Details

analyze13.0ms (0.4%)

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 (41.7%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 84 to 55 computations (34.5% saved)

simplify57.0ms (1.7%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	46.5b	(/.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))
▶	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 107 to 73 computations (31.8% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	0.5b	(/.f64 1 (*.f64 i i))

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

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

rewrite51.0ms (1.5%)

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 → 48

Calls

2 calls:

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

simplify94.0ms (2.8%)

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

72 → 65

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

prune70.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	64	3	67

Error

Counts

67 → 3

Alt Table

Status	Error	Program
	46.5b	(/.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))
	30.5b	(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)))))
▶	17.5b	(sqrt.f64 (/.f64 1/16 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2)))

Compiler

Compiled 847 to 700 computations (17.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (-.f64 4 (pow.f64 i -2)) 2)
✓	0.2b	(/.f64 1/16 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2))
✓	8.0b	(sqrt.f64 (/.f64 1/16 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2)))

series8.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(sqrt.f64 (/.f64 1/16 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2)))
3.0ms	(/.f64 1/16 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2))
2.0ms	(pow.f64 (-.f64 4 (pow.f64 i -2)) 2)

rewrite58.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

429×	`log-prod_binary64`
275×	`pow2_binary64`
190×	`expm1-udef_binary64`
190×	`log1p-udef_binary64`
186×	`pow1/3_binary64`

Counts

3 → 102

Calls

3 calls:

56.0ms	(pow.f64 (-.f64 4 (pow.f64 i -2)) 2)
56.0ms	(/.f64 1/16 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2))
56.0ms	(sqrt.f64 (/.f64 1/16 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	38
1	247	33
2	2589	33
3	4831	33
0	0	0
1	0	0

simplify61.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

720×	`associate-l_binary64`
529×	`times-frac_binary64`
482×	`associate-r_binary64`
447×	`unswap-sqr_binary64`
444×	`fma-neg_binary64`

Counts

138 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	534
1	188	532
2	470	528
3	1326	528
4	4032	528
5	5423	528

prune125.0ms (3.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	140	3	143

Error

Counts

143 → 3

Alt Table

Status	Error	Program
	46.5b	(/.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))
▶	30.5b	(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)))))
✓	17.5b	(sqrt.f64 (/.f64 1/16 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2)))

Compiler

Compiled 2165 to 1872 computations (13.5% saved)

localize11.0ms (0.3%)

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))

series11.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

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

rewrite85.0ms (2.5%)

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 → 106

Calls

3 calls:

83.0ms	(fma.f64 i (.f64 i (fma.f64 i i 1/4)) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))
83.0ms	(fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))
83.0ms	(*.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

simplify189.0ms (5.6%)

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

142 → 121

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

prune110.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	121	3	124

Error

Counts

124 → 3

Alt Table

Status	Error	Program
▶	46.5b	(/.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))
✓	30.5b	(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)))))
✓	17.5b	(sqrt.f64 (/.f64 1/16 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2)))

Compiler

Compiled 3003 to 2141 computations (28.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1)
✓	0.1b	(.f64 (.f64 i i) (*.f64 i i))
✓	16.0b	(/.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))
✓	42.5b	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))

series13.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

5.0ms	(-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1)
3.0ms	(/.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))
3.0ms	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))
3.0ms	(.f64 (.f64 i i) (*.f64 i i))

rewrite85.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

508×	`prod-diff_binary64`
200×	`log1p-udef_binary64`
199×	`expm1-udef_binary64`
161×	`egg-rr`
151×	`times-frac_binary64`

Counts

4 → 161

Calls

4 calls:

82.0ms	(-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1)
82.0ms	(.f64 (.f64 i i) (*.f64 i i))
82.0ms	(/.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))
82.0ms	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	61
1	255	48
2	3542	48
3	4998	48
0	0	0
1	0	0

simplify111.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

602×	`distribute-rgt-neg-in_binary64`
550×	`distribute-lft-neg-in_binary64`
485×	`associate-l_binary64`
444×	`fma-neg_binary64`
414×	`unswap-sqr_binary64`

Counts

209 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	408
1	110	406
2	292	402
3	864	402
4	2624	402
5	4683	402
6	4968	402
7	4932	402

prune192.0ms (5.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	183	3	186

Error

Counts

186 → 3

Alt Table

Status	Error	Program
✓	46.5b	(/.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))
✓	30.5b	(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)))))
✓	17.5b	(sqrt.f64 (/.f64 1/16 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2)))

Compiler

Compiled 4316 to 2921 computations (32.3% saved)

regimes534.0ms (15.8%)

Accuracy

Total 0.3b remaining (98.5%)

Threshold costs 0.3b (98.5%)

Counts

203 → 1

Compiler

Compiled 7282 to 5633 computations (22.6% 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

end63.0ms (1.9%)

Compiler: Compiled 77 to 57 computations (26% saved)

Details

analyze13.0ms (0.4%)

sample1.4s (41.7%)

simplify57.0ms (1.7%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series5.0ms (0.1%)

rewrite51.0ms (1.5%)

simplify94.0ms (2.8%)

prune70.0ms (2.1%)

localize7.0ms (0.2%)

series8.0ms (0.2%)

rewrite58.0ms (1.7%)

simplify61.0ms (1.8%)

prune125.0ms (3.7%)

localize11.0ms (0.3%)

series11.0ms (0.3%)

rewrite85.0ms (2.5%)

simplify189.0ms (5.6%)

prune110.0ms (3.2%)

localize10.0ms (0.3%)

series13.0ms (0.4%)

rewrite85.0ms (2.5%)

simplify111.0ms (3.3%)

prune192.0ms (5.7%)

regimes534.0ms (15.8%)

simplify2.0ms (0.1%)

end63.0ms (1.9%)

Profiling