Details

analyze428.0ms (13.5%)

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%	57.7%	1.7%	9
45.2%	51.1%	3.7%	10
57.7%	33.5%	8.7%	11
59.7%	29.4%	10.9%	12
62%	25%	13%	13
68.3%	17.4%	14.4%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.0s (32%)

Results

776.0ms	7763×	body	128	valid
95.0ms	674×	body	128	invalid
56.0ms	159×	body	1024	valid
51.0ms	211×	body	512	valid
22.0ms	123×	body	256	valid

Compiler

Compiled 30 to 20 computations (33.3% saved)

preprocess24.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

75×	`fma-def_binary64`
22×	`+-commutative_binary64`
22×	`*-commutative_binary64`
20×	`distribute-lft-out_binary64`
15×	`associate-+l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	52
1	58	40
2	149	40
3	213	40
4	224	40
5	226	40
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort d2 d3)

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
7×	`distribute-lft-out_binary64`
6×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	10
2	46	10
3	74	10
4	85	10
5	86	10

Stop Event

1×

saturated

Counts

1 → 2

prune8.0ms (0.3%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	0.1b	(+.f64 (+.f64 (.f64 d1 3) (.f64 d1 d2)) (*.f64 d1 d3))

Compiler

Compiled 69 to 45 computations (34.8% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

series7.0ms (0.2%)

Counts

1 → 28

Calls

9 calls:

1.0ms	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))	d1	-inf
1.0ms	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))	d3	inf
1.0ms	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))	d3	-inf
1.0ms	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))	d2	-inf
1.0ms	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))	d2	inf

rewrite42.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	186	10
2	2726	10

Stop Event

1×	node limit

Counts

1 → 53

simplify13.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
8×	`+-commutative_binary64`
7×	`*-commutative_binary64`
6×	`distribute-rgt-in_binary64`
5×	`associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	250
1	44	250
2	66	250
3	82	250
4	83	250

Stop Event

1×

saturated

Counts

81 → 62

prune53.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	58	4	62
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	59	5	64

Error

0.0b

Counts

64 → 5

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	31.3b	(fma.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) 3) (.f64 d1 (+.f64 d2 d3)))
▶	0.0b	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))
	30.3b	(pow.f64 (sqrt.f64 (*.f64 d1 (+.f64 3 (+.f64 d2 d3)))) 2)
	32.2b	(/.f64 (*.f64 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3)) d1) (fma.f64 (+.f64 d2 d3) (-.f64 (+.f64 d2 d3) 3) 9))

Compiler

Compiled 885 to 420 computations (52.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 d3))
✓	0.1b	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))

series19.0ms (0.6%)

Counts

2 → 60

Calls

18 calls:

5.0ms	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))	d2	inf
1.0ms	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))	d1	-inf
1.0ms	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))	d1	inf
1.0ms	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))	d2	-inf
1.0ms	(*.f64 d1 (+.f64 d2 d3))	d1	-inf

rewrite44.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

892×	`log1p-expm1-u_binary64`
892×	`expm1-log1p-u_binary64`
92×	`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	175	17
2	2403	17

Stop Event

1×	node limit

Counts

2 → 51

simplify17.0ms (0.5%)

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	43	480
2	73	480
3	88	480
4	89	480

Stop Event

1×

saturated

Counts

111 → 62

prune41.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	62	5	67

Error

0.0b

Counts

67 → 5

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	31.3b	(fma.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) 3) (.f64 d1 (+.f64 d2 d3)))
✓	0.0b	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))
▶	30.3b	(pow.f64 (sqrt.f64 (*.f64 d1 (+.f64 3 (+.f64 d2 d3)))) 2)
	32.2b	(/.f64 (*.f64 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3)) d1) (fma.f64 (+.f64 d2 d3) (-.f64 (+.f64 d2 d3) 3) 9))

Compiler

Compiled 870 to 427 computations (50.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
✓	0.1b	(sqrt.f64 (*.f64 d1 (+.f64 3 (+.f64 d2 d3))))
✓	0.3b	(pow.f64 (sqrt.f64 (*.f64 d1 (+.f64 3 (+.f64 d2 d3)))) 2)

series531.0ms (16.8%)

Counts

2 → 16

Calls

18 calls:

