Details

analyze110.0ms (2.7%)

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)

sample1.0s (25.5%)

Results

968.0ms	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify45.0ms (1.1%)

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)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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))
✓	0.0b	(hypot.f64 a b)

series90.0ms (2.2%)

Counts

3 → 72

Calls

3 calls:

43.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
36.0ms	(pow.f64 (hypot.f64 a b) 4)
11.0ms	(hypot.f64 a b)

rewrite12.0ms (0.3%)

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:

9.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
2.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(hypot.f64 a b)

simplify95.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-neg_binary64`
421×	`fma-def_binary64`
279×	`associate-r_binary64`
275×	`associate-l_binary64`
184×	`times-frac_binary64`

Counts

124 → 114

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

prune101.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	113	3	116

Error

Counts

116 → 3

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 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
	16.0b	(/.f64 (+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3) (pow.f64 (fma.f64 b (.f64 b 4) -1) 3)) (+.f64 (.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4)) (-.f64 (.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 b (.f64 b 4) -1)) (.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))))

Compiler

Compiled 2400 to 1537 computations (36% saved)

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
✓	0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series37.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
13.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

7.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify86.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

756×	`fma-neg_binary64`
637×	`unswap-sqr_binary64`
348×	`cancel-sign-sub-inv_binary64`
316×	`fma-def_binary64`
208×	`hypot-def_binary64`

Counts

91 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	1701
1	200	1574
2	539	1403
3	2283	1395
4	4384	1395
5	5007	1395

prune84.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	84	3	87

Error

Counts

87 → 3

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 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
▶	16.0b	(/.f64 (+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3) (pow.f64 (fma.f64 b (.f64 b 4) -1) 3)) (+.f64 (.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4)) (-.f64 (.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 b (.f64 b 4) -1)) (.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))))

Compiler

Compiled 2005 to 1094 computations (45.4% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4))
✓	0.1b	(pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)
✓	3.6b	(+.f64 (.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4)) (-.f64 (.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 b (.f64 b 4) -1)) (.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (.f64 b 4) -1))))
✓	15.1b	(/.f64 (+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3) (pow.f64 (fma.f64 b (.f64 b 4) -1) 3)) (+.f64 (.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4)) (-.f64 (.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 b (.f64 b 4) -1)) (.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))))

series891.0ms (21.8%)

Counts

4 → 96

Calls

4 calls:

780.0ms	(/.f64 (+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3) (pow.f64 (fma.f64 b (.f64 b 4) -1) 3)) (+.f64 (.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4)) (-.f64 (.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 b (.f64 b 4) -1)) (.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))))
55.0ms	(+.f64 (.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4)) (-.f64 (.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 b (.f64 b 4) -1)) (.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (.f64 b 4) -1))))
30.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)
26.0ms	(*.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4))

rewrite53.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64`
47×	`unpow-prod-down_binary64`
43×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
27×	`times-frac_binary64`

Counts

4 → 167

Calls

4 calls:

19.0ms	(/.f64 (+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3) (pow.f64 (fma.f64 b (.f64 b 4) -1) 3)) (+.f64 (.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4)) (-.f64 (.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 b (.f64 b 4) -1)) (.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))))
8.0ms	(+.f64 (.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4)) (-.f64 (.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 b (.f64 b 4) -1)) (.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (.f64 b 4) -1))))
5.0ms	(*.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4))
2.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)

simplify270.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

738×	`times-frac_binary64`
316×	`+-commutative_binary64`
271×	`fma-def_binary64`
268×	`associate-+r+_binary64`
240×	`*-commutative_binary64`

Counts

263 → 287

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1002	19771
1	3133	19340
2	5040	19340

prune833.0ms (20.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	287	0	287
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	287	3	290

Error

Counts

290 → 3

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 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
✓	16.0b	(/.f64 (+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3) (pow.f64 (fma.f64 b (.f64 b 4) -1) 3)) (+.f64 (.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4)) (-.f64 (.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 b (.f64 b 4) -1)) (.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))))

Compiler

Compiled 32229 to 22817 computations (29.2% saved)

regimes193.0ms (4.7%)

Accuracy

Total 0.0b remaining (51.9%)

Threshold costs 0.0b (51.9%)

Counts

23 → 1

Compiler

Compiled 4044 to 2873 computations (29% 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

end86.0ms (2.1%)

Compiler: Compiled 117 to 80 computations (31.6% saved)

Details

analyze110.0ms (2.7%)

sample1.0s (25.5%)

simplify45.0ms (1.1%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series90.0ms (2.2%)

rewrite12.0ms (0.3%)

simplify95.0ms (2.3%)

prune101.0ms (2.5%)

localize12.0ms (0.3%)

series37.0ms (0.9%)

rewrite13.0ms (0.3%)

simplify86.0ms (2.1%)

prune84.0ms (2%)

localize21.0ms (0.5%)

series891.0ms (21.8%)

rewrite53.0ms (1.3%)

simplify270.0ms (6.6%)

prune833.0ms (20.4%)

regimes193.0ms (4.7%)

simplify2.0ms (0.1%)

end86.0ms (2.1%)

Profiling