Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
81.2%	18.7%	0%	5
90.6%	9.4%	0%	6
95.3%	4.7%	0%	7
97.6%	2.3%	0%	8
98.8%	1.2%	0%	9
99.4%	0.6%	0%	10
99.7%	0.3%	0%	11
99.8%	0.1%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample1.1s (43.2%)

Results

407.0ms	2027×	body	512	valid
403.0ms	4741×	body	128	valid
149.0ms	1037×	body	256	valid
122.0ms	451×	body	1024	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify10.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

12.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.7b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

Compiler

Compiled 39 to 31 computations (20.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	2.8b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

series5.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite59.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

896×	`expm1-log1p-u_binary64`
733×	`prod-diff_binary64`
137×	`egg-rr`
85×	`add-sqr-sqrt_binary64`
83×	`log1p-expm1-u_binary64`

Counts

2 → 137

Calls

2 calls:

56.0ms	(/.f64 1 (+.f64 x 1))
56.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	168	20
2	2226	20
3	5239	20
0	0	0
1	0	0

simplify75.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-neg_binary64`
429×	`cancel-sign-sub-inv_binary64`
405×	`associate-/r*_binary64`
338×	`div-sub_binary64`
334×	`sub-neg_binary64`

Counts

161 → 165

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	372
1	98	366
2	234	366
3	577	364
4	1646	363
5	4272	363
6	4983	363
7	4917	363

prune170.0ms (6.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	163	3	166

Error

0.3b

Counts

166 → 3

Alt Table

Status	Error	Program
✓	12.7b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
	51.0b	(.f64 (-.f64 (pow.f64 (+.f64 1 x) -3) (pow.f64 x -3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) -2) (+.f64 (pow.f64 x -2) (/.f64 1 (.f64 x (+.f64 1 x)))))))
▶	34.3b	(-.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 2)))

Compiler

Compiled 3447 to 2574 computations (25.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (pow.f64 x 3))
✓	0.4b	(/.f64 1 (pow.f64 x 2))
✓	6.0b	(-.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 2)))

series8.0ms (0.3%)

Counts

3 → 3

Calls

3 calls:

3.0ms	(-.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 2)))
2.0ms	(/.f64 1 (pow.f64 x 3))
2.0ms	(/.f64 1 (pow.f64 x 2))

rewrite111.0ms (4.3%)

Algorithm

2×	batch-egg-rewrite

Rules

768×	`prod-diff_binary64`
557×	`fma-udef_binary64`
282×	`fma-def_binary64`
217×	`fma-neg_binary64`
170×	`egg-rr`

Counts

3 → 170

Calls

3 calls:

108.0ms	(/.f64 1 (pow.f64 x 3))
108.0ms	(/.f64 1 (pow.f64 x 2))
108.0ms	(-.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	231	18
2	2434	18
3	4808	18
4	4690	18
5	5027	18
0	0	0
1	0	0

simplify136.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

959×	`sqr-pow_binary64`
561×	`cube-prod_binary64`
543×	`fabs-mul_binary64`
538×	`unswap-sqr_binary64`
499×	`associate-/l/_binary64`

Counts

173 → 173

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	22	21
2	40	21
3	81	21
4	176	21
5	634	21
6	1648	21
7	1659	21
8	1871	21
9	2106	21
10	2436	21
11	2548	21
12	2970	21
13	3444	21
14	3742	21
15	3955	21
16	4079	21
17	4125	21
18	4152	21
19	4811	21
20	4834	21

prune125.0ms (4.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	173	3	176

Error

Counts

176 → 3

Alt Table

Status	Error	Program
▶	34.0b	(-.f64 (pow.f64 x -3) (pow.f64 x -2))
✓	12.7b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
	51.0b	(.f64 (-.f64 (pow.f64 (+.f64 1 x) -3) (pow.f64 x -3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) -2) (+.f64 (pow.f64 x -2) (/.f64 1 (.f64 x (+.f64 1 x)))))))

Compiler

Compiled 2743 to 2106 computations (23.2% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.0b	(-.f64 (pow.f64 x -3) (pow.f64 x -2))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(-.f64 (pow.f64 x -3) (pow.f64 x -2))

rewrite65.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

725×	`log1p-expm1-u_binary64`
725×	`expm1-log1p-u_binary64`
567×	`prod-diff_binary64`
78×	`add-sqr-sqrt_binary64`
77×	`egg-rr`

Counts

1 → 77

Calls

1 calls:

63.0ms

(-.f64 (pow.f64 x -3) (pow.f64 x -2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	164	10
2	1828	10
3	5346	10
0	0	0
1	0	0

simplify61.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

538×	`unswap-sqr_binary64`
434×	`div-sub_binary64`
398×	`neg-mul-1_binary64`
365×	`fma-def_binary64`
340×	`times-frac_binary64`

