Details

analyze135.0ms (7.2%)

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
25%	62.4%	12.6%	6
25%	46.8%	28.2%	7
31.2%	35.9%	32.9%	8
39%	25%	36%	9
42.9%	18.7%	38.3%	10
47.2%	12.9%	39.9%	11
49.4%	9.6%	41.1%	12
51.6%	6.5%	41.9%	13
52.7%	4.8%	42.4%	14

Compiler

Compiled 16 to 10 computations (37.5% saved)

sample861.0ms (46.3%)

Symmetry

(sort x y)

Results

810.0ms	8256×	body	128	valid
17.0ms	191×	body	128	invalid

Compiler

Compiled 47 to 29 computations (38.3% saved)

simplify9.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

33×	`fma-def_binary64`
8×	`*-commutative_binary64`
7×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	19	14
2	45	12
3	68	12
4	70	12
5	70	12

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

Compiler

Compiled 76 to 42 computations (44.7% saved)

localize8.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

series46.0ms (2.5%)

Counts

2 → 48

Calls

2 calls:

40.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 x 2) y))
6.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))

rewrite11.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64`
4×	`sum-log_binary64`
4×	`fma-def_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

2 → 32

Calls

2 calls:

5.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))
4.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 x 2) y))

simplify80.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-neg_binary64`
565×	`associate-l_binary64`
455×	`associate-r_binary64`
449×	`fma-def_binary64`
360×	`unswap-sqr_binary64`

Counts

80 → 62

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	63	1146
1	222	922
2	730	836
3	3350	836
4	4931	836
5	5210	836

prune48.0ms (2.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	61	3	64

Error

Counts

64 → 3

Alt Table

Status	Error	Program
	0.0b	(+.f64 (fma.f64 x x (.f64 (.f64 x 2) y)) (*.f64 y y))
▶	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
	1.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (fma.f64 2 x y) (.f64 x x))) (cbrt.f64 (fma.f64 y (fma.f64 2 x y) (.f64 x x)))) (cbrt.f64 (fma.f64 y (fma.f64 2 x y) (*.f64 x x))))

Compiler

Compiled 1288 to 621 computations (51.8% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series18.0ms (0.9%)

Counts

3 → 18

Calls

3 calls:

6.0ms	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
6.0ms	(+.f64 (pow.f64 y 2) (pow.f64 x 2))
5.0ms	(.f64 2 (.f64 y x))

rewrite22.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`fma-def_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`

Counts

3 → 59

Calls

3 calls:

8.0ms	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
5.0ms	(+.f64 (pow.f64 y 2) (pow.f64 x 2))
4.0ms	(.f64 2 (.f64 y x))

simplify58.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-neg_binary64`
651×	`associate-l_binary64`
513×	`associate-r_binary64`
471×	`fma-def_binary64`
319×	`distribute-rgt-neg-in_binary64`

Counts

77 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	88	905
1	248	787
2	837	728
3	3406	728
4	5028	728

prune68.0ms (3.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	96	2	98

Error

Counts

98 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (.f64 2 (.f64 y x)) (fma.f64 y y (pow.f64 x 2)))
	0.0b	(+.f64 (fma.f64 x x (.f64 (.f64 x 2) y)) (*.f64 y y))

Compiler

Compiled 1826 to 1103 computations (39.6% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

series16.0ms (0.9%)

Counts

1 → 24

Calls

1 calls:

16.0ms

(+.f64 (*.f64 2 (*.f64 y x)) (fma.f64 y y (pow.f64 x 2)))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`+-commutative_binary64`
1×	`associate-+r+_binary64`
1×	`fma-udef_binary64`
1×	`flip-+_binary64`

Counts

1 → 15

Calls

1 calls:

4.0ms

(+.f64 (*.f64 2 (*.f64 y x)) (fma.f64 y y (pow.f64 x 2)))

simplify68.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

525×	`cancel-sign-sub-inv_binary64`
352×	`associate-l_binary64`
324×	`distribute-rgt-out_binary64`
304×	`associate-r_binary64`
304×	`fma-neg_binary64`

Counts

39 → 35

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	617
1	121	579
2	451	493
3	2265	493
4	4677	493
5	4957	493

prune38.0ms (2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	63	2	65

Error

Counts

65 → 2

Alt Table

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

Compiler

Compiled 1116 to 610 computations (45.3% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

series15.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(fma.f64 x x (.f64 (.f64 x 2) y))
6.0ms	(+.f64 (fma.f64 x x (.f64 (.f64 x 2) y)) (*.f64 y y))

rewrite3.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`fma-def_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 27

Calls

2 calls:

2.0ms	(+.f64 (fma.f64 x x (.f64 (.f64 x 2) y)) (*.f64 y y))
0.0ms	(fma.f64 x x (.f64 (.f64 x 2) y))

simplify99.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

550×	`associate-+l+_binary64`
523×	`associate-+r+_binary64`
400×	`unswap-sqr_binary64`
345×	`*-commutative_binary64`
254×	`distribute-rgt-neg-in_binary64`

Counts

75 → 55

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	1043
1	134	880
2	325	750
3	1344	750
4	3493	750
5	4922	750
6	4992	750
7	4819	750

prune31.0ms (1.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	55	2	57

Error

Counts

57 → 2

Alt Table

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

Compiler

Compiled 966 to 481 computations (50.2% saved)

regimes136.0ms (7.3%)

Accuracy

Total 0.0b remaining (48.1%)

Threshold costs 0.0b (48.1%)

Counts

33 → 1

Compiler

Compiled 1396 to 851 computations (39% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	9	15
2	9	15

end61.0ms (3.3%)

Remove: (sort x y)
Compiler: Compiled 80 to 49 computations (38.8% saved)

Details

analyze135.0ms (7.2%)

sample861.0ms (46.3%)

simplify9.0ms (0.5%)

prune3.0ms (0.2%)

localize8.0ms (0.5%)

series46.0ms (2.5%)

rewrite11.0ms (0.6%)

simplify80.0ms (4.3%)

prune48.0ms (2.6%)

localize7.0ms (0.4%)

series18.0ms (0.9%)

rewrite22.0ms (1.2%)

simplify58.0ms (3.1%)

prune68.0ms (3.7%)

localize7.0ms (0.4%)

series16.0ms (0.9%)

rewrite5.0ms (0.2%)

simplify68.0ms (3.6%)

prune38.0ms (2%)

localize7.0ms (0.4%)

series15.0ms (0.8%)

rewrite3.0ms (0.2%)

simplify99.0ms (5.3%)

prune31.0ms (1.7%)

regimes136.0ms (7.3%)

simplify2.0ms (0.1%)

end61.0ms (3.3%)

Profiling