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)

sample1.1s (49.5%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 84 to 55 computations (34.5% saved)

simplify57.0ms (2.5%)

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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	46.9b	(/.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))
▶	0.4b	(/.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))
✓	0.4b	(/.f64 1/4 (-.f64 4 (/.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))

rewrite50.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

882×	`log1p-expm1-u_binary64`
882×	`expm1-log1p-u_binary64`
92×	`add-sqr-sqrt_binary64`
91×	`add-cbrt-cube_binary64`
91×	`add-log-exp_binary64`

Counts

2 → 47

Calls

2 calls:

50.0ms	(/.f64 1 (*.f64 i i))
49.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	202	14
2	2288	14
3	5374	14
0	0	0
1	0	0

simplify96.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

590×	`distribute-rgt-neg-in_binary64`
538×	`distribute-lft-neg-in_binary64`
472×	`associate-l_binary64`
438×	`fma-neg_binary64`
414×	`unswap-sqr_binary64`

Counts

71 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	273
1	104	271
2	280	267
3	846	267
4	2593	267
5	4622	267
6	4902	267
7	4992	267

prune59.0ms (2.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	64	2	66

Error

Counts

66 → 2

Alt Table

Status	Error	Program
▶	26.4b	(*.f64 (/.f64 1/4 (-.f64 16 (/.f64 1 (pow.f64 i 4)))) (+.f64 4 (pow.f64 i -2)))
	30.3b	(neg.f64 (fma.f64 i (.f64 i (fma.f64 i i 1/4)) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))

Compiler

Compiled 798 to 668 computations (16.3% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (pow.f64 i 4))
✓	0.3b	(/.f64 1/4 (-.f64 16 (/.f64 1 (pow.f64 i 4))))
✓	25.8b	(*.f64 (/.f64 1/4 (-.f64 16 (/.f64 1 (pow.f64 i 4)))) (+.f64 4 (pow.f64 i -2)))

series12.0ms (0.5%)

Counts

3 → 24

Calls

3 calls:

5.0ms	(/.f64 1 (pow.f64 i 4))
3.0ms	(*.f64 (/.f64 1/4 (-.f64 16 (/.f64 1 (pow.f64 i 4)))) (+.f64 4 (pow.f64 i -2)))
3.0ms	(/.f64 1/4 (-.f64 16 (/.f64 1 (pow.f64 i 4))))

rewrite69.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

398×	`prod-diff_binary64`
250×	`expm1-udef_binary64`
250×	`log1p-udef_binary64`
151×	`log1p-expm1-u_binary64`
151×	`expm1-log1p-u_binary64`

Counts

3 → 103

Calls

3 calls:

67.0ms	(/.f64 1 (pow.f64 i 4))
67.0ms	(/.f64 1/4 (-.f64 16 (/.f64 1 (pow.f64 i 4))))
67.0ms	(*.f64 (/.f64 1/4 (-.f64 16 (/.f64 1 (pow.f64 i 4)))) (+.f64 4 (pow.f64 i -2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	329	24
2	3689	24
3	4999	24
0	0	0
1	0	0

simplify72.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

547×	`times-frac_binary64`
457×	`sub-neg_binary64`
433×	`associate-/r*_binary64`
422×	`unswap-sqr_binary64`
287×	`fma-def_binary64`

Counts

127 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	381
1	192	379
2	538	371
3	1688	371
4	3441	371
5	4733	371
6	4915	371

prune95.0ms (4.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	132	2	134

Error

Counts

134 → 2

Alt Table

Status	Error	Program
✓	26.4b	(*.f64 (/.f64 1/4 (-.f64 16 (/.f64 1 (pow.f64 i 4)))) (+.f64 4 (pow.f64 i -2)))
▶	30.3b	(neg.f64 (fma.f64 i (.f64 i (fma.f64 i i 1/4)) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))

Compiler

Compiled 2386 to 2013 computations (15.6% saved)

localize11.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 i (.f64 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 i (fma.f64 i i 1/4))

series14.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(fma.f64 i (.f64 i (fma.f64 i i 1/4)) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))
5.0ms	(fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))
3.0ms	(*.f64 i (fma.f64 i i 1/4))

rewrite63.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

534×	`log-prod_binary64`
225×	`expm1-udef_binary64`
225×	`log1p-udef_binary64`
194×	`log-pow_binary64`
187×	`fma-def_binary64`

Counts

3 → 103

Calls

3 calls:

61.0ms	(fma.f64 i (.f64 i (fma.f64 i i 1/4)) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))
61.0ms	(fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))
61.0ms	(*.f64 i (fma.f64 i i 1/4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	47
1	294	47
2	2892	47
3	4969	47
0	0	0
1	0	0

simplify185.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

748×	`unswap-sqr_binary64`
714×	`distribute-rgt-out_binary64`
623×	`sqr-pow_binary64`
596×	`distribute-lft-out_binary64`
568×	`*-commutative_binary64`

Counts

139 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	452
1	64	432
2	153	420
3	411	420
4	1493	420
5	3328	420
6	3320	420
7	3674	420
8	4015	420
9	4425	420
10	4308	420
11	4708	420
12	4703	420
13	4935	420
14	4870	420

prune93.0ms (4.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	119	2	121

Error

Counts

121 → 2

Alt Table

Status	Error	Program
✓	26.4b	(*.f64 (/.f64 1/4 (-.f64 16 (/.f64 1 (pow.f64 i 4)))) (+.f64 4 (pow.f64 i -2)))
✓	30.3b	(neg.f64 (fma.f64 i (.f64 i (fma.f64 i i 1/4)) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))

Compiler

Compiled 2918 to 2085 computations (28.5% saved)

regimes189.0ms (8.2%)

Accuracy

Total 0.4b remaining (98.4%)

Threshold costs 0.4b (98.4%)

Counts

104 → 1

Compiler

Compiled 2872 to 2421 computations (15.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	11	13
2	15	13
3	17	13
4	18	13
5	18	13

end59.0ms (2.6%)

Compiler: Compiled 56 to 44 computations (21.4% saved)

Details

analyze7.0ms (0.3%)

sample1.1s (49.5%)

simplify57.0ms (2.5%)

prune4.0ms (0.2%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite50.0ms (2.2%)

simplify96.0ms (4.2%)

prune59.0ms (2.6%)

localize8.0ms (0.4%)

series12.0ms (0.5%)

rewrite69.0ms (3%)

simplify72.0ms (3.2%)

prune95.0ms (4.2%)

localize11.0ms (0.5%)

series14.0ms (0.6%)

rewrite63.0ms (2.8%)

simplify185.0ms (8.1%)

prune93.0ms (4.1%)

regimes189.0ms (8.2%)

simplify2.0ms (0.1%)

end59.0ms (2.6%)

Profiling