Details

analyze95.0ms (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%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample82.0ms (4.7%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 41 to 27 computations (34.1% saved)

simplify43.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

770×	`unswap-sqr_binary64`
631×	`associate-l_binary64`
623×	`fma-def_binary64`
311×	`fma-neg_binary64`
283×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	30	21
2	60	21
3	159	21
4	518	17
5	1687	17
6	3597	17
7	5026	17

prune4.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 97 to 64 computations (34% saved)

localize9.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a b)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)

series94.0ms (5.4%)

Counts

3 → 72

Calls

3 calls:

44.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
37.0ms	(pow.f64 (hypot.f64 a b) 4)
12.0ms	(hypot.f64 a b)

rewrite9.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
7×	`fma-def_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`unpow-prod-down_binary64`

Counts

3 → 52

Calls

3 calls:

6.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
1.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(hypot.f64 a b)

simplify102.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-neg_binary64`
421×	`fma-def_binary64`
280×	`associate-r_binary64`
276×	`associate-l_binary64`
184×	`times-frac_binary64`

Counts

124 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	2123
1	343	2010
2	979	1901
3	4070	1899
4	4922	1899
5	4944	1899

prune97.0ms (5.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	113	2	115

Error

0.0b

Counts

115 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
▶	0.0b	(+.f64 (pow.f64 a 4) (+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) -1))

Compiler

Compiled 2315 to 1483 computations (35.9% saved)

localize12.0ms (0.7%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 a 4) (+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) -1))
✓	1.2b	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

series48.0ms (2.8%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(+.f64 (pow.f64 a 4) (+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) -1))
24.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

rewrite11.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
7×	`fma-def_binary64`
7×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 34

Calls

2 calls:

9.0ms	(+.f64 (pow.f64 a 4) (+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) -1))
0.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

simplify76.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

549×	`fma-neg_binary64`
458×	`distribute-rgt-in_binary64`
438×	`distribute-lft-in_binary64`
348×	`fma-def_binary64`
321×	`distribute-neg-in_binary64`

Counts

82 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	71	1982
1	184	1668
2	570	1662
3	3261	1662
4	5198	1662

prune66.0ms (3.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	72	2	74

Error

0.0b

Counts

74 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(+.f64 (pow.f64 a 4) (+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) -1))

Compiler

Compiled 1892 to 1178 computations (37.7% saved)

regimes241.0ms (14%)

Accuracy

Total 0.0b remaining (17%)

Threshold costs 0.0b (17%)

Counts

40 → 1

Compiler

Compiled 4317 to 3151 computations (27% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	16	27
2	16	27

end1.0ms (0%)

Compiler: Compiled 21 to 15 computations (28.6% saved)

sample729.0ms (42.3%)

Algorithm

1×

intervals

Results

444.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 78 to 55 computations (29.5% saved)

Details

analyze95.0ms (5.5%)

sample82.0ms (4.7%)

simplify43.0ms (2.5%)

prune4.0ms (0.3%)

localize9.0ms (0.5%)

series94.0ms (5.4%)

rewrite9.0ms (0.6%)

simplify102.0ms (5.9%)

prune97.0ms (5.6%)

localize12.0ms (0.7%)

series48.0ms (2.8%)

rewrite11.0ms (0.6%)

simplify76.0ms (4.4%)

prune66.0ms (3.8%)

regimes241.0ms (14%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample729.0ms (42.3%)

Profiling