Counts

89 → 82

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	165
1	26	165
2	48	165
3	102	165
4	220	165
5	806	165
6	2480	165
7	4305	165
8	5118	165

prune51.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	82	3	85

Error

Counts

85 → 3

Alt Table

Status	Error	Program
✓	34.0b	(-.f64 (pow.f64 x -3) (pow.f64 x -2))
✓	12.7b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
▶	51.0b	(.f64 (-.f64 (pow.f64 (+.f64 1 x) -3) (pow.f64 x -3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) -2) (+.f64 (pow.f64 x -2) (/.f64 1 (.f64 x (+.f64 1 x)))))))

Compiler

Compiled 1722 to 1209 computations (29.8% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (*.f64 x (+.f64 1 x)))
✓	0.4b	(/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) -2) (+.f64 (pow.f64 x -2) (/.f64 1 (*.f64 x (+.f64 1 x))))))
✓	2.8b	(-.f64 (pow.f64 (+.f64 1 x) -3) (pow.f64 x -3))
✓	37.5b	(.f64 (-.f64 (pow.f64 (+.f64 1 x) -3) (pow.f64 x -3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) -2) (+.f64 (pow.f64 x -2) (/.f64 1 (.f64 x (+.f64 1 x)))))))

series15.0ms (0.6%)

Counts

4 → 48

Calls

4 calls:

5.0ms	(/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) -2) (+.f64 (pow.f64 x -2) (/.f64 1 (*.f64 x (+.f64 1 x))))))
4.0ms	(.f64 (-.f64 (pow.f64 (+.f64 1 x) -3) (pow.f64 x -3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) -2) (+.f64 (pow.f64 x -2) (/.f64 1 (.f64 x (+.f64 1 x)))))))
3.0ms	(-.f64 (pow.f64 (+.f64 1 x) -3) (pow.f64 x -3))
2.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))

rewrite80.0ms (3.1%)

Algorithm

2×	batch-egg-rewrite

Rules

608×	`prod-diff_binary64`
199×	`log1p-expm1-u_binary64`
199×	`expm1-log1p-u_binary64`
194×	`add-sqr-sqrt_binary64`
184×	`add-cbrt-cube_binary64`

Counts

4 → 126

Calls

4 calls:

77.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))
77.0ms	(/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) -2) (+.f64 (pow.f64 x -2) (/.f64 1 (*.f64 x (+.f64 1 x))))))
77.0ms	(-.f64 (pow.f64 (+.f64 1 x) -3) (pow.f64 x -3))
77.0ms	(.f64 (-.f64 (pow.f64 (+.f64 1 x) -3) (pow.f64 x -3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) -2) (+.f64 (pow.f64 x -2) (/.f64 1 (.f64 x (+.f64 1 x)))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	91
1	411	91
2	4449	91
3	5543	91
0	0	0
1	0	0

simplify95.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

751×	`fma-def_binary64`
474×	`associate-l_binary64`
409×	`cancel-sign-sub-inv_binary64`
385×	`associate-/r*_binary64`
343×	`fma-neg_binary64`

Counts

174 → 186

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	779
1	227	747
2	607	747
3	1576	744
4	4370	744
5	4813	744
6	4953	744

prune172.0ms (6.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	186	3	189

Error

Counts

189 → 3

Alt Table

Status	Error	Program
✓	34.0b	(-.f64 (pow.f64 x -3) (pow.f64 x -2))
✓	12.7b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
✓	51.0b	(.f64 (-.f64 (pow.f64 (+.f64 1 x) -3) (pow.f64 x -3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) -2) (+.f64 (pow.f64 x -2) (/.f64 1 (.f64 x (+.f64 1 x)))))))

Compiler

Compiled 6286 to 4936 computations (21.5% saved)

regimes109.0ms (4.2%)

Accuracy

Total 0.2b remaining (62%)

Threshold costs 0.2b (62%)

Counts

36 → 3

Compiler

Compiled 1020 to 796 computations (22% saved)

bsearch1.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

17×	`distribute-rgt-neg-in_binary64`
16×	`sub-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
15×	`neg-sub0_binary64`
14×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	88
1	59	77
2	83	77
3	110	77
4	128	77
5	140	77
6	147	77
7	149	77
8	145	77

end76.0ms (3%)

Compiler: Compiled 154 to 120 computations (22.1% saved)

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13

Details

analyze6.0ms (0.2%)

sample1.1s (43.2%)

simplify10.0ms (0.4%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite59.0ms (2.3%)

simplify75.0ms (2.9%)

prune170.0ms (6.6%)

localize6.0ms (0.2%)

series8.0ms (0.3%)

rewrite111.0ms (4.3%)

simplify136.0ms (5.3%)

prune125.0ms (4.8%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite65.0ms (2.5%)

simplify61.0ms (2.3%)

prune51.0ms (2%)

localize13.0ms (0.5%)

series15.0ms (0.6%)

rewrite80.0ms (3.1%)

simplify95.0ms (3.7%)

prune172.0ms (6.7%)

regimes109.0ms (4.2%)

bsearch1.0ms (0%)

simplify6.0ms (0.2%)

end76.0ms (3%)

Profiling

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13