Details

analyze240.0ms (7.1%)

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)

sample1.0s (30.7%)

Results

963.0ms	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify44.0ms (1.3%)

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 (0.1%)

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 (0.3%)

Local error

Found 3 expressions with local error:

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

series91.0ms (2.7%)

Counts

3 → 72

Calls

3 calls:

40.0ms	(pow.f64 (hypot.f64 a b) 4)
39.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
12.0ms	(hypot.f64 a b)

rewrite58.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

99× egg-rr

Counts

3 → 99

Calls

2 calls:

56.0ms	((+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) (hypot.f64 a b) (pow.f64 (hypot.f64 a b) 4))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	212	28
2	2417	28
3	5319	28
0	0	0
1	0	0

simplify125.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-neg_binary64`
562×	`cancel-sign-sub-inv_binary64`
307×	`fma-def_binary64`
297×	`neg-mul-1_binary64`
289×	`neg-sub0_binary64`

Counts

171 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	1453
1	217	1409
2	654	1303
3	2646	1303
4	4298	1303
5	5065	1303

prune133.0ms (3.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	147	3	150

Error

Counts

150 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
	11.1b	(.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))
▶	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))

Compiler

Compiled 3025 to 1961 computations (35.2% saved)

localize15.0ms (0.4%)

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))

series48.0ms (1.4%)

Counts

4 → 84

Calls

4 calls:

22.0ms	(+.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))
16.0ms	(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)))
2.0ms	(.f64 2 (.f64 a a))

rewrite69.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

93× egg-rr

Counts

4 → 93

Calls

2 calls:

66.0ms

((fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 2 (*.f64 a a))) (pow.f64 a 4)) (+.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)) (*.f64 2 (*.f64 a a)) (fma.f64 b b (*.f64 2 (*.f64 a a))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	70
1	308	70
2	3372	70
3	5081	70
0	0	0
1	0	0

simplify89.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

981×	`fma-def_binary64`
744×	`fma-neg_binary64`
352×	`associate-l_binary64`
348×	`unswap-sqr_binary64`
347×	`sub-neg_binary64`

Counts

177 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	1298
1	76	1254
2	213	1164
3	643	1138
4	1871	1138
5	4594	1138
6	4854	1138
7	5138	1138

prune127.0ms (3.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	118	3	121

Error

Counts

121 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
▶	11.1b	(.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))
✓	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))

Compiler

Compiled 3552 to 2014 computations (43.3% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 a b)
✓	0.1b	(/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))
✓	0.1b	(pow.f64 (fma.f64 b (*.f64 b 4) -1) 2)
✓	10.4b	(.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))

series299.0ms (8.9%)

Counts

3 → 60

Calls

3 calls:

230.0ms

(*.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (*.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))

66.0ms

(/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))

3.0ms

(pow.f64 (fma.f64 b (*.f64 b 4) -1) 2)

rewrite82.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

94× egg-rr

Counts

3 → 94

Calls

2 calls:

79.0ms

((*.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (*.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))) (pow.f64 (fma.f64 b (*.f64 b 4) -1) 2) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	70
1	382	48
2	4148	48
3	4899	48
0	0	0
1	0	0

simplify89.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

537×	`fma-def_binary64`
397×	`associate-+l+_binary64`
345×	`times-frac_binary64`
307×	`associate-/l*_binary64`
251×	`associate-/r*_binary64`

Counts

154 → 154

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	427	5470
1	1462	5400
2	5423	5400

prune369.0ms (10.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	258	0	258
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	258	3	261

Error

Counts

261 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	11.1b	(.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (/.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))
✓	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))

Compiler

Compiled 14177 to 10175 computations (28.2% saved)

regimes353.0ms (10.5%)

Accuracy

Total 0.0b remaining (71%)

Threshold costs 0.0b (71%)

Counts

59 → 1

Compiler

Compiled 7602 to 5439 computations (28.5% saved)

simplify2.0ms (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

end79.0ms (2.3%)

Compiler: Compiled 97 to 67 computations (30.9% saved)

Details

analyze240.0ms (7.1%)

sample1.0s (30.7%)

simplify44.0ms (1.3%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

series91.0ms (2.7%)

rewrite58.0ms (1.7%)

simplify125.0ms (3.7%)

prune133.0ms (3.9%)

localize15.0ms (0.4%)

series48.0ms (1.4%)

rewrite69.0ms (2%)

simplify89.0ms (2.6%)

prune127.0ms (3.8%)

localize15.0ms (0.5%)

series299.0ms (8.9%)

rewrite82.0ms (2.4%)

simplify89.0ms (2.6%)

prune369.0ms (10.9%)

regimes353.0ms (10.5%)

simplify2.0ms (0.1%)

end79.0ms (2.3%)

Profiling