Details

analyze6.0ms (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)

sample1.0s (55.7%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 58 to 38 computations (34.5% saved)

preprocess27.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

554×	`associate-/r*_binary64`
513×	`distribute-rgt-in_binary64`
416×	`associate-/r/_binary64`
349×	`fma-def_binary64`
319×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	40	26
2	200	17
3	1316	13
4	3585	13
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify24.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

554×	`associate-/r*_binary64`
513×	`distribute-rgt-in_binary64`
416×	`associate-/r/_binary64`
349×	`fma-def_binary64`
319×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	40	26
2	200	17
3	1316	13
4	3585	13

Stop Event

1×	node limit

Counts

1 → 2

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

4.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	47.9b	(/.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))
▶	4.7b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))

Compiler

Compiled 107 to 74 computations (30.8% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
✓	10.7b	(/.f64 i (pow.f64 i 3))

series5.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))	i	0
1.0ms	(/.f64 i (pow.f64 i 3))	i	0
1.0ms	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))	i	-inf
1.0ms	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))	i	inf
1.0ms	(/.f64 i (pow.f64 i 3))	i	-inf

rewrite54.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

437×	`log-prod_binary64`
172×	`expm1-udef_binary64`
172×	`log1p-udef_binary64`
168×	`pow1/3_binary64`
150×	`pow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	211	14
2	2654	14

Stop Event

1×	node limit

Counts

2 → 68

simplify34.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

438×	`associate-l_binary64`
438×	`fma-neg_binary64`
413×	`unswap-sqr_binary64`
320×	`cancel-sign-sub-inv_binary64`
291×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	273
1	104	271
2	285	267
3	1068	267
4	4284	267

Stop Event

1×	node limit

Counts

92 → 85

prune52.0ms (2.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	84	3	87

Error

Counts

87 → 3

Alt Table

Status	Error	Program
	47.9b	(/.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))
	32.0b	(-.f64 (.f64 i (.f64 i -1/4)) (pow.f64 i 4))
▶	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))

Compiler

Compiled 1135 to 891 computations (21.5% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
✓	0.4b	(/.f64 1 (pow.f64 i 2))

series5.0ms (0.3%)

Counts

2 → 12

Calls

6 calls:

1.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))	i	0
1.0ms	(/.f64 1 (pow.f64 i 2))	i	0
1.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))	i	-inf
1.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))	i	inf
1.0ms	(/.f64 1 (pow.f64 i 2))	i	inf

rewrite41.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

386×	`log-prod_binary64`
246×	`pow2_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`
168×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	224	14
2	2581	14

Stop Event

1×	node limit

Counts

2 → 61

simplify30.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

448×	`associate-l_binary64`
438×	`fma-neg_binary64`
413×	`unswap-sqr_binary64`
320×	`cancel-sign-sub-inv_binary64`
291×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	189
1	104	187
2	285	183
3	1067	183
4	4298	183

Stop Event

1×	node limit

Counts

73 → 76

prune47.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	76	3	79

Error

Counts

79 → 3

Alt Table

Status	Error	Program
	47.9b	(/.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))
▶	32.0b	(-.f64 (.f64 i (.f64 i -1/4)) (pow.f64 i 4))
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))

Compiler

Compiled 960 to 806 computations (16% saved)

localize7.0ms (0.4%)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	1	1
Total	3	3

Error

Counts

3 → 3

Alt Table

Status	Error	Program
▶	47.9b	(/.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))
✓	32.0b	(-.f64 (.f64 i (.f64 i -1/4)) (pow.f64 i 4))
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 i i) (*.f64 i i))
✓	15.5b	(/.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))
✓	43.9b	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))

series8.0ms (0.4%)

Counts

3 → 36

Calls

9 calls:

1.0ms	(/.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))	i	0
1.0ms	(/.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))	i	-inf
1.0ms	(/.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))	i	inf
1.0ms	(.f64 (.f64 i i) (*.f64 i i))	i	-inf
1.0ms	(.f64 (.f64 i i) (*.f64 i i))	i	inf

rewrite65.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

508×	`prod-diff_binary64`
200×	`log1p-udef_binary64`
151×	`times-frac_binary64`
122×	`egg-rr`
120×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	51
1	255	40
2	3902	40

Stop Event

1×	node limit

Counts

3 → 122

simplify38.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

451×	`associate-l_binary64`
438×	`fma-neg_binary64`
413×	`unswap-sqr_binary64`
320×	`cancel-sign-sub-inv_binary64`
291×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	321
1	104	319
2	285	315
3	1067	315
4	4313	315

Stop Event

1×	node limit

Counts

158 → 139

prune101.0ms (5.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	139	3	142

Error

Counts

142 → 3

Alt Table

Status	Error	Program
✓	47.9b	(/.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))
✓	32.0b	(-.f64 (.f64 i (.f64 i -1/4)) (pow.f64 i 4))
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))

Compiler

Compiled 3136 to 2166 computations (30.9% saved)

regimes189.0ms (10.3%)

Accuracy

Total 0.3b remaining (99%)

Threshold costs 0.3b (99%)

Counts

92 → 1

Compiler

Compiled 3728 to 2779 computations (25.5% 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	10	13
1	14	13
2	20	13
3	22	13
4	23	13

Stop Event

1×

saturated

end54.0ms (2.9%)

Stop Event

1×

done

Compiler

Compiled 66 to 51 computations (22.7% saved)

Details

analyze6.0ms (0.3%)

sample1.0s (55.7%)

preprocess27.0ms (1.5%)

simplify24.0ms (1.3%)

prune4.0ms (0.2%)

localize5.0ms (0.3%)

series5.0ms (0.3%)

rewrite54.0ms (2.9%)

simplify34.0ms (1.8%)

prune52.0ms (2.8%)

localize8.0ms (0.4%)

series5.0ms (0.3%)

rewrite41.0ms (2.3%)

simplify30.0ms (1.6%)

prune47.0ms (2.5%)

localize7.0ms (0.4%)

prune2.0ms (0.1%)

localize8.0ms (0.4%)

series8.0ms (0.4%)

rewrite65.0ms (3.5%)

simplify38.0ms (2.1%)

prune101.0ms (5.5%)

regimes189.0ms (10.3%)

simplify2.0ms (0.1%)

end54.0ms (2.9%)

Profiling