Details

analyze497.0ms (17.7%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
37.4%	62.4%	0.1%	8
40.6%	56.9%	2.5%	9
45.2%	50.7%	4%	10
57.7%	33.5%	8.7%	11
59.7%	29.4%	11%	12
62%	25%	13%	13
68.3%	17.4%	14.4%	14

Compiler

Compiled 17 to 12 computations (29.4% saved)

sample1.1s (38.6%)

Results

989.0ms	8220×	body	128	valid
75.0ms	681×	body	128	invalid
5.0ms	15×	body	1024	valid
3.0ms	11×	body	512	valid
2.0ms	10×	body	256	valid

Compiler

Compiled 34 to 24 computations (29.4% saved)

preprocess28.0ms (1%)

Algorithm

2×	egg-herbie

Rules

358×	`fma-def_binary64`
173×	`associate-+l+_binary64`
120×	`associate-+r+_binary64`
94×	`distribute-lft-out_binary64`
66×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	68
1	62	56
2	171	40
3	490	40
4	892	40
5	1112	40
6	1142	40
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort d2 d3)

Compiler

Compiled 16 to 11 computations (31.3% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

114×	`fma-def_binary64`
59×	`associate-+l+_binary64`
40×	`associate-+r+_binary64`
34×	`distribute-lft-out_binary64`
27×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	21	14
2	51	10
3	159	10
4	305	10
5	408	10
6	420	10

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 d1 (+.f64 37 (+.f64 d2 d3)))
	0.0b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))

Compiler

Compiled 75 to 51 computations (32% saved)

localize21.0ms (0.7%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 37 (+.f64 d2 d3)))

series7.0ms (0.2%)

Counts

1 → 36

Calls

9 calls:

1.0ms	(*.f64 d1 (+.f64 37 (+.f64 d2 d3)))	d1	-inf
1.0ms	(*.f64 d1 (+.f64 37 (+.f64 d2 d3)))	d1	0
1.0ms	(*.f64 d1 (+.f64 37 (+.f64 d2 d3)))	d3	-inf
1.0ms	(*.f64 d1 (+.f64 37 (+.f64 d2 d3)))	d2	-inf
1.0ms	(*.f64 d1 (+.f64 37 (+.f64 d2 d3)))	d2	inf

rewrite43.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

680×	`prod-diff_binary64`
301×	`fma-def_binary64`
173×	`expm1-udef_binary64`
173×	`log1p-udef_binary64`
149×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	187	10
2	2743	10

Stop Event

1×	node limit

Counts

1 → 53

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

27×	`fma-def_binary64`
9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
4×	`associate-+r+_binary64`
4×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	330
1	49	330
2	69	330
3	81	330

Stop Event

1×

saturated

Counts

89 → 65

prune53.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	63	4	67

Error

Counts

67 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 37 (+.f64 d2 d3)))
▶	0.0b	(fma.f64 d1 (+.f64 37 d2) (*.f64 d1 d3))
	0.0b	(fma.f64 d1 37 (*.f64 d1 (+.f64 d2 d3)))
	30.3b	(pow.f64 (sqrt.f64 (*.f64 d1 (+.f64 37 (+.f64 d2 d3)))) 2)

Compiler

Compiled 850 to 397 computations (53.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 d1 (+.f64 37 d2) (*.f64 d1 d3))

series9.0ms (0.3%)

Counts

1 → 36

Calls

9 calls:

2.0ms	(fma.f64 d1 (+.f64 37 d2) (*.f64 d1 d3))	d1	0
1.0ms	(fma.f64 d1 (+.f64 37 d2) (*.f64 d1 d3))	d1	-inf
1.0ms	(fma.f64 d1 (+.f64 37 d2) (*.f64 d1 d3))	d1	inf
1.0ms	(fma.f64 d1 (+.f64 37 d2) (*.f64 d1 d3))	d3	-inf
1.0ms	(fma.f64 d1 (+.f64 37 d2) (*.f64 d1 d3))	d2	-inf

rewrite36.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

822×	`log1p-expm1-u_binary64`
822×	`expm1-log1p-u_binary64`
88×	`add-sqr-sqrt_binary64`
85×	`*-un-lft-identity_binary64`
85×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	170	10
2	2141	10

Stop Event

1×	node limit

Counts

1 → 24

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def_binary64`
9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
5×	`associate-+r+_binary64`
5×	`associate-+l+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	331
1	36	330
2	66	330
3	87	330
4	88	330

Stop Event

1×

saturated

Counts

60 → 35

prune21.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	35	4	39

Error

Counts

39 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 37 (+.f64 d2 d3)))
✓	0.0b	(fma.f64 d1 (+.f64 37 d2) (*.f64 d1 d3))
▶	0.0b	(fma.f64 d1 37 (*.f64 d1 (+.f64 d2 d3)))
	30.3b	(pow.f64 (sqrt.f64 (*.f64 d1 (+.f64 37 (+.f64 d2 d3)))) 2)

Compiler

Compiled 447 to 278 computations (37.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 d3))
✓	0.0b	(fma.f64 d1 37 (*.f64 d1 (+.f64 d2 d3)))

series13.0ms (0.5%)

Counts

2 → 60

Calls

18 calls:

