Details

analyze111.0ms (5.9%)

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)

sample690.0ms (36.4%)

Symmetry

(sort x y)

Results

646.0ms	8256×	body	128	valid
7.0ms	93×	body	128	invalid

Compiler

Compiled 29 to 14 computations (51.7% saved)

simplify8.0ms (0.4%)

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))

rewrite13.0ms (0.7%)

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))

simplify54.0ms (2.9%)

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

prune36.0ms (1.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	3	65

Error

0.0b

Counts

65 → 3

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
	0.0b	(+.f64 (.f64 x (+.f64 x y)) (.f64 y (+.f64 x y)))
	36.1b	(cbrt.f64 (pow.f64 (+.f64 y x) 6))

Compiler

Compiled 955 to 303 computations (68.3% saved)

localize7.0ms (0.4%)

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)))

series21.0ms (1.1%)

Counts

3 → 18

Calls

3 calls:

9.0ms	(+.f64 (pow.f64 y 2) (pow.f64 x 2))
7.0ms	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
4.0ms	(.f64 2 (.f64 y x))

rewrite21.0ms (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:

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

simplify67.0ms (3.5%)

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

prune64.0ms (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	95	3	98

Error

0.0b

Counts

98 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
▶	0.0b	(+.f64 (.f64 x (+.f64 x y)) (.f64 y (+.f64 x y)))
	36.1b	(cbrt.f64 (pow.f64 (+.f64 y x) 6))

Compiler

Compiled 1803 to 1094 computations (39.3% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series16.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

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

rewrite20.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-*r/_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`flip-+_binary64`

Counts

3 → 73

Calls

3 calls:

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

simplify93.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

873×	`fma-neg_binary64`
399×	`*-commutative_binary64`
387×	`associate-+l+_binary64`
371×	`cancel-sign-sub-inv_binary64`
370×	`associate-+r+_binary64`

Counts

145 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	1613
1	380	1512
2	1536	1408
3	3300	1408
4	4869	1408
5	4958	1408

prune65.0ms (3.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	129	3	132

Error

0.0b

Counts

132 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
✓	0.0b	(+.f64 (.f64 x (+.f64 x y)) (.f64 y (+.f64 x y)))
▶	36.1b	(cbrt.f64 (pow.f64 (+.f64 y x) 6))

Compiler

Compiled 2285 to 504 computations (77.9% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 y x) 6)
✓	34.5b	(cbrt.f64 (pow.f64 (+.f64 y x) 6))

series18.0ms (1%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(pow.f64 (+.f64 y x) 6)
5.0ms	(cbrt.f64 (pow.f64 (+.f64 y x) 6))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
8×	`cbrt-prod_binary64`
8×	`unpow-prod-down_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 38

Calls

2 calls:

3.0ms	(pow.f64 (+.f64 y x) 6)
3.0ms	(cbrt.f64 (pow.f64 (+.f64 y x) 6))

simplify90.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

537×	`exp-prod_binary64`
455×	`associate-l_binary64`
423×	`log-prod_binary64`
404×	`associate-r_binary64`
365×	`fma-def_binary64`

Counts

86 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	1307
1	212	1197
2	591	1116
3	2500	1061
4	4308	1061
5	4983	1061

prune45.0ms (2.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	80	4	84

Error

Counts

84 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
✓	0.0b	(+.f64 (.f64 x (+.f64 x y)) (.f64 y (+.f64 x y)))
✓	36.1b	(cbrt.f64 (pow.f64 (+.f64 y x) 6))
	1.5b	(*.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 4) (cbrt.f64 (pow.f64 (+.f64 x y) 2)))

Compiler

Compiled 1000 to 625 computations (37.5% saved)

regimes202.0ms (10.7%)

Accuracy

Total 0.0b remaining (71.3%)

Threshold costs 0.0b (71.3%)

Counts

52 → 1

Compiler

Compiled 2391 to 1483 computations (38% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	7	12

end221.0ms (11.7%)

Compiler: Compiled 95 to 57 computations (40% saved)

Details

analyze111.0ms (5.9%)

sample690.0ms (36.4%)

simplify8.0ms (0.4%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series5.0ms (0.3%)

rewrite13.0ms (0.7%)

simplify54.0ms (2.9%)

prune36.0ms (1.9%)

localize7.0ms (0.4%)

series21.0ms (1.1%)

rewrite21.0ms (1.1%)

simplify67.0ms (3.5%)

prune64.0ms (3.4%)

localize7.0ms (0.4%)

series16.0ms (0.8%)

rewrite20.0ms (1.1%)

simplify93.0ms (4.9%)

prune65.0ms (3.5%)

localize6.0ms (0.3%)

series18.0ms (1%)

rewrite7.0ms (0.3%)

simplify90.0ms (4.8%)

prune45.0ms (2.3%)

regimes202.0ms (10.7%)

simplify2.0ms (0.1%)

end221.0ms (11.7%)

Profiling