Details

analyze101.0ms (1.9%)

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)

sample1.5s (28.7%)

Results

1.4s	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify51.0ms (1%)

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)

localize7.0ms (0.1%)

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))

series82.0ms (1.6%)

Counts

3 → 72

Calls

3 calls:

38.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
34.0ms	(pow.f64 (hypot.f64 a b) 4)
11.0ms	(hypot.f64 a b)

rewrite209.0ms (4%)

Algorithm

3×	egg-rewrite

Rules

64×	`egg`
39×	`egg`
35×	`egg`

Counts

3 → 138

Calls

3 calls:

75.0ms	(pow.f64 (hypot.f64 a b) 4)
71.0ms	(hypot.f64 a b)
59.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	212	17
2	2417	17
3	5319	17
0	4	4
1	79	4
2	869	4
3	4730	4
4	5665	4
0	6	7
1	125	7
2	1253	7
3	4864	7
4	4994	7

simplify79.0ms (1.5%)

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

210 → 187

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

prune201.0ms (3.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	186	3	189

Error

Counts

189 → 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 3783 to 2422 computations (36% saved)

localize52.0ms (1%)

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))

series74.0ms (1.4%)

Counts

4 → 84

Calls

4 calls:

44.0ms	(fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))
20.0ms	(+.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))
8.0ms	(fma.f64 b b (.f64 2 (.f64 a a)))
2.0ms	(.f64 2 (.f64 a a))

rewrite285.0ms (5.4%)

Algorithm

4×	egg-rewrite

Rules

50×	`egg`
50×	`egg`
40×	`egg`
23×	`egg`

Counts

4 → 163

Calls

4 calls:

81.0ms	(.f64 2 (.f64 a a))
77.0ms	(fma.f64 b b (.f64 2 (.f64 a a)))
70.0ms	(+.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))
53.0ms	(fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	221	21
2	2208	21
3	5784	21
0	15	31
1	308	31
2	3372	31
3	5081	31
0	5	7
1	101	7
2	1050	7
3	4707	7
4	5835	7
0	7	11
1	140	11
2	1492	11
3	4959	11
4	4936	11

simplify99.0ms (1.9%)

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

247 → 187

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

prune185.0ms (3.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	187	3	190

Error

Counts

190 → 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 5447 to 3077 computations (43.5% saved)

localize13.0ms (0.3%)

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))))

series261.0ms (5%)

Counts

3 → 60

Calls

3 calls:

199.0ms

(*.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))))

59.0ms

(/.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)

rewrite246.0ms (4.7%)

Algorithm

3×	egg-rewrite

Rules

76×	`egg`
39×	`egg`
29×	`egg`

Counts

3 → 144

Calls

3 calls:

117.0ms

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

78.0ms

(*.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))))

47.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	382	17
2	4148	17
3	4899	17
0	8	11
1	157	11
2	1500	11
3	5398	11
0	12	20
1	251	20
2	2794	20
3	4796	20
4	4739	20
5	4913	20

simplify228.0ms (4.3%)

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

204 → 203

Iterations

Useful iterations: 1 (0.0ms)

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

prune815.0ms (15.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	341	0	341
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	341	3	344

Error

Counts

344 → 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 17448 to 12356 computations (29.2% saved)

regimes680.0ms (12.9%)

Accuracy

Total 0.0b remaining (71%)

Threshold costs 0.0b (71%)

Counts

62 → 1

Compiler

Compiled 7794 to 5601 computations (28.1% saved)

simplify2.0ms (0%)

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

end78.0ms (1.5%)

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

Details

analyze101.0ms (1.9%)

sample1.5s (28.7%)

simplify51.0ms (1%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series82.0ms (1.6%)

rewrite209.0ms (4%)

simplify79.0ms (1.5%)

prune201.0ms (3.8%)

localize52.0ms (1%)

series74.0ms (1.4%)

rewrite285.0ms (5.4%)

simplify99.0ms (1.9%)

prune185.0ms (3.5%)

localize13.0ms (0.3%)

series261.0ms (5%)

rewrite246.0ms (4.7%)

simplify228.0ms (4.3%)

prune815.0ms (15.5%)

regimes680.0ms (12.9%)

simplify2.0ms (0%)

end78.0ms (1.5%)

Profiling