Details

analyze242.0ms (7%)

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)

sample44.0ms (1.3%)

Algorithm

1×

intervals

Results

30.0ms

256×

body

128

valid

Compiler

Compiled 41 to 27 computations (34.1% saved)

simplify51.0ms (1.5%)

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

prune7.0ms (0.2%)

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

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)

localize14.0ms (0.4%)

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)

series165.0ms (4.8%)

Counts

3 → 72

Calls

3 calls:

74.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
65.0ms	(pow.f64 (hypot.f64 a b) 4)
25.0ms	(hypot.f64 a b)

rewrite16.0ms (0.5%)

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:

8.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
3.0ms	(pow.f64 (hypot.f64 a b) 4)
1.0ms	(hypot.f64 a b)

simplify177.0ms (5.1%)

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

prune177.0ms (5.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

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))
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 2311 to 1477 computations (36.1% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 a a) (.f64 b b))
✓	0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
✓	0.0b	(.f64 4 (.f64 b b))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series81.0ms (2.3%)

Counts

4 → 84

Calls

4 calls:

41.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
23.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
12.0ms	(+.f64 (.f64 a a) (.f64 b b))
5.0ms	(.f64 4 (.f64 b b))

rewrite39.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64`
10×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`fma-def_binary64`
9×	`add-cbrt-cube_binary64`

Counts

4 → 76

Calls

4 calls:

13.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
8.0ms	(.f64 4 (.f64 b b))
7.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
5.0ms	(+.f64 (.f64 a a) (.f64 b b))

simplify194.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

682×	`associate-l_binary64`
617×	`fma-def_binary64`
585×	`associate-r_binary64`
564×	`fma-neg_binary64`
242×	`distribute-rgt-in_binary64`

Counts

160 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2183
1	320	1975
2	966	1803
3	4484	1803
4	5000	1803

prune250.0ms (7.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	132	2	134

Error

Counts

134 → 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 2992 to 1496 computations (50% saved)

regimes498.0ms (14.5%)

Accuracy

Total 0.0b remaining (48%)

Threshold costs 0.0b (48%)

Counts

38 → 1

Compiler

Compiled 3857 to 2837 computations (26.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	12	17
2	12	17

end1.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

sample1.5s (42.5%)

Algorithm

1×

intervals

Results

895.0ms	8000×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 69 to 47 computations (31.9% saved)

Details

analyze242.0ms (7%)

sample44.0ms (1.3%)

simplify51.0ms (1.5%)

prune7.0ms (0.2%)

localize14.0ms (0.4%)

series165.0ms (4.8%)

rewrite16.0ms (0.5%)

simplify177.0ms (5.1%)

prune177.0ms (5.1%)

localize18.0ms (0.5%)

series81.0ms (2.3%)

rewrite39.0ms (1.1%)

simplify194.0ms (5.7%)

prune250.0ms (7.3%)

regimes498.0ms (14.5%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.5s (42.5%)

Profiling