Details

analyze7.0ms (0.3%)

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 29 to 19 computations (34.5% saved)

sample1.2s (45.5%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 84 to 55 computations (34.5% saved)

simplify56.0ms (2.1%)

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 (0.2%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	48.9b	(/.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))
▶	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 107 to 73 computations (31.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	0.4b	(/.f64 1 (*.f64 i i))

series5.0ms (0.2%)

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))

rewrite15.0ms (0.6%)

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:

7.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
3.0ms	(/.f64 1 (*.f64 i i))

simplify121.0ms (4.6%)

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 (2.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	112	4	116

Error

Counts

116 → 4

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	1.4b	(/.f64 (/.f64 1/4 (.f64 (cbrt.f64 (-.f64 4 (/.f64 1 (.f64 i i)))) (cbrt.f64 (-.f64 4 (/.f64 1 (.f64 i i)))))) (cbrt.f64 (-.f64 4 (/.f64 1 (.f64 i i)))))
	32.2b	(*.f64 -1/4 (pow.f64 i 2))
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 1903 to 1430 computations (24.9% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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 (0.4%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
3.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
2.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

rewrite52.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-sqr-sqrt_binary64`
96×	`*-un-lft-identity_binary64`
96×	`times-frac_binary64`
47×	`add-cube-cbrt_binary64`
30×	`associate-r_binary64`

Counts

3 → 167

Calls

3 calls:

24.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
7.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
6.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

simplify127.0ms (4.8%)

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

203 → 242

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	259	4188
1	697	3891
2	2091	3770
3	4611	3768
4	5010	3768

prune201.0ms (7.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	241	1	242
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	243	3	246

Error

Counts

246 → 3

Alt Table

Status	Error	Program
▶	0.9b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (/.f64 1 i)))) (/.f64 1/2 (sqrt.f64 (+.f64 2 (/.f64 1 i))))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	32.2b	(*.f64 -1/4 (pow.f64 i 2))
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 5834 to 5042 computations (13.6% saved)

localize15.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
✓	0.6b	(/.f64 1/2 (sqrt.f64 (+.f64 2 (/.f64 1 i))))
✓	0.6b	(/.f64 1 (sqrt.f64 (+.f64 2 (/.f64 1 i))))
✓	0.7b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (/.f64 1 i)))) (/.f64 1/2 (sqrt.f64 (+.f64 2 (/.f64 1 i)))))

series21.0ms (0.8%)

Counts

3 → 28

Calls

3 calls:

12.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 2 (/.f64 1 i))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (/.f64 1 i))))
2.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (/.f64 1 i)))) (/.f64 1/2 (sqrt.f64 (+.f64 2 (/.f64 1 i)))))

rewrite75.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`times-frac_binary64`
115×	`*-un-lft-identity_binary64`
113×	`add-sqr-sqrt_binary64`
81×	`sqrt-prod_binary64`
67×	`add-cube-cbrt_binary64`

Counts

3 → 209

Calls

3 calls:

30.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (/.f64 1 i)))) (/.f64 1/2 (sqrt.f64 (+.f64 2 (/.f64 1 i)))))
13.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (/.f64 1 i))))
8.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 2 (/.f64 1 i))))

simplify154.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

502×	`cancel-sign-sub-inv_binary64`
463×	`associate-/r*_binary64`
398×	`associate-/l*_binary64`
327×	`associate-*l/_binary64`
304×	`fma-def_binary64`

Counts

237 → 248

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	6174
1	615	5180
2	1865	5165
3	4362	4801
4	5184	4801

prune295.0ms (11.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	313	0	313
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	313	3	316

Error

Counts

316 → 3

Alt Table

Status	Error	Program
✓	0.9b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (/.f64 1 i)))) (/.f64 1/2 (sqrt.f64 (+.f64 2 (/.f64 1 i))))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
▶	32.2b	(*.f64 -1/4 (pow.f64 i 2))
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 10905 to 9638 computations (11.6% saved)

localize8.0ms (0.3%)

prune2.0ms (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
✓	0.9b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (/.f64 1 i)))) (/.f64 1/2 (sqrt.f64 (+.f64 2 (/.f64 1 i))))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	32.2b	(*.f64 -1/4 (pow.f64 i 2))
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 42 to 36 computations (14.3% saved)

regimes121.0ms (4.5%)

Accuracy

Total 0.1b remaining (92.6%)

Threshold costs 0.1b (92.6%)

Counts

60 → 1

Compiler

Compiled 2346 to 2019 computations (13.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	19	26
2	25	26
3	27	26
4	28	26
5	26	26

end64.0ms (2.4%)

Compiler: Compiled 78 to 68 computations (12.8% saved)

Details

analyze7.0ms (0.3%)

sample1.2s (45.5%)

simplify56.0ms (2.1%)

prune4.0ms (0.2%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite15.0ms (0.6%)

simplify121.0ms (4.6%)

prune78.0ms (2.9%)

localize7.0ms (0.3%)

series10.0ms (0.4%)

rewrite52.0ms (2%)

simplify127.0ms (4.8%)

prune201.0ms (7.6%)

localize15.0ms (0.6%)

series21.0ms (0.8%)

rewrite75.0ms (2.8%)

simplify154.0ms (5.8%)

prune295.0ms (11.1%)

localize8.0ms (0.3%)

prune2.0ms (0.1%)

regimes121.0ms (4.5%)

simplify2.0ms (0.1%)

end64.0ms (2.4%)

Profiling