Details

analyze79.0ms (6.4%)

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%	56.2%	18.8%	6
25%	40.6%	34.4%	7
31.2%	31.2%	37.6%	8
39%	21.1%	39.9%	9
42.9%	16%	41.1%	10
47.2%	10.7%	42%	11
49.4%	8.1%	42.5%	12
51.6%	5.4%	43%	13
52.7%	4.1%	43.2%	14

Compiler

Compiled 10 to 5 computations (50% saved)

sample37.0ms (3%)

Algorithm

1×

intervals

Symmetry

(sort x y)

Results

5.0ms	256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 21 to 11 computations (47.6% saved)

simplify12.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

70×	`fma-def_binary64`
24×	`associate-+l+_binary64`
18×	`associate-+r+_binary64`
10×	`distribute-rgt-in_binary64`
8×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	12	10
2	26	10
3	46	10
4	81	10
5	101	10
6	117	10
7	130	10
8	132	10
9	132	10

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 27 to 12 computations (55.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(*.f64 (+.f64 x y) (+.f64 x y))

rewrite11.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
8×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`distribute-lft-out_binary64`
6×	`swap-sqr_binary64`

Counts

1 → 42

Calls

1 calls:

7.0ms

(*.f64 (+.f64 x y) (+.f64 x y))

simplify52.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

728×	`associate-+l+_binary64`
594×	`unswap-sqr_binary64`
430×	`distribute-rgt-in_binary64`
422×	`distribute-lft-in_binary64`
327×	`fma-def_binary64`

Counts

66 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	994
1	200	853
2	739	757
3	2462	692
4	5240	692

prune44.0ms (3.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	5	65

Error

Counts

65 → 5

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
▶	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
	1.2b	(.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x y) (+.f64 x y))) (cbrt.f64 (.f64 (+.f64 x y) (+.f64 x y)))) (cbrt.f64 (*.f64 (+.f64 x y) (+.f64 x y))))
	27.7b	(*.f64 x (fma.f64 y 2 x))
	0.0b	(+.f64 (.f64 x (+.f64 x y)) (.f64 y (+.f64 x y)))

Compiler

Compiled 1020 to 319 computations (68.7% saved)

localize7.0ms (0.6%)

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

series19.0ms (1.6%)

Counts

3 → 18

Calls

3 calls:

9.0ms	(+.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 (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
10×	`*-un-lft-identity_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))

simplify63.0ms (5.1%)

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

prune72.0ms (5.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	96	4	100

Error

Counts

100 → 4

Alt Table

Status	Error	Program
	27.7b	(*.f64 x (fma.f64 y 2 x))
▶	0.0b	(+.f64 (.f64 2 (.f64 y x)) (fma.f64 y y (pow.f64 x 2)))
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
	0.0b	(+.f64 (.f64 x (+.f64 x y)) (.f64 y (+.f64 x y)))

Compiler

Compiled 1849 to 1115 computations (39.7% saved)

localize7.0ms (0.5%)

Local error

Found 3 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))
✓	0.0b	(fma.f64 y y (pow.f64 x 2))

series15.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

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

rewrite5.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_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))

simplify67.0ms (5.4%)

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

prune52.0ms (4.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	1	2
Picked	0	1	1
Done	1	0	1
Total	83	3	86

Error

Counts

86 → 3

Alt Table

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

Compiler

Compiled 1472 to 777 computations (47.2% saved)

localize5.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

6.0ms

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

rewrite1.0ms (0.1%)

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

simplify45.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

824×	`associate-+l+_binary64`
820×	`associate-+r+_binary64`
311×	`distribute-lft-in_binary64`
310×	`distribute-rgt-in_binary64`
296×	`distribute-rgt-out_binary64`

Counts

34 → 28

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	473
1	48	376
2	92	373
3	310	367
4	1673	367
5	5874	367

prune16.0ms (1.3%)

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

Compiler

Compiled 382 to 179 computations (53.1% saved)

regimes153.0ms (12.4%)

Accuracy

Total 0.0b remaining (83.3%)

Threshold costs 0.0b (83.3%)

Counts

33 → 1

Compiler

Compiled 1833 to 1079 computations (41.1% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	12	17
2	12	17

end8.0ms (0.6%)

Remove: (sort x y)
Compiler: Compiled 42 to 27 computations (35.7% saved)

sample428.0ms (34.6%)

Algorithm

1×

intervals

Results

190.0ms	8000×	body	128	valid
2.0ms	103×	body	128	invalid

Compiler

Compiled 64 to 37 computations (42.2% saved)

Details

analyze79.0ms (6.4%)

sample37.0ms (3%)

simplify12.0ms (0.9%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series6.0ms (0.5%)

rewrite11.0ms (0.9%)

simplify52.0ms (4.2%)

prune44.0ms (3.6%)

localize7.0ms (0.6%)

series19.0ms (1.6%)

rewrite20.0ms (1.6%)

simplify63.0ms (5.1%)

prune72.0ms (5.8%)

localize7.0ms (0.5%)

series15.0ms (1.2%)

rewrite5.0ms (0.4%)

simplify67.0ms (5.4%)

prune52.0ms (4.2%)

localize5.0ms (0.4%)

series6.0ms (0.5%)

rewrite1.0ms (0.1%)

simplify45.0ms (3.7%)

prune16.0ms (1.3%)

regimes153.0ms (12.4%)

simplify3.0ms (0.2%)

end8.0ms (0.6%)

sample428.0ms (34.6%)

Profiling