Details

analyze69.0ms (2.9%)

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)

sample228.0ms (9.7%)

Algorithm

1×

intervals

Results

215.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 57 to 38 computations (33.3% saved)

simplify50.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
516×	`cancel-sign-sub-inv_binary64`
510×	`distribute-rgt-in_binary64`
489×	`distribute-lft-in_binary64`
415×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	39	28
2	177	19
3	904	13
4	2320	13
5	4069	13
6	5047	13

prune6.0ms (0.2%)

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

0.4b

Counts

2 → 2

Alt Table

Status	Error	Program
	44.2b	(/.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))
▶	0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 82 to 58 computations (29.3% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 1 (*.f64 i i))
0.5b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

rewrite109.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

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 → 81

Calls

2 calls:

8.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms	(/.f64 1 (*.f64 i i))

Compiler

Compiled 1183 to 881 computations (25.5% saved)

series31.0ms (1.3%)

Error

0.0b

Counts

2 → 15

Calls

2 calls:

16.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
6.0ms	(/.f64 1 (*.f64 i i))

Compiler

Compiled 344 to 299 computations (13.1% saved)

simplify109.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

480×	`associate-/l*_binary64`
434×	`cancel-sign-sub-inv_binary64`
311×	`associate-/r/_binary64`
309×	`div-sub_binary64`
273×	`associate-/l/_binary64`

Counts

96 → 73

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	160	1569
1	311	1476
2	702	1379
3	1706	1379
4	4566	1323
5	4987	1323

prune39.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	72	3	75

Error

Counts

75 → 3

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	31.6b	(.f64 -1/4 (.f64 i i))
▶	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 544 to 413 computations (24.1% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

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)))

rewrite229.0ms (9.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

109×	`add-sqr-sqrt_binary64`
100×	`*-un-lft-identity_binary64`
96×	`times-frac_binary64`
48×	`add-cube-cbrt_binary64`
30×	`associate-r_binary64`

Counts

4 → 174

Calls

4 calls:

31.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
10.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
8.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
6.0ms	(+.f64 2 (/.f64 1 i))

Compiler

Compiled 3702 to 3248 computations (12.3% saved)

series76.0ms (3.2%)

Error

Counts

4 → 42

Calls

4 calls:

15.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
15.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
13.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
8.0ms	(+.f64 2 (/.f64 1 i))

Compiler

Compiled 1242 to 1067 computations (14.1% saved)

simplify189.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

573×	`associate-*l/_binary64`
499×	`associate-/l*_binary64`
288×	`associate-/l/_binary64`
200×	`associate-/r*_binary64`
190×	`times-frac_binary64`

Counts

216 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	4308
1	682	3985
2	2002	3861
3	4601	3861
4	4993	3861
5	4914	3861

prune102.0ms (4.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	150	3	153

Error

Counts

153 → 3

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
▶	31.6b	(.f64 -1/4 (.f64 i i))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 2196 to 1858 computations (15.4% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(.f64 -1/4 (.f64 i i))

rewrite16.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `add-sqr-sqrt_binary64` `associate-l_binary64`
2×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
1×	`add-log-exp_binary64` `unswap-sqr_binary64` `associate-r_binary64` `*-commutative_binary64`

Counts

1 → 19

Calls

1 calls:

6.0ms

(*.f64 -1/4 (*.f64 i i))

Compiler

Compiled 173 to 101 computations (41.6% saved)

series7.0ms (0.3%)

Error

Counts

1 → 3

Calls

1 calls:

6.0ms

(*.f64 -1/4 (*.f64 i i))

Compiler

Compiled 42 to 35 computations (16.7% saved)

simplify62.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

678×	`associate-/l/_binary64`
559×	`associate-/r/_binary64`
350×	`distribute-rgt-in_binary64`
315×	`distribute-lft-in_binary64`
211×	`log-prod_binary64`

Counts

22 → 11

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	225
1	74	189
2	173	180
3	415	180
4	623	180
5	1003	180
6	1910	180
7	4651	180
8	4850	180

prune6.0ms (0.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	11	0	11
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	11	3	14

Error

Counts

14 → 3

Alt Table

Status	Error	Program
	0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	31.6b	(.f64 -1/4 (.f64 i i))
	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 81 to 62 computations (23.5% saved)

regimes121.0ms (5.1%)

Accuracy

Total 0.1b remaining (94.8%)

Threshold costs 0.1b (94.8%)

Compiler

Compiled 1372 to 1115 computations (18.7% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64` `*-commutative_binary64`
1×	`1-exp_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `distribute-neg-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	19	22
2	25	22
3	27	22
4	28	22
5	25	22

end1.0ms (0%)

Compiler: Compiled 16 to 14 computations (12.5% saved)

sample874.0ms (37.2%)

Algorithm

1×

intervals

Results

426.0ms	8000×	body	128	valid
103.0ms	8000×	pre	128	true

Compiler

Compiled 79 to 61 computations (22.8% saved)

Details

analyze69.0ms (2.9%)

sample228.0ms (9.7%)

simplify50.0ms (2.1%)

prune6.0ms (0.2%)

localize6.0ms (0.3%)

rewrite109.0ms (4.6%)

series31.0ms (1.3%)

simplify109.0ms (4.7%)

prune39.0ms (1.6%)

localize11.0ms (0.5%)

rewrite229.0ms (9.8%)

series76.0ms (3.2%)

simplify189.0ms (8.1%)

prune102.0ms (4.3%)

localize3.0ms (0.1%)

rewrite16.0ms (0.7%)

series7.0ms (0.3%)

simplify62.0ms (2.6%)

prune6.0ms (0.3%)

regimes121.0ms (5.1%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample874.0ms (37.2%)

Profiling