Details

analyze150.0ms (8.1%)

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)

sample899.0ms (48.2%)

Symmetry

(sort x y)

Results

850.0ms	8256×	body	128	valid
21.0ms	204×	body	128	invalid

Compiler

Compiled 47 to 29 computations (38.3% saved)

simplify7.0ms (0.4%)

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

prune7.0ms (0.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize7.0ms (0.4%)

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))

series13.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))
6.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 x 2) y))

rewrite9.0ms (0.5%)

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))
3.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 x 2) y))

simplify75.0ms (4%)

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

prune44.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	58	4	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	4	63

Error

Counts

63 → 4

Alt Table

Status	Error	Program
	0.0b	(+.f64 (fma.f64 x x (.f64 (.f64 x 2) y)) (*.f64 y y))
	34.1b	(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (fma.f64 y 2 x) (fma.f64 y 2 x))) (pow.f64 y 4)) (-.f64 (.f64 x (fma.f64 y 2 x)) (*.f64 y y)))
	0.0b	(fma.f64 y (fma.f64 2 x y) (*.f64 x x))
▶	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))

Compiler

Compiled 1302 to 635 computations (51.2% saved)

localize11.0ms (0.6%)

Local error

Found 3 expressions with local error:

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

series17.0ms (0.9%)

Counts

3 → 18

Calls

3 calls:

7.0ms	(+.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))
4.0ms	(.f64 2 (.f64 y x))

rewrite20.0ms (1.1%)

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:

10.0ms	(+.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))
3.0ms	(.f64 2 (.f64 y x))

simplify55.0ms (3%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-neg_binary64`
654×	`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

prune80.0ms (4.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	96	3	99

Error

Counts

99 → 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)) (fma.f64 y y (pow.f64 x 2)))
	0.0b	(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

Compiler

Compiled 1824 to 1105 computations (39.4% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series17.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(fma.f64 y y (pow.f64 x 2))
7.0ms	(+.f64 (.f64 2 (.f64 y x)) (fma.f64 y y (pow.f64 x 2)))

rewrite5.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64`
2×	`fma-udef_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

2 → 25

Calls

2 calls:

4.0ms	(+.f64 (.f64 2 (.f64 y x)) (fma.f64 y y (pow.f64 x 2)))
0.0ms	(fma.f64 y y (pow.f64 x 2))

simplify66.0ms (3.5%)

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

73 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	892
1	127	842
2	459	756
3	2273	756
4	4685	756
5	4965	756

prune50.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	82	3	85

Error

Counts

85 → 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)) (fma.f64 y y (pow.f64 x 2)))
▶	0.0b	(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

Compiler

Compiled 1450 to 768 computations (47% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

6.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

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

simplify38.0ms (2%)

Algorithm

1×	egg-herbie

Rules

824×	`associate-+l+_binary64`
820×	`associate-+r+_binary64`
313×	`distribute-lft-in_binary64`
313×	`distribute-rgt-in_binary64`
298×	`distribute-rgt-out_binary64`

Counts

34 → 28

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	473
1	49	373
2	98	367
3	316	367
4	1706	367
5	5952	367

prune15.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	28	3	31

Error

Counts

31 → 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)) (fma.f64 y y (pow.f64 x 2)))
✓	0.0b	(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

Compiler

Compiled 383 to 181 computations (52.7% saved)

regimes65.0ms (3.5%)

Accuracy

Total 0.0b remaining (83.1%)

Threshold costs 0.0b (83.1%)

Counts

24 → 1

Compiler

Compiled 864 to 548 computations (36.6% 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

end195.0ms (10.4%)

Compiler: Compiled 91 to 55 computations (39.6% saved)

Details

analyze150.0ms (8.1%)

sample899.0ms (48.2%)

simplify7.0ms (0.4%)

prune7.0ms (0.4%)

localize7.0ms (0.4%)

series13.0ms (0.7%)

rewrite9.0ms (0.5%)

simplify75.0ms (4%)

prune44.0ms (2.3%)

localize11.0ms (0.6%)

series17.0ms (0.9%)

rewrite20.0ms (1.1%)

simplify55.0ms (3%)

prune80.0ms (4.3%)

localize7.0ms (0.4%)

series17.0ms (0.9%)

rewrite5.0ms (0.3%)

simplify66.0ms (3.5%)

prune50.0ms (2.7%)

localize5.0ms (0.3%)

series6.0ms (0.3%)

rewrite1.0ms (0%)

simplify38.0ms (2%)

prune15.0ms (0.8%)

regimes65.0ms (3.5%)

simplify2.0ms (0.1%)

end195.0ms (10.4%)

Profiling