Details

analyze91.0ms (3.9%)

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%	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)

sample81.0ms (3.5%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 41 to 27 computations (34.1% saved)

simplify43.0ms (1.8%)

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 (0.2%)

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

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)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series86.0ms (3.7%)

Counts

3 → 72

Calls

3 calls:

41.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
33.0ms	(pow.f64 (hypot.f64 a b) 4)
12.0ms	(hypot.f64 a b)

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

4.0ms	(+.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)

simplify96.0ms (4.1%)

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 → 120

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

prune126.0ms (5.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	120	2	122

Error

Counts

122 → 2

Alt Table

Status	Error	Program
	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
▶	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))

Compiler

Compiled 2459 to 1554 computations (36.8% saved)

localize11.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))
✓	0.6b	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

series44.0ms (1.9%)

Counts

2 → 48

Calls

2 calls:

22.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))
22.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`associate-+r+_binary64`
22×	`*-un-lft-identity_binary64`
21×	`prod-diff_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`

Counts

2 → 56

Calls

2 calls:

8.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))
0.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

simplify109.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1022×	`fma-neg_binary64`
406×	`fma-def_binary64`
323×	`distribute-rgt-in_binary64`
316×	`distribute-lft-in_binary64`
218×	`associate-l_binary64`

Counts

104 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	2771
1	213	2370
2	569	2351
3	3145	2351
4	4559	2351
5	4958	2351

prune102.0ms (4.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	101	2	103

Error

Counts

103 → 2

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
✓	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))

Compiler

Compiled 3060 to 2054 computations (32.9% saved)

localize14.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 b b (.f64 2 (.f64 a a)))
✓	0.0b	(.f64 2 (.f64 a a))
✓	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
✓	0.2b	(fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))

series51.0ms (2.2%)

Counts

4 → 84

Calls

4 calls:

19.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
17.0ms	(fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))
8.0ms	(fma.f64 b b (.f64 2 (.f64 a a)))
5.0ms	(.f64 2 (.f64 a a))

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`

Counts

4 → 60

Calls

4 calls:

4.0ms	(.f64 2 (.f64 a a))
2.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
0.0ms	(fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))
0.0ms	(fma.f64 b b (.f64 2 (.f64 a a)))

simplify108.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

568×	`fma-neg_binary64`
418×	`cancel-sign-sub-inv_binary64`
359×	`fma-def_binary64`
344×	`distribute-rgt-in_binary64`
339×	`distribute-lft-in_binary64`

Counts

144 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	2635
1	242	2459
2	680	2315
3	3080	2315
4	4844	2315
5	5073	2315

prune107.0ms (4.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Error

Counts

115 → 2

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
✓	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))

Compiler

Compiled 3266 to 1814 computations (44.5% saved)

regimes510.0ms (21.8%)

Accuracy

Total 0.0b remaining (43.4%)

Threshold costs 0.0b (43.4%)

Counts

89 → 1

Compiler

Compiled 9363 to 6773 computations (27.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	37
1	28	37
2	29	37
3	27	37

end1.0ms (0%)

Compiler: Compiled 27 to 22 computations (18.5% saved)

sample714.0ms (30.6%)

Algorithm

1×

intervals

Results

418.0ms	8000×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 94 to 67 computations (28.7% saved)

Details

analyze91.0ms (3.9%)

sample81.0ms (3.5%)

simplify43.0ms (1.8%)

prune4.0ms (0.2%)

localize7.0ms (0.3%)

series86.0ms (3.7%)

rewrite7.0ms (0.3%)

simplify96.0ms (4.1%)

prune126.0ms (5.4%)

localize11.0ms (0.5%)

series44.0ms (1.9%)

rewrite13.0ms (0.5%)

simplify109.0ms (4.7%)

prune102.0ms (4.4%)

localize14.0ms (0.6%)

series51.0ms (2.2%)

rewrite10.0ms (0.4%)

simplify108.0ms (4.6%)

prune107.0ms (4.6%)

regimes510.0ms (21.8%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample714.0ms (30.6%)

Profiling