Details

analyze5.0ms (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
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample916.0ms (41.9%)

Results

850.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify44.0ms (2%)

Algorithm

1×	egg-herbie

Rules

972×	`fma-def_binary64`
722×	`fma-neg_binary64`
154×	`cancel-sign-sub-inv_binary64`
107×	`distribute-rgt-in_binary64`
80×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	33	14
2	76	12
3	182	12
4	377	9
5	542	9
6	869	9
7	1535	9
8	2446	9
9	2827	9
10	2939	9
11	3065	9
12	3071	9
13	3071	9

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	0.2b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

Compiler

Compiled 65 to 50 computations (23.1% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 9 -12)
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

series5.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(fma.f64 x 9 -12)
2.0ms	(fma.f64 x (fma.f64 x 9 -12) 3)

rewrite39.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

568×	`log1p-expm1-u_binary64`
568×	`expm1-log1p-u_binary64`
253×	`unpow-prod-down_binary64`
243×	`log-prod_binary64`
166×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	142	14
2	1500	14

Stop Event

1×	node limit

Counts

2 → 66

Calls

2 calls:

38.0ms	(fma.f64 x 9 -12)
38.0ms	(fma.f64 x (fma.f64 x 9 -12) 3)

simplify37.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-neg_binary64`
466×	`cancel-sign-sub-inv_binary64`
418×	`distribute-rgt-neg-in_binary64`
413×	`fma-def_binary64`
296×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	198
1	38	182
2	69	156
3	141	144
4	380	144
5	1208	144
6	2780	144
7	4663	144

Stop Event

1×	node limit

Counts

90 → 80

prune60.0ms (2.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	78	4	82

Error

0.0b

Counts

82 → 4

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
	0.8b	(pow.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) 2)
	0.5b	(*.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) 2))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

Compiler

Compiled 1100 to 883 computations (19.7% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.2b	(*.f64 9 (pow.f64 x 2))

series5.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

3.0ms	(*.f64 9 (pow.f64 x 2))
2.0ms	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

rewrite58.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

494×	`log-prod_binary64`
395×	`fma-def_binary64`
203×	`expm1-udef_binary64`
203×	`log1p-udef_binary64`
193×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	250	21
2	3132	19

Stop Event

1×	node limit

Counts

2 → 148

Calls

2 calls:

56.0ms	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
56.0ms	(*.f64 9 (pow.f64 x 2))

simplify32.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-def_binary64`
757×	`fma-neg_binary64`
415×	`distribute-rgt-neg-in_binary64`
350×	`cancel-sign-sub-inv_binary64`
293×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	48
1	27	44
2	52	40
3	121	36
4	331	36
5	1109	36
6	2423	36
7	4614	36

Stop Event

1×	node limit

Counts

154 → 155

prune133.0ms (6.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	155	4	159

Error

Counts

159 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
	11.3b	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))
▶	0.2b	(-.f64 (+.f64 3 (pow.f64 (.f64 x 3) 2)) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

Compiler

Compiled 2960 to 2017 computations (31.9% saved)

localize12.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 3 (pow.f64 (.f64 x 3) 2)) (.f64 12 x))
✓	0.4b	(pow.f64 (*.f64 x 3) 2)

series5.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(pow.f64 (*.f64 x 3) 2)
2.0ms	(-.f64 (+.f64 3 (pow.f64 (.f64 x 3) 2)) (.f64 12 x))

rewrite61.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

485×	`log-prod_binary64`
405×	`fma-def_binary64`
193×	`fma-neg_binary64`
193×	`expm1-udef_binary64`
193×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	234	21
2	3013	19

Stop Event

1×	node limit

Counts

2 → 167

Calls

2 calls:

58.0ms	(-.f64 (+.f64 3 (pow.f64 (.f64 x 3) 2)) (.f64 12 x))
58.0ms	(pow.f64 (*.f64 x 3) 2)

simplify40.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-neg_binary64`
462×	`cancel-sign-sub-inv_binary64`
417×	`distribute-rgt-neg-in_binary64`
416×	`fma-def_binary64`
294×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	228
1	33	212
2	64	196
3	153	174
4	404	174
5	1226	174
6	2800	174
7	4662	174

Stop Event

1×	node limit

Counts

191 → 175

prune178.0ms (8.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	175	4	179

Error

Counts

179 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
▶	11.3b	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))
✓	0.2b	(-.f64 (+.f64 3 (pow.f64 (.f64 x 3) 2)) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

Compiler

Compiled 3285 to 2288 computations (30.4% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))
✓	0.1b	(*.f64 (pow.f64 x 4) 81)
✓	19.1b	(sqrt.f64 (*.f64 (pow.f64 x 4) 81))

series7.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(*.f64 (pow.f64 x 4) 81)
2.0ms	(sqrt.f64 (*.f64 (pow.f64 x 4) 81))
2.0ms	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))

rewrite64.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

440×	`fma-def_binary64`
239×	`fma-neg_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
172×	`egg-rr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	276	28
2	3443	26

Stop Event

1×	node limit

Counts

3 → 172

Calls

3 calls:

61.0ms	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))
61.0ms	(*.f64 (pow.f64 x 4) 81)
61.0ms	(sqrt.f64 (*.f64 (pow.f64 x 4) 81))

simplify36.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-neg_binary64`
474×	`associate-l_binary64`
463×	`cancel-sign-sub-inv_binary64`
405×	`fma-def_binary64`
342×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	312
1	40	296
2	80	280
3	198	258
4	572	258
5	2046	258
6	4175	258

Stop Event

1×	node limit

Counts

208 → 181

prune161.0ms (7.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	181	4	185

Error

Counts

185 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	11.3b	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))
✓	0.2b	(-.f64 (+.f64 3 (pow.f64 (.f64 x 3) 2)) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

Compiler

Compiled 3299 to 2312 computations (29.9% saved)

regimes198.0ms (9%)

Accuracy

Total 0.1b remaining (87.5%)

Threshold costs 0.1b (87.5%)

Counts

48 → 1

Compiler

Compiled 2176 to 1645 computations (24.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11

Stop Event

1×

saturated

end64.0ms (2.9%)

Compiler: Compiled 63 to 51 computations (19% saved)

Details

analyze5.0ms (0.2%)

sample916.0ms (41.9%)

simplify44.0ms (2%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series5.0ms (0.2%)

rewrite39.0ms (1.8%)

simplify37.0ms (1.7%)

prune60.0ms (2.7%)

localize6.0ms (0.3%)

series5.0ms (0.2%)

rewrite58.0ms (2.7%)

simplify32.0ms (1.5%)

prune133.0ms (6.1%)

localize12.0ms (0.6%)

series5.0ms (0.2%)

rewrite61.0ms (2.8%)

simplify40.0ms (1.8%)

prune178.0ms (8.1%)

localize8.0ms (0.4%)

series7.0ms (0.3%)

rewrite64.0ms (2.9%)

simplify36.0ms (1.6%)

prune161.0ms (7.4%)

regimes198.0ms (9%)

simplify2.0ms (0.1%)

end64.0ms (2.9%)

Profiling