123.0ms	(pow.f64 (sqrt.f64 (*.f64 d1 (+.f64 3 (+.f64 d2 d3)))) 2)	d1	inf
89.0ms	(pow.f64 (sqrt.f64 (*.f64 d1 (+.f64 3 (+.f64 d2 d3)))) 2)	d1	0
73.0ms	(pow.f64 (sqrt.f64 (*.f64 d1 (+.f64 3 (+.f64 d2 d3)))) 2)	d1	-inf
30.0ms	(sqrt.f64 (*.f64 d1 (+.f64 3 (+.f64 d2 d3))))	d1	inf
29.0ms	(pow.f64 (sqrt.f64 (*.f64 d1 (+.f64 3 (+.f64 d2 d3)))) 2)	d3	inf

rewrite56.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

680×	`prod-diff_binary64`
198×	`expm1-udef_binary64`
198×	`log1p-udef_binary64`
118×	`add-sqr-sqrt_binary64`
114×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	252	22
2	3165	22

Stop Event

1×	node limit

Counts

2 → 70

simplify38.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

463×	`fma-neg_binary64`
357×	`fma-def_binary64`
272×	`distribute-lft-neg-in_binary64`
271×	`distribute-rgt-neg-in_binary64`
250×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	526
1	307	514
2	936	491
3	3720	479

Stop Event

1×	node limit

Counts

86 → 93

prune92.0ms (2.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	155	5	160

Error

Counts

160 → 5

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	31.3b	(fma.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) 3) (.f64 d1 (+.f64 d2 d3)))
✓	0.0b	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))
▶	24.6b	(.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))) (.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))) d1))
	32.2b	(/.f64 (*.f64 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3)) d1) (fma.f64 (+.f64 d2 d3) (-.f64 (+.f64 d2 d3) 3) 9))

Compiler

Compiled 2759 to 1656 computations (40% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))) d1)
✓	0.2b	(.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))) (.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))) d1))

series47.0ms (1.5%)

Counts

2 → 56

Calls

18 calls:

6.0ms	(*.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))) d1)	d2	-inf
6.0ms	(*.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))) d1)	d2	inf
6.0ms	(*.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))) d1)	d3	-inf
6.0ms	(*.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))) d1)	d3	inf
4.0ms	(*.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))) d1)	d1	inf

rewrite47.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

543×	`prod-diff_binary64`
280×	`fma-def_binary64`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`
143×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	221	22
2	3006	22

Stop Event

1×	node limit

Counts

2 → 33

simplify33.0ms (1%)

Algorithm

1×	egg-herbie

Rules

450×	`cancel-sign-sub-inv_binary64`
259×	`fma-neg_binary64`
258×	`associate-r_binary64`
250×	`fma-def_binary64`
221×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	812
1	247	808
2	637	790
3	2236	774

Stop Event

1×	node limit

Counts

89 → 61

prune39.0ms (1.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	61	5	66

Error

Counts

66 → 5

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))
	31.3b	(fma.f64 (sqrt.f64 d1) (.f64 (sqrt.f64 d1) 3) (.f64 d1 (+.f64 d2 d3)))
✓	0.0b	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))
✓	24.6b	(.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))) (.f64 (sqrt.f64 (+.f64 3 (+.f64 d2 d3))) d1))
	32.2b	(/.f64 (*.f64 (+.f64 27 (pow.f64 (+.f64 d2 d3) 3)) d1) (fma.f64 (+.f64 d2 d3) (-.f64 (+.f64 d2 d3) 3) 9))

Compiler

Compiled 1200 to 807 computations (32.8% saved)

regimes334.0ms (10.5%)

Accuracy

Total 0.0b remaining (83.3%)

Threshold costs 0.0b (83.3%)

Counts

81 → 1

Compiler

Compiled 4636 to 3300 computations (28.8% 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

end211.0ms (6.7%)

Stop Event

1×

fuel

Compiler

Compiled 121 to 77 computations (36.4% saved)

Details

analyze428.0ms (13.5%)

sample1.0s (32%)

preprocess24.0ms (0.8%)

simplify7.0ms (0.2%)

prune8.0ms (0.3%)

localize4.0ms (0.1%)

series7.0ms (0.2%)

rewrite42.0ms (1.3%)

simplify13.0ms (0.4%)

prune53.0ms (1.7%)

localize5.0ms (0.2%)

series19.0ms (0.6%)

rewrite44.0ms (1.4%)

simplify17.0ms (0.5%)

prune41.0ms (1.3%)

localize6.0ms (0.2%)

series531.0ms (16.8%)

rewrite56.0ms (1.8%)

simplify38.0ms (1.2%)

prune92.0ms (2.9%)

localize6.0ms (0.2%)

series47.0ms (1.5%)

rewrite47.0ms (1.5%)

simplify33.0ms (1%)

prune39.0ms (1.2%)

regimes334.0ms (10.5%)

simplify2.0ms (0.1%)

end211.0ms (6.7%)

Profiling