Details

analyze8.0ms (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)

sample1.4s (46.4%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 84 to 55 computations (34.5% saved)

simplify56.0ms (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

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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	46.1b	(/.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))
▶	0.6b	(/.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
✓	0.4b	(/.f64 1 (*.f64 i i))
✓	0.6b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

series8.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
2.0ms	(/.f64 1 (*.f64 i i))

rewrite15.0ms (0.5%)

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))))
4.0ms	(/.f64 1 (*.f64 i i))

simplify124.0ms (4.2%)

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

prune89.0ms (3%)

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) (/.f64 1 i)))
	30.6b	(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)))))
✓	0.6b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 1871 to 1404 computations (25% saved)

localize24.0ms (0.8%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (sqrt.f64 4) (/.f64 1 i))
✓	0.1b	(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 (sqrt.f64 4) (/.f64 1 i)))
✓	0.1b	(/.f64 1/4 (+.f64 2 (/.f64 1 i)))

series7.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 (sqrt.f64 4) (/.f64 1 i)))
2.0ms	(/.f64 1/4 (+.f64 2 (/.f64 1 i)))
1.0ms	(-.f64 (sqrt.f64 4) (/.f64 1 i))

rewrite109.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

581×	`times-frac_binary64`
542×	`add-sqr-sqrt_binary64`
455×	`*-un-lft-identity_binary64`
220×	`add-cube-cbrt_binary64`
138×	`difference-of-squares_binary64`

Counts

3 → 439

Calls

3 calls:

19.0ms	(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 (sqrt.f64 4) (/.f64 1 i)))
11.0ms	(-.f64 (sqrt.f64 4) (/.f64 1 i))
6.0ms	(/.f64 1/4 (+.f64 2 (/.f64 1 i)))

simplify432.0ms (14.6%)

Algorithm

1×	egg-herbie

Rules

655×	`fma-def_binary64`
441×	`times-frac_binary64`
284×	`fma-neg_binary64`
270×	`div-sub_binary64`
232×	`cancel-sign-sub-inv_binary64`

Counts

475 → 423

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	385	14809
1	914	13938
2	2601	13450
3	4461	13450
4	4986	13450
5	4891	13450

prune405.0ms (13.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	423	0	423
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	423	3	426

Error

Counts

426 → 3

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 (sqrt.f64 4) (/.f64 1 i)))
▶	30.6b	(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)))))
✓	0.6b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 13068 to 10958 computations (16.1% saved)

localize13.0ms (0.4%)

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	(*.f64 16 (pow.f64 i 8))
✓	0.0b	(fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))

series12.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

5.0ms	(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 (0.2%)

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

simplify48.0ms (1.6%)

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

prune62.0ms (2.1%)

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 (/.f64 1/4 (+.f64 2 (/.f64 1 i))) (-.f64 (sqrt.f64 4) (/.f64 1 i)))
✓	30.6b	(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)))))
✓	0.6b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 1860 to 1282 computations (31.1% saved)

regimes95.0ms (3.2%)

Accuracy

Total 0.1b remaining (94.9%)

Threshold costs 0.1b (94.9%)

Counts

53 → 1

Compiler

Compiled 1582 to 1271 computations (19.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	18	22
2	17	22

end65.0ms (2.2%)

Compiler: Compiled 77 to 63 computations (18.2% saved)

Details

analyze8.0ms (0.3%)

sample1.4s (46.4%)

simplify56.0ms (1.9%)

prune4.0ms (0.1%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite15.0ms (0.5%)

simplify124.0ms (4.2%)

prune89.0ms (3%)

localize24.0ms (0.8%)

series7.0ms (0.2%)

rewrite109.0ms (3.7%)

simplify432.0ms (14.6%)

prune405.0ms (13.7%)

localize13.0ms (0.4%)

series12.0ms (0.4%)

rewrite6.0ms (0.2%)

simplify48.0ms (1.6%)

prune62.0ms (2.1%)

regimes95.0ms (3.2%)

simplify2.0ms (0.1%)

end65.0ms (2.2%)

Profiling