Details

analyze402.0ms (14.7%)

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%	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 (36.8%)

Symmetry

(sort d2 d3)

Results

766.0ms	7732×	body	128	valid
73.0ms	654×	body	128	invalid
60.0ms	181×	body	1024	valid
51.0ms	214×	body	512	valid
20.0ms	129×	body	256	valid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	10
2	44	10
3	64	10
4	66	10
5	67	10
6	67	10

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 41 to 27 computations (34.1% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.3%)

Counts

1 → 28

Calls

1 calls:

7.0ms

(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

rewrite105.0ms (3.8%)

Algorithm

2×	batch-egg-rewrite

Rules

684×	`prod-diff_binary64`
527×	`fma-udef_binary64`
301×	`fma-def_binary64`
202×	`fma-neg_binary64`
172×	`expm1-udef_binary64`

Counts

1 → 55

Calls

1 calls:

104.0ms

(*.f64 d1 (+.f64 3 (+.f64 d2 d3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	186	10
2	2498	10
3	4842	10
4	4783	10
5	4988	10
0	0	0
1	0	0

simplify13.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

83 → 64

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	250
1	36	250
2	57	250
3	66	250
4	67	250
5	67	250

prune38.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	4	65

Error

Counts

65 → 4

Alt Table

Status	Error	Program
	23.4b	(/.f64 (*.f64 (-.f64 9 (pow.f64 (+.f64 d2 d3) 2)) d1) (-.f64 3 (+.f64 d2 d3)))
	0.4b	(fma.f64 (.f64 (cbrt.f64 (.f64 d1 3)) (cbrt.f64 (.f64 d1 3))) (cbrt.f64 (.f64 d1 3)) (*.f64 d1 (+.f64 d2 d3)))
	0.0b	(fma.f64 d1 (+.f64 3 d2) (*.f64 d1 d3))
▶	0.0b	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))

Compiler

Compiled 894 to 420 computations (53% 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 3 (*.f64 d1 (+.f64 d2 d3)))

series14.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

8.0ms	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))
6.0ms	(*.f64 d1 (+.f64 d2 d3))

rewrite50.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

892×	`expm1-log1p-u_binary64`
813×	`prod-diff_binary64`
90×	`add-sqr-sqrt_binary64`
86×	`log1p-expm1-u_binary64`
84×	`add-log-exp_binary64`

Counts

2 → 52

Calls

2 calls:

49.0ms	(*.f64 d1 (+.f64 d2 d3))
49.0ms	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	175	17
2	2205	17
3	5394	17
0	0	0
1	0	0

simplify20.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

112 → 62

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	499
1	40	480
2	61	480
3	67	480
4	68	480
5	67	480

prune35.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	62	4	66

Error

Counts

66 → 4

Alt Table

Status	Error	Program
	23.4b	(/.f64 (*.f64 (-.f64 9 (pow.f64 (+.f64 d2 d3) 2)) d1) (-.f64 3 (+.f64 d2 d3)))
	0.4b	(fma.f64 (.f64 (cbrt.f64 (.f64 d1 3)) (cbrt.f64 (.f64 d1 3))) (cbrt.f64 (.f64 d1 3)) (*.f64 d1 (+.f64 d2 d3)))
▶	0.0b	(fma.f64 d1 (+.f64 3 d2) (*.f64 d1 d3))
✓	0.0b	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))

Compiler

Compiled 860 to 426 computations (50.5% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(fma.f64 d1 (+.f64 3 d2) (*.f64 d1 d3))

rewrite41.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

813×	`log1p-expm1-u_binary64`
813×	`expm1-log1p-u_binary64`
228×	`prod-diff_binary64`
86×	`add-sqr-sqrt_binary64`
80×	`add-log-exp_binary64`

Counts

1 → 24

Calls

1 calls:

40.0ms

(fma.f64 d1 (+.f64 3 d2) (*.f64 d1 d3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	169	10
2	2043	10
3	5380	10
0	0	0
1	0	0

simplify16.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Counts

60 → 34

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	331
1	38	330
2	59	330
3	67	330
4	68	330
5	67	330

prune20.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	34	4	38

Error

Counts

38 → 4

Alt Table

Status	Error	Program
	23.4b	(/.f64 (*.f64 (-.f64 9 (pow.f64 (+.f64 d2 d3) 2)) d1) (-.f64 3 (+.f64 d2 d3)))
▶	0.4b	(fma.f64 (.f64 (cbrt.f64 (.f64 d1 3)) (cbrt.f64 (.f64 d1 3))) (cbrt.f64 (.f64 d1 3)) (*.f64 d1 (+.f64 d2 d3)))
✓	0.0b	(fma.f64 d1 (+.f64 3 d2) (*.f64 d1 d3))
✓	0.0b	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))

