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)

sample274.0ms (12.3%)

Algorithm

1×

intervals

Results

190.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 56 to 37 computations (33.9% saved)

simplify53.0ms (2.4%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	47.8b	(/.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)

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))

rewrite16.0ms (0.7%)

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:

8.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
3.0ms	(/.f64 1 (*.f64 i i))

simplify150.0ms (6.7%)

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

prune85.0ms (3.8%)

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 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
▶	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	31.6b	(neg.f64 (fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))

Compiler

Compiled 1873 to 1406 computations (24.9% saved)

localize9.0ms (0.4%)

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)))

series9.0ms (0.4%)

Counts

3 → 36

Calls

3 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)))
2.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))

rewrite56.0ms (2.5%)

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:

23.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
9.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
8.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

simplify128.0ms (5.8%)

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

prune221.0ms (9.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	242	0	242
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	242	3	245

Error

Counts

245 → 3

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
▶	31.6b	(neg.f64 (fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))

Compiler

Compiled 5826 to 5028 computations (13.7% saved)

localize14.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))
✓	0.0b	(fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))
✓	0.0b	(*.f64 16 (pow.f64 i 8))

series12.0ms (0.5%)

Counts

3 → 24

Calls

3 calls:

4.0ms	(fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))
4.0ms	(fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))
3.0ms	(*.f64 16 (pow.f64 i 8))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`add-exp-log_binary64`
7×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

3 → 47

Calls

3 calls:

4.0ms	(*.f64 16 (pow.f64 i 8))
0.0ms	(fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))
0.0ms	(fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))

simplify47.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

969×	`distribute-rgt-in_binary64`
967×	`distribute-lft-in_binary64`
601×	`fma-def_binary64`
249×	`associate-l_binary64`
218×	`associate-r_binary64`

Counts

71 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	1165
1	162	1063
2	365	1039
3	1330	1039
4	5671	1039

prune64.0ms (2.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	75	3	78

Error

Counts

78 → 3

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	31.6b	(neg.f64 (fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))

Compiler

Compiled 1861 to 1283 computations (31.1% saved)

regimes103.0ms (4.6%)

Accuracy

Total 0.1b remaining (93.9%)

Threshold costs 0.1b (93.9%)

Counts

54 → 1

Compiler

Compiled 1582 to 1279 computations (19.2% saved)

simplify3.0ms (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	11	22
1	17	22
2	23	22
3	25	22
4	26	22
5	24	22

end1.0ms (0%)

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

sample954.0ms (42.9%)

Algorithm

1×

intervals

Results

555.0ms	8000×	body	128	valid
100.0ms	8000×	pre	128	true

Compiler

Compiled 92 to 70 computations (23.9% saved)

Details

analyze7.0ms (0.3%)

sample274.0ms (12.3%)

simplify53.0ms (2.4%)

prune4.0ms (0.2%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite16.0ms (0.7%)

simplify150.0ms (6.7%)

prune85.0ms (3.8%)

localize9.0ms (0.4%)

series9.0ms (0.4%)

rewrite56.0ms (2.5%)

simplify128.0ms (5.8%)

prune221.0ms (9.9%)

localize14.0ms (0.6%)

series12.0ms (0.5%)

rewrite6.0ms (0.3%)

simplify47.0ms (2.1%)

prune64.0ms (2.9%)

regimes103.0ms (4.6%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample954.0ms (42.9%)

Profiling