	50%	9
11.6%	38.4%	50%	10
11.8%	38.2%	50%	11
11.8%	38.2%	50%	12
11.8%	38.1%	50%	13
11.9%	38.1%	50%	14

Compiler

Compiled 29 to 19 computations (34.5% saved)

sample1.1s (25.3%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 55 to 36 computations (34.5% saved)

simplify60.0ms (1.3%)

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

prune4.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	50.6b	(/.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))
▶	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 107 to 73 computations (31.8% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	0.7b	(/.f64 1 (*.f64 i i))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
2.0ms	(/.f64 1 (*.f64 i i))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
35×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

2 → 85

Calls

2 calls:

6.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
3.0ms	(/.f64 1 (*.f64 i i))

simplify138.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

484×	`cancel-sign-sub-inv_binary64`
484×	`fma-neg_binary64`
262×	`associate-/l/_binary64`
260×	`unsub-neg_binary64`
197×	`neg-mul-1_binary64`

Counts

109 → 114

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	157	1670
1	304	1577
2	701	1474
3	1855	1474
4	4205	1414
5	4887	1414
6	4999	1414
7	4867	1414

prune78.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	113	3	116

Error

Counts

116 → 3

Alt Table

Status	Error	Program
	0.1b	(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
▶	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 1869 to 1408 computations (24.7% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 2 (/.f64 1 i))
✓	0.0b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	0.1b	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
✓	0.1b	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

series10.0ms (0.2%)

Counts

4 → 39

Calls

4 calls:

3.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
3.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
3.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
1.0ms	(+.f64 2 (/.f64 1 i))

rewrite61.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`add-sqr-sqrt_binary64`
101×	`*-un-lft-identity_binary64`
96×	`times-frac_binary64`
49×	`add-cube-cbrt_binary64`
30×	`associate-r_binary64`

Counts

4 → 185

Calls

4 calls:

26.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
6.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
6.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
4.0ms	(+.f64 2 (/.f64 1 i))

simplify130.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-/l*_binary64`
456×	`fma-def_binary64`
288×	`associate-/l/_binary64`
277×	`fma-neg_binary64`
200×	`associate-/r*_binary64`

Counts

224 → 263

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	265	4371
1	704	4054
2	2098	3932
3	4620	3930
4	5026	3930

prune234.0ms (5.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	263	0	263
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	263	3	266

Error

Counts

266 → 3

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 6249 to 5401 computations (13.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
✓	0.1b	(/.f64 1/4 (+.f64 2 (/.f64 1 i)))
	0.7b	(/.f64 1 (*.f64 i i))
✓	31.8b	(sqrt.f64 (/.f64 1 (*.f64 i i)))

series8.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
3.0ms	(/.f64 1/4 (+.f64 2 (/.f64 1 i)))
1.0ms	(sqrt.f64 (/.f64 1 (*.f64 i i)))

rewrite129.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

627×	`times-frac_binary64`
482×	`add-sqr-sqrt_binary64`
474×	`*-un-lft-identity_binary64`
315×	`sqrt-prod_binary64`
176×	`difference-of-squares_binary64`

Counts

3 → 416

Calls

3 calls:

21.0ms	(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
6.0ms	(/.f64 1/4 (+.f64 2 (/.f64 1 i)))
3.0ms	(sqrt.f64 (/.f64 1 (*.f64 i i)))

simplify466.0ms (10.5%)

Algorithm

1×	egg-herbie

Rules

442×	`fma-def_binary64`
430×	`associate-/l/_binary64`
359×	`div-sub_binary64`
308×	`times-frac_binary64`
279×	`distribute-rgt-in_binary64`

Counts

452 → 363

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	353	18086
1	855	17810
2	2163	16001
3	4661	14812
4	4614	14811
5	4900	14811

prune379.0ms (8.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	403	0	403
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	403	3	406

Error

Counts

406 → 3

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 (sqrt.f64 4) (sqrt.f64 (/.f64 1 (*.f64 i i)))))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 11482 to 9463 computations (17.6% saved)

regimes93.0ms (2.1%)

Accuracy

Total 0.3b remaining (97.4%)

Threshold costs 0.3b (97.4%)

Counts

41 → 1

Compiler

Compiled 1316 to 1063 computations (19.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	19	13
3	21	13
4	22	13
5	20	13

end51.0ms (1.1%)

Compiler: Compiled 64 to 53 computations (17.2% saved)

Details

analyze1.4s (32.5%)

sample1.1s (25.3%)

simplify60.0ms (1.3%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series6.0ms (0.1%)

rewrite14.0ms (0.3%)

simplify138.0ms (3.1%)

prune78.0ms (1.7%)

localize7.0ms (0.2%)

series10.0ms (0.2%)

rewrite61.0ms (1.4%)

simplify130.0ms (2.9%)

prune234.0ms (5.2%)

localize10.0ms (0.2%)

series8.0ms (0.2%)

rewrite129.0ms (2.9%)

simplify466.0ms (10.5%)

prune379.0ms (8.5%)

regimes93.0ms (2.1%)

simplify2.0ms (0.1%)

end51.0ms (1.1%)

Profiling