Compiler

Compiled 473 to 296 computations (37.4% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 d1 (+.f64 d2 d3))
✓	0.1b	(fma.f64 (.f64 (cbrt.f64 (.f64 d1 3)) (cbrt.f64 (.f64 d1 3))) (cbrt.f64 (.f64 d1 3)) (*.f64 d1 (+.f64 d2 d3)))
✓	0.5b	(.f64 (cbrt.f64 (.f64 d1 3)) (cbrt.f64 (*.f64 d1 3)))
✓	0.6b	(cbrt.f64 (*.f64 d1 3))

series311.0ms (11.4%)

Counts

3 → 60

Calls

3 calls:

230.0ms	(fma.f64 (.f64 (cbrt.f64 (.f64 d1 3)) (cbrt.f64 (.f64 d1 3))) (cbrt.f64 (.f64 d1 3)) (*.f64 d1 (+.f64 d2 d3)))
44.0ms	(.f64 (cbrt.f64 (.f64 d1 3)) (cbrt.f64 (*.f64 d1 3)))
37.0ms	(cbrt.f64 (*.f64 d1 3))

rewrite57.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

544×	`log-prod_binary64`
311×	`fma-def_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
179×	`log-pow_binary64`

Counts

3 → 81

Calls

3 calls:

56.0ms	(fma.f64 (.f64 (cbrt.f64 (.f64 d1 3)) (cbrt.f64 (.f64 d1 3))) (cbrt.f64 (.f64 d1 3)) (*.f64 d1 (+.f64 d2 d3)))
56.0ms	(.f64 (cbrt.f64 (.f64 d1 3)) (cbrt.f64 (*.f64 d1 3)))
56.0ms	(cbrt.f64 (*.f64 d1 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	233	25
2	2779	25
3	5078	25
0	0	0
1	0	0

simplify137.0ms (5%)

Algorithm

1×	egg-herbie

Rules

980×	`fma-def_binary64`
776×	`unswap-sqr_binary64`
662×	`sqr-pow_binary64`
474×	`*-commutative_binary64`
322×	`associate-l_binary64`

Counts

141 → 100

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	645
1	75	590
2	149	590
3	354	590
4	1062	590
5	1797	590
6	1997	590
7	2255	590
8	2629	590
9	3025	590
10	3521	590
11	3962	590
12	4583	590
13	4856	590
14	4777	590

prune130.0ms (4.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	192	4	196

Error

Counts

196 → 4

Alt Table

Status	Error	Program
	23.4b	(/.f64 (*.f64 (-.f64 9 (pow.f64 (+.f64 d2 d3) 2)) d1) (-.f64 3 (+.f64 d2 d3)))
✓	0.4b	(fma.f64 (.f64 (cbrt.f64 (.f64 d1 3)) (cbrt.f64 (.f64 d1 3))) (cbrt.f64 (.f64 d1 3)) (*.f64 d1 (+.f64 d2 d3)))
✓	0.0b	(fma.f64 d1 (+.f64 3 d2) (*.f64 d1 d3))
✓	0.0b	(fma.f64 d1 3 (*.f64 d1 (+.f64 d2 d3)))

Compiler

Compiled 3933 to 2414 computations (38.6% saved)

regimes158.0ms (5.8%)

Accuracy

Total 0.0b remaining (82.2%)

Threshold costs 0.0b (82.2%)

Counts

43 → 1

Compiler

Compiled 2292 to 1636 computations (28.6% 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
2	10	11

end127.0ms (4.6%)

Remove: (sort d2 d3)
Compiler: Compiled 106 to 70 computations (34% saved)

Details

analyze402.0ms (14.7%)

sample1.0s (36.8%)

simplify7.0ms (0.3%)

prune4.0ms (0.1%)

localize4.0ms (0.2%)

series7.0ms (0.3%)

rewrite105.0ms (3.8%)

simplify13.0ms (0.5%)

prune38.0ms (1.4%)

localize6.0ms (0.2%)

series14.0ms (0.5%)

rewrite50.0ms (1.8%)

simplify20.0ms (0.7%)

prune35.0ms (1.3%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite41.0ms (1.5%)

simplify16.0ms (0.6%)

prune20.0ms (0.7%)

localize11.0ms (0.4%)

series311.0ms (11.4%)

rewrite57.0ms (2.1%)

simplify137.0ms (5%)

prune130.0ms (4.8%)

regimes158.0ms (5.8%)

simplify2.0ms (0.1%)

end127.0ms (4.6%)

Profiling