1.0ms	(fma.f64 d1 37 (*.f64 d1 (+.f64 d2 d3)))	d1	-inf
1.0ms	(fma.f64 d1 37 (*.f64 d1 (+.f64 d2 d3)))	d1	inf
1.0ms	(fma.f64 d1 37 (*.f64 d1 (+.f64 d2 d3)))	d3	-inf
1.0ms	(fma.f64 d1 37 (*.f64 d1 (+.f64 d2 d3)))	d1	0
1.0ms	(fma.f64 d1 37 (*.f64 d1 (+.f64 d2 d3)))	d2	-inf

rewrite47.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

901×	`log1p-expm1-u_binary64`
901×	`expm1-log1p-u_binary64`
93×	`add-sqr-sqrt_binary64`
90×	`*-un-lft-identity_binary64`
90×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	176	17
2	2429	17

Stop Event

1×	node limit

Counts

2 → 51

simplify17.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def_binary64`
9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
5×	`associate-+r+_binary64`
5×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	499
1	38	480
2	67	480
3	86	480
4	87	480

Stop Event

1×

saturated

Counts

111 → 64

prune34.0ms (1.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	64	4	68

Error

Counts

68 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 37 (+.f64 d2 d3)))
✓	0.0b	(fma.f64 d1 (+.f64 37 d2) (*.f64 d1 d3))
✓	0.0b	(fma.f64 d1 37 (*.f64 d1 (+.f64 d2 d3)))
▶	30.3b	(pow.f64 (sqrt.f64 (*.f64 d1 (+.f64 37 (+.f64 d2 d3)))) 2)

Compiler

Compiled 819 to 399 computations (51.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 d1 (+.f64 37 (+.f64 d2 d3)))
✓	0.1b	(sqrt.f64 (*.f64 d1 (+.f64 37 (+.f64 d2 d3))))
✓	0.3b	(pow.f64 (sqrt.f64 (*.f64 d1 (+.f64 37 (+.f64 d2 d3)))) 2)

series458.0ms (16.3%)

Counts

2 → 16

Calls

18 calls:

81.0ms	(pow.f64 (sqrt.f64 (*.f64 d1 (+.f64 37 (+.f64 d2 d3)))) 2)	d1	0
80.0ms	(pow.f64 (sqrt.f64 (*.f64 d1 (+.f64 37 (+.f64 d2 d3)))) 2)	d1	-inf
66.0ms	(pow.f64 (sqrt.f64 (*.f64 d1 (+.f64 37 (+.f64 d2 d3)))) 2)	d1	inf
28.0ms	(sqrt.f64 (*.f64 d1 (+.f64 37 (+.f64 d2 d3))))	d1	inf
28.0ms	(sqrt.f64 (*.f64 d1 (+.f64 37 (+.f64 d2 d3))))	d1	0

rewrite63.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

680×	`prod-diff_binary64`
201×	`expm1-udef_binary64`
201×	`log1p-udef_binary64`
119×	`add-sqr-sqrt_binary64`
114×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	253	22
2	3186	22

Stop Event

1×	node limit

Counts

2 → 70

simplify37.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

483×	`fma-neg_binary64`
345×	`fma-def_binary64`
272×	`distribute-lft-neg-in_binary64`
270×	`distribute-rgt-neg-in_binary64`
247×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	532
1	295	516
2	903	491
3	3638	479

Stop Event

1×	node limit

Counts

86 → 93

prune123.0ms (4.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	158	4	162

Error

Counts

162 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 37 (+.f64 d2 d3)))
✓	0.0b	(fma.f64 d1 (+.f64 37 d2) (*.f64 d1 d3))
✓	0.0b	(fma.f64 d1 37 (*.f64 d1 (+.f64 d2 d3)))
✓	30.3b	(pow.f64 (sqrt.f64 (*.f64 d1 (+.f64 37 (+.f64 d2 d3)))) 2)

Compiler

Compiled 2699 to 1622 computations (39.9% saved)

regimes104.0ms (3.7%)

Accuracy

Total 0.0b remaining (88.7%)

Threshold costs 0.0b (88.7%)

Counts

22 → 1

Compiler

Compiled 1322 to 919 computations (30.5% 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

end57.0ms (2%)

Stop Event

1×

done

Remove

(sort d2 d3)

Compiler

Compiled 89 to 59 computations (33.7% saved)

Details

analyze497.0ms (17.7%)

sample1.1s (38.6%)

preprocess28.0ms (1%)

simplify9.0ms (0.3%)

prune3.0ms (0.1%)

localize21.0ms (0.7%)

series7.0ms (0.2%)

rewrite43.0ms (1.5%)

simplify12.0ms (0.4%)

prune53.0ms (1.9%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite36.0ms (1.3%)

simplify14.0ms (0.5%)

prune21.0ms (0.7%)

localize6.0ms (0.2%)

series13.0ms (0.5%)

rewrite47.0ms (1.7%)

simplify17.0ms (0.6%)

prune34.0ms (1.2%)

localize6.0ms (0.2%)

series458.0ms (16.3%)

rewrite63.0ms (2.2%)

simplify37.0ms (1.3%)

prune123.0ms (4.4%)

regimes104.0ms (3.7%)

simplify2.0ms (0.1%)

end57.0ms (2%)

Profiling