Details

analyze100.0ms (6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	50%	12.6%	6
43.7%	40.6%	15.7%	7
56.2%	23.4%	20.4%	8
57.8%	21.1%	21.2%	9
64%	12.5%	23.5%	10
64.8%	10.7%	24.5%	11
67.9%	6.4%	25.7%	12
68.3%	5.4%	26.3%	13
69.9%	3.3%	26.9%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample814.0ms (48.3%)

Results

783.0ms	8256×	body	128	valid
14.0ms	143×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

preprocess18.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

30×	`fma-def_binary64`
17×	`*-commutative_binary64`
10×	`distribute-rgt-out_binary64`
8×	`associate-r_binary64`
8×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	38	20
2	77	20
3	130	20
4	134	20
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

17×	`fma-def_binary64`
13×	`*-commutative_binary64`
6×	`distribute-rgt-out_binary64`
5×	`associate-r_binary64`
5×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	20	10
2	43	10
3	74	10
4	78	10

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
▶	0.0b	(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))
	0.0b	(.f64 2 (.f64 x (+.f64 x y)))

Compiler

Compiled 58 to 37 computations (36.2% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))
✓	0.0b	(+.f64 (.f64 x x) (.f64 x y))

series15.0ms (0.9%)

Counts

2 → 48

Calls

12 calls:

3.0ms	(+.f64 (.f64 x x) (.f64 x y))	y	-inf
2.0ms	(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))	y	-inf
1.0ms	(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))	y	0
1.0ms	(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))	y	inf
1.0ms	(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))	x	-inf

rewrite47.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

864×	`log1p-expm1-u_binary64`
864×	`expm1-log1p-u_binary64`
89×	`add-sqr-sqrt_binary64`
85×	`add-cbrt-cube_binary64`
84×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	178	17
2	2419	17

Stop Event

1×	node limit

Counts

2 → 65

simplify83.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

599×	`sqr-pow_binary64`
386×	`cube-prod_binary64`
344×	`fma-def_binary64`
321×	`fabs-mul_binary64`
274×	`pow-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	408
1	25	372
2	53	372
3	114	372
4	265	372
5	731	372
6	1165	372
7	1653	372
8	1820	372
9	1956	372
10	2129	372
11	2378	372
12	2696	372
13	3070	372
14	3526	372
15	4104	372
16	4812	372

Stop Event

1×	node limit

Counts

113 → 76

prune47.0ms (2.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	75	3	78

Error

Counts

78 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))
▶	0.0b	(pow.f64 (.f64 (.f64 2 x) (+.f64 x y)) 1)
	11.5b	(.f64 2 (.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (+.f64 x y))))

Compiler

Compiled 1073 to 589 computations (45.1% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 2 x) (+.f64 x y))

series7.0ms (0.4%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(.f64 (.f64 2 x) (+.f64 x y))	y	-inf
1.0ms	(.f64 (.f64 2 x) (+.f64 x y))	y	inf
1.0ms	(.f64 (.f64 2 x) (+.f64 x y))	y	0
1.0ms	(.f64 (.f64 2 x) (+.f64 x y))	x	-inf
1.0ms	(.f64 (.f64 2 x) (+.f64 x y))	x	inf

rewrite39.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

820×	`expm1-log1p-u_binary64`
780×	`prod-diff_binary64`
81×	`add-sqr-sqrt_binary64`
78×	`log1p-expm1-u_binary64`
77×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	158	10
2	2231	10

Stop Event

1×	node limit

Counts

1 → 26

simplify80.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

599×	`sqr-pow_binary64`
386×	`cube-prod_binary64`
343×	`fma-def_binary64`
324×	`fabs-mul_binary64`
274×	`pow-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	276
1	23	222
2	50	222
3	108	222
4	257	222
5	745	222
6	1187	222
7	1675	222
8	1842	222
9	1978	222
10	2151	222
11	2398	222
12	2716	222
13	3090	222
14	3549	222
15	4129	222
16	4839	222

Stop Event

1×	node limit

Counts

50 → 32

prune25.0ms (1.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	32	3	35

Error

Counts

35 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))
✓	0.0b	(pow.f64 (.f64 (.f64 2 x) (+.f64 x y)) 1)
▶	11.5b	(.f64 2 (.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (+.f64 x y))))

Compiler

Compiled 522 to 337 computations (35.4% saved)

localize11.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 x) (+.f64 x y))
✓	0.3b	(.f64 (cbrt.f64 (.f64 x x)) (*.f64 (cbrt.f64 x) (+.f64 x y)))
✓	0.6b	(cbrt.f64 x)
✓	21.4b	(cbrt.f64 (*.f64 x x))

series100.0ms (5.9%)

Counts

4 → 36

Calls

18 calls:

28.0ms	(.f64 (cbrt.f64 (.f64 x x)) (*.f64 (cbrt.f64 x) (+.f64 x y)))	x	-inf
17.0ms	(*.f64 (cbrt.f64 x) (+.f64 x y))	x	-inf
12.0ms	(*.f64 (cbrt.f64 x) (+.f64 x y))	y	-inf
9.0ms	(cbrt.f64 x)	x	-inf
8.0ms	(*.f64 (cbrt.f64 x) (+.f64 x y))	y	inf

rewrite55.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

906×	`expm1-log1p-u_binary64`
814×	`prod-diff_binary64`
96×	`egg-rr`
95×	`associate-r_binary64`
93×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	193	25
2	2590	25

Stop Event

1×	node limit

Counts

4 → 96

simplify42.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1007×	`fma-neg_binary64`
656×	`fma-def_binary64`
343×	`cancel-sign-sub-inv_binary64`
313×	`unswap-sqr_binary64`
254×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	337
1	59	322
2	138	304
3	349	304
4	1183	304
5	2903	304
6	4902	304

Stop Event

1×	node limit

Counts

132 → 111

prune48.0ms (2.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	111	3	114

Error

Counts

114 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (+.f64 (.f64 x x) (*.f64 x y)))
✓	0.0b	(pow.f64 (.f64 (.f64 2 x) (+.f64 x y)) 1)
✓	11.5b	(.f64 2 (.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (+.f64 x y))))

Compiler

Compiled 1742 to 748 computations (57.1% saved)

regimes83.0ms (4.9%)

Accuracy

Total 0.0b remaining (71.6%)

Threshold costs 0.0b (71.6%)

Counts

24 → 1

Compiler

Compiled 1004 to 716 computations (28.7% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	14	10

Stop Event

1×

saturated

end47.0ms (2.8%)

Stop Event

1×

done

Compiler

Compiled 55 to 37 computations (32.7% saved)

Details

analyze100.0ms (6%)

sample814.0ms (48.3%)

preprocess18.0ms (1.1%)

simplify7.0ms (0.4%)

prune3.0ms (0.2%)

localize5.0ms (0.3%)

series15.0ms (0.9%)

rewrite47.0ms (2.8%)

simplify83.0ms (4.9%)

prune47.0ms (2.8%)

localize5.0ms (0.3%)

series7.0ms (0.4%)

rewrite39.0ms (2.3%)

simplify80.0ms (4.8%)

prune25.0ms (1.5%)

localize11.0ms (0.6%)

series100.0ms (5.9%)

rewrite55.0ms (3.3%)

simplify42.0ms (2.5%)

prune48.0ms (2.9%)

regimes83.0ms (4.9%)

simplify3.0ms (0.2%)

end47.0ms (2.8%)

Profiling