Details

analyze90.0ms (5.5%)

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)

sample689.0ms (42.3%)

Symmetry

(sort x y)

Results

651.0ms	8256×	body	128	valid
6.0ms	79×	body	128	invalid

Compiler

Compiled 29 to 14 computations (51.7% saved)

simplify15.0ms (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 (0.3%)

Counts

1 → 24

Calls

1 calls:

6.0ms

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

rewrite8.0ms (0.5%)

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))

simplify50.0ms (3.1%)

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

prune45.0ms (2.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	4	65

Error

Counts

65 → 4

Alt Table

Status	Error	Program
	0.0b	(+.f64 (.f64 x (+.f64 x y)) (.f64 y (+.f64 x y)))
▶	0.0b	(+.f64 (.f64 2 (.f64 y x)) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
	27.2b	(.f64 y (+.f64 y (.f64 2 x)))
	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))))

Compiler

Compiled 1013 to 317 computations (68.7% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series18.0ms (1.1%)

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))
5.0ms	(.f64 2 (.f64 y x))

rewrite25.0ms (1.5%)

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:

13.0ms	(+.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))

simplify63.0ms (3.9%)

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

prune71.0ms (4.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	96	3	99

Error

Counts

99 → 3

Alt Table

Status	Error	Program
	3.4b	(expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))
	27.2b	(.f64 y (+.f64 y (.f64 2 x)))
▶	0.0b	(+.f64 (.f64 2 (.f64 y x)) (fma.f64 y y (pow.f64 x 2)))

Compiler

Compiled 1818 to 1103 computations (39.3% saved)

localize7.0ms (0.4%)

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

series8.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

8.0ms

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

rewrite14.0ms (0.8%)

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:

13.0ms

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

simplify66.0ms (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

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

prune48.0ms (2.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	63	3	66

Error

Counts

66 → 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 y (+.f64 (.f64 x 2) y)) (pow.f64 x 2))

Compiler

Compiled 1136 to 624 computations (45.1% saved)

localize6.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

series13.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

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

rewrite12.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 40

Calls

2 calls:

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

simplify76.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

493×	`distribute-rgt-in_binary64`
478×	`distribute-lft-in_binary64`
458×	`sub-neg_binary64`
448×	`fma-def_binary64`
311×	`+-commutative_binary64`

Counts

88 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	76	964
1	236	934
2	839	917
3	2874	917
4	4398	917
5	5053	917

prune49.0ms (3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	79	2	81

Error

Counts

81 → 2

Alt Table

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

Compiler

Compiled 1343 to 837 computations (37.7% saved)

regimes187.0ms (11.5%)

Accuracy

Total 0.0b remaining (68.2%)

Threshold costs 0.0b (68.2%)

Counts

45 → 1

Compiler

Compiled 2452 to 1455 computations (40.7% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	13	16
2	13	16

end51.0ms (3.2%)

Remove: (sort x y)
Compiler: Compiled 77 to 51 computations (33.8% saved)

Details

analyze90.0ms (5.5%)

sample689.0ms (42.3%)

simplify15.0ms (0.9%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series6.0ms (0.3%)

rewrite8.0ms (0.5%)

simplify50.0ms (3.1%)

prune45.0ms (2.7%)

localize7.0ms (0.4%)

series18.0ms (1.1%)

rewrite25.0ms (1.5%)

simplify63.0ms (3.9%)

prune71.0ms (4.3%)

localize7.0ms (0.4%)

series8.0ms (0.5%)

rewrite14.0ms (0.8%)

simplify66.0ms (4%)

prune48.0ms (2.9%)

localize6.0ms (0.4%)

series13.0ms (0.8%)

rewrite12.0ms (0.7%)

simplify76.0ms (4.7%)

prune49.0ms (3%)

regimes187.0ms (11.5%)

simplify3.0ms (0.2%)

end51.0ms (3.2%)

Profiling