Details

analyze80.0ms (4.9%)

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)

sample34.0ms (2.1%)

Algorithm

1×

intervals

Symmetry

(sort x y)

Results

5.0ms	256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 21 to 11 computations (47.6% saved)

simplify8.0ms (0.5%)

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))

series5.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

5.0ms

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

rewrite15.0ms (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:

6.0ms

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

simplify52.0ms (3.2%)

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

prune38.0ms (2.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	2	65

Error

0.0b

Counts

65 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
	39.9b	(/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (fma.f64 y y (.f64 x (-.f64 x y))) (fma.f64 y y (.f64 x (-.f64 x y)))))

Status

Error

Program

▶

0.0b

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

39.9b

(/.f64 (*.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (*.f64 (fma.f64 y y (*.f64 x (-.f64 x y))) (fma.f64 y y (*.f64 x (-.f64 x y)))))

Compiler

Compiled 983 to 315 computations (68% saved)

localize10.0ms (0.6%)

Local error

Found 2 expressions with local error:

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

series11.0ms (0.7%)

Counts

2 → 12

Calls

2 calls:

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

rewrite13.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
7×	`add-log-exp_binary64`
3×	`associate-l_binary64`

Counts

2 → 36

Calls

2 calls:

8.0ms	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
3.0ms	(.f64 2 (.f64 y x))

simplify67.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

580×	`associate-l_binary64`
560×	`fma-neg_binary64`
449×	`associate-r_binary64`
328×	`fma-def_binary64`
298×	`distribute-rgt-neg-in_binary64`

Counts

48 → 62

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	71	668
1	195	590
2	684	537
3	2857	537
4	4813	537
5	5062	537

prune40.0ms (2.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	62	2	64

Error

0.0b

Counts

64 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
▶	39.9b	(/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (fma.f64 y y (.f64 x (-.f64 x y))) (fma.f64 y y (.f64 x (-.f64 x y)))))

Status

Error

Program

✓

0.0b

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

▶

39.9b

(/.f64 (*.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (*.f64 (fma.f64 y y (*.f64 x (-.f64 x y))) (fma.f64 y y (*.f64 x (-.f64 x y)))))

Compiler

Compiled 1206 to 739 computations (38.7% saved)

localize11.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y y (*.f64 x (-.f64 x y)))
✓	0.2b	(*.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
✓	0.3b	(.f64 (fma.f64 y y (.f64 x (-.f64 x y))) (fma.f64 y y (*.f64 x (-.f64 x y))))
✓	38.0b	(/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (fma.f64 y y (.f64 x (-.f64 x y))) (fma.f64 y y (.f64 x (-.f64 x y)))))

series72.0ms (4.5%)

Counts

4 → 96

Calls

4 calls:

36.0ms	(/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (fma.f64 y y (.f64 x (-.f64 x y))) (fma.f64 y y (.f64 x (-.f64 x y)))))
20.0ms	(*.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
10.0ms	(.f64 (fma.f64 y y (.f64 x (-.f64 x y))) (fma.f64 y y (*.f64 x (-.f64 x y))))
6.0ms	(fma.f64 y y (*.f64 x (-.f64 x y)))

rewrite58.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`*-un-lft-identity_binary64`
46×	`distribute-lft-out_binary64`
40×	`cube-prod_binary64`
40×	`unpow-prod-down_binary64`
26×	`swap-sqr_binary64`

Counts

4 → 139

Calls

4 calls:

19.0ms	(/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (fma.f64 y y (.f64 x (-.f64 x y))) (fma.f64 y y (.f64 x (-.f64 x y)))))
18.0ms	(*.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
5.0ms	(.f64 (fma.f64 y y (.f64 x (-.f64 x y))) (fma.f64 y y (*.f64 x (-.f64 x y))))
0.0ms	(fma.f64 y y (*.f64 x (-.f64 x y)))

simplify170.0ms (10.6%)

Algorithm

1×	egg-herbie

Rules

453×	`fma-neg_binary64`
357×	`unswap-sqr_binary64`
279×	`associate-l_binary64`
265×	`cancel-sign-sub-inv_binary64`
259×	`associate-r_binary64`

Counts

235 → 199

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	6184
1	523	5111
2	2466	4235
3	4597	4235
4	5000	4235
5	4999	4235

prune152.0ms (9.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	216	2	218

Error

0.0b

Counts

218 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
✓	39.9b	(/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (fma.f64 y y (.f64 x (-.f64 x y))) (fma.f64 y y (.f64 x (-.f64 x y)))))

Status

Error

Program

✓

0.0b

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

✓

39.9b

(/.f64 (*.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (*.f64 (fma.f64 y y (*.f64 x (-.f64 x y))) (fma.f64 y y (*.f64 x (-.f64 x y)))))

Compiler

Compiled 8902 to 3983 computations (55.3% saved)

regimes349.0ms (21.7%)

Accuracy

Total 0.0b remaining (24.1%)

Threshold costs 0.0b (24.1%)

Counts

63 → 1

Compiler

Compiled 4696 to 2830 computations (39.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	12	10
2	10	10

end5.0ms (0.3%)

Remove: (sort x y)
Compiler: Compiled 27 to 12 computations (55.6% saved)

sample415.0ms (25.8%)

Algorithm

1×

intervals

Results

164.0ms	8000×	body	128	valid
3.0ms	117×	body	128	invalid

Compiler

Compiled 71 to 40 computations (43.7% saved)

Details

analyze80.0ms (4.9%)

sample34.0ms (2.1%)

simplify8.0ms (0.5%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series5.0ms (0.3%)

rewrite15.0ms (0.9%)

simplify52.0ms (3.2%)

prune38.0ms (2.4%)

localize10.0ms (0.6%)

series11.0ms (0.7%)

rewrite13.0ms (0.8%)

simplify67.0ms (4.1%)

prune40.0ms (2.5%)

localize11.0ms (0.7%)

series72.0ms (4.5%)

rewrite58.0ms (3.6%)

simplify170.0ms (10.6%)

prune152.0ms (9.4%)

regimes349.0ms (21.7%)

simplify2.0ms (0.1%)

end5.0ms (0.3%)

sample415.0ms (25.8%)

Profiling