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)

sample1.1s (46.4%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 84 to 55 computations (34.5% saved)

simplify21.0ms (0.9%)

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

3.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.8b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
	45.5b	(/.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))

Compiler

Compiled 107 to 74 computations (30.8% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 4 (/.f64 i (pow.f64 i 3)))
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
✓	8.7b	(/.f64 i (pow.f64 i 3))

series7.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
2.0ms	(/.f64 i (pow.f64 i 3))
2.0ms	(-.f64 4 (/.f64 i (pow.f64 i 3)))

rewrite90.0ms (3.9%)

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	30
1	211	21
2	2654	21

Stop Event

1×	node limit

Counts

3 → 113

Calls

3 calls:

89.0ms	(-.f64 4 (/.f64 i (pow.f64 i 3)))
89.0ms	(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
89.0ms	(/.f64 i (pow.f64 i 3))

simplify38.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

453×	`associate-l_binary64`
438×	`fma-neg_binary64`
320×	`cancel-sign-sub-inv_binary64`
296×	`associate-r_binary64`
251×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	372
1	108	370
2	295	366
3	1091	366
4	4377	366

Stop Event

1×	node limit

Counts

149 → 135

prune131.0ms (5.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	134	3	137

Error

Counts

137 → 3

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
	45.5b	(/.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))
	32.0b	(neg.f64 (+.f64 (pow.f64 i 4) (*.f64 1/4 (pow.f64 i 2))))

Compiler

Compiled 1799 to 1454 computations (19.2% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 4 (/.f64 1 (pow.f64 i 2)))
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
✓	0.7b	(/.f64 1 (pow.f64 i 2))

series7.0ms (0.3%)

Counts

3 → 15

Calls

3 calls:

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

rewrite46.0ms (2%)

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	21
1	224	21
2	2581	21

Stop Event

1×	node limit

Counts

3 → 105

Calls

3 calls:

44.0ms	(-.f64 4 (/.f64 1 (pow.f64 i 2)))
44.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
44.0ms	(/.f64 1 (pow.f64 i 2))

simplify32.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

457×	`associate-l_binary64`
438×	`fma-neg_binary64`
320×	`cancel-sign-sub-inv_binary64`
298×	`associate-r_binary64`
238×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	198
1	105	196
2	288	192
3	1074	192
4	4370	192

Stop Event

1×	node limit

Counts

120 → 123

prune77.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	123	3	126

Error

Counts

126 → 3

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
	45.5b	(/.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))
▶	32.0b	(neg.f64 (+.f64 (pow.f64 i 4) (*.f64 1/4 (pow.f64 i 2))))

Compiler

Compiled 1559 to 1327 computations (14.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 i 4) (*.f64 1/4 (pow.f64 i 2)))
✓	0.2b	(*.f64 1/4 (pow.f64 i 2))

series6.0ms (0.3%)

Counts

2 → 3

Calls

2 calls:

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

rewrite40.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

909×	`prod-diff_binary64`
801×	`expm1-log1p-u_binary64`
89×	`log1p-expm1-u_binary64`
86×	`add-cbrt-cube_binary64`
85×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	197	18
2	2288	18

Stop Event

1×	node limit

Counts

2 → 52

Calls

2 calls:

39.0ms	(+.f64 (pow.f64 i 4) (*.f64 1/4 (pow.f64 i 2)))
39.0ms	(*.f64 1/4 (pow.f64 i 2))

simplify56.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

788×	`sqr-pow_binary64`
353×	`cube-prod_binary64`
342×	`unswap-sqr_binary64`
327×	`pow-sqr_binary64`
217×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	16	15
2	32	15
3	66	15
4	181	15
5	670	15
6	1331	15
7	1455	15
8	1624	15
9	1823	15
10	2094	15
11	2453	15
12	2904	15
13	3426	15
14	4054	15
15	4805	15

Stop Event

1×	node limit

Counts

55 → 55

prune48.0ms (2.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	55	3	58

Error

Counts

58 → 3

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
▶	45.5b	(/.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))
✓	32.0b	(neg.f64 (+.f64 (pow.f64 i 4) (*.f64 1/4 (pow.f64 i 2))))

Compiler

Compiled 872 to 604 computations (30.7% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 i i) (*.f64 i i))
✓	16.5b	(/.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))
✓	41.4b	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))

series8.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

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))

2.0ms

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

2.0ms

(*.f64 (*.f64 i i) (*.f64 i i))

rewrite72.0ms (3.1%)

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

Calls

3 calls:

67.0ms

(*.f64 (*.f64 i i) (*.f64 i i))

67.0ms

(/.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))

67.0ms

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

simplify37.0ms (1.6%)

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

prune116.0ms (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
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
✓	45.5b	(/.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))
✓	32.0b	(neg.f64 (+.f64 (pow.f64 i 4) (*.f64 1/4 (pow.f64 i 2))))

Compiler

Compiled 3137 to 2168 computations (30.9% saved)

regimes310.0ms (13.4%)

Accuracy

Total 0.3b remaining (98.6%)

Threshold costs 0.3b (98.6%)

Counts

138 → 1

Compiler

Compiled 4538 to 3531 computations (22.2% 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

end60.0ms (2.6%)

Compiler: Compiled 67 to 53 computations (20.9% saved)

Details

analyze8.0ms (0.3%)

sample1.1s (46.4%)

simplify21.0ms (0.9%)

prune4.0ms (0.2%)

localize5.0ms (0.2%)

series7.0ms (0.3%)

rewrite90.0ms (3.9%)

simplify38.0ms (1.6%)

prune131.0ms (5.7%)

localize5.0ms (0.2%)

series7.0ms (0.3%)

rewrite46.0ms (2%)

simplify32.0ms (1.4%)

prune77.0ms (3.3%)

localize6.0ms (0.2%)

series6.0ms (0.3%)

rewrite40.0ms (1.7%)

simplify56.0ms (2.4%)

prune48.0ms (2.1%)

localize8.0ms (0.3%)

series8.0ms (0.3%)

rewrite72.0ms (3.1%)

simplify37.0ms (1.6%)

prune116.0ms (5%)

regimes310.0ms (13.4%)

simplify2.0ms (0.1%)

end60.0ms (2.6%)

Profiling