Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 10 to 5 computations (50% saved)

sample741.0ms (16.4%)

Results

667.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 14 computations (51.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`count-2_binary64`
1×	`associate-l_binary64`
1×	`distribute-rgt-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	11	4
2	14	4
3	15	4
4	15	4

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(hypot.f64 x x)

Compiler

Compiled 20 to 9 computations (55% saved)

localize2.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(hypot.f64 x x)

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(hypot.f64 x x)

rewrite141.0ms (3.1%)

Algorithm

1×	egg-rewrite

Rules

40× egg

Counts

1 → 40

Calls

1 calls:

140.0ms

(hypot.f64 x x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	60	4
2	660	4
3	4745	4
4	5428	4

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Counts

52 → 43

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	24	80
3	25	80
4	29	80
5	47	80
6	58	80
7	63	80
8	75	80
9	72	80
10	58	80

prune105.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	38	5	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	6	44

Error

0.0b

Counts

44 → 6

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	1.7b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
▶	0.6b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	32.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.2b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 469 to 228 computations (51.4% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)
✓	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

series26.0ms (0.6%)

Counts

2 → 0

Calls

2 calls:

17.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
9.0ms	(sqrt.f64 (hypot.f64 x x))

rewrite156.0ms (3.5%)

Algorithm

2×	egg-rewrite

Rules

48×	`egg`
48×	`egg`

Counts

2 → 96

Calls

2 calls:

81.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
73.0ms	(sqrt.f64 (hypot.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	4
1	106	4
2	1032	4
3	4509	4
4	5547	4
0	4	6
1	79	6
2	850	6
3	4571	6
4	5392	6

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

96 → 95

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune69.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	138	6	144

Error

0.0b

Counts

144 → 6

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
▶	1.0b	(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2) 2)
	32.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.2b	(*.f64 (sqrt.f64 2) x)
	23.6b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (pow.f64 (hypot.f64 x x) 1/6))

Compiler

Compiled 1579 to 842 computations (46.7% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (hypot.f64 x x) 1/4)
	0.1b	(hypot.f64 x x)
✓	0.5b	(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2) 2)
✓	0.5b	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2)

series629.0ms (13.9%)

Counts

3 → 36

Calls

3 calls:

219.0ms	(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2) 2)
210.0ms	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2)
199.0ms	(pow.f64 (hypot.f64 x x) 1/4)

rewrite171.0ms (3.8%)

Algorithm

3×	egg-rewrite

Rules

58×	`egg`
54×	`egg`
46×	`egg`

Counts

3 → 158

Calls

3 calls:

75.0ms	(pow.f64 (hypot.f64 x x) 1/4)
48.0ms	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2)
45.0ms	(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	152	6
2	1382	6
3	5047	6
0	8	4
1	174	4
2	1412	4
3	5227	4
0	5	7
1	108	7
2	1093	7
3	4587	7
4	5666	7

simplify86.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

845×	`fma-neg_binary64`
483×	`fma-def_binary64`
395×	`associate-+l+_binary64`
393×	`*-commutative_binary64`
342×	`associate-+r+_binary64`

Counts

194 → 170

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	648
1	68	648
2	114	564
3	379	348
4	1568	312
5	3697	312
6	4996	312
7	4896	312

prune94.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	213	6	219

Error

0.0b

Counts

219 → 6

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
✓	1.0b	(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2) 2)
	32.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.2b	(*.f64 (sqrt.f64 2) x)
▶	23.6b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (pow.f64 (hypot.f64 x x) 1/6))

Compiler

Compiled 2885 to 1685 computations (41.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (hypot.f64 x x))
✓	0.6b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5)
✓	4.0b	(pow.f64 (hypot.f64 x x) 1/6)
✓	21.2b	(pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2)

series1.5s (32.8%)

Counts

4 → 48

Calls

4 calls:

820.0ms	(pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2)
252.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5)
206.0ms	(cbrt.f64 (hypot.f64 x x))
201.0ms	(pow.f64 (hypot.f64 x x) 1/6)

rewrite272.0ms (6%)

Algorithm

4×	egg-rewrite

Rules

53×	`egg`
46×	`egg`
41×	`egg`
34×	`egg`

Counts

4 → 174

Calls

4 calls:

77.0ms	(pow.f64 (hypot.f64 x x) 1/6)
77.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 5)
71.0ms	(cbrt.f64 (hypot.f64 x x))
45.0ms	(pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	168	7
2	1671	7
3	4862	7
0	5	7
1	107	7
2	1099	7
3	4483	7
4	5588	7
0	6	9
1	124	7
2	1309	7
3	4921	7
4	5040	7
0	4	6
1	77	6
2	845	6
3	4565	6
4	5385	6

simplify116.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

390×	`fma-def_binary64`
232×	`distribute-rgt-in_binary64`
211×	`associate-l_binary64`
205×	`exp-diff_binary64`
196×	`associate-r_binary64`

Counts

222 → 189

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	36	828
1	82	828
2	124	672
3	293	480
4	732	480
5	2070	476
6	4494	476
7	4814	476
8	4992	476
9	4815	476

prune96.0ms (2.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	188	7	195

Error

Counts

195 → 7

Alt Table

Status	Error	Program
	41.3b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 10))) (sqrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/3)))) (pow.f64 (hypot.f64 x x) 1/6))
✓	0.1b	(hypot.f64 x x)
✓	1.0b	(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2) 2)
	32.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.2b	(*.f64 (sqrt.f64 2) x)
✓	23.6b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (pow.f64 (hypot.f64 x x) 1/6))

Compiler

Compiled 3682 to 2169 computations (41.1% saved)

regimes187.0ms (4.1%)

Accuracy

Total 0.1b remaining (70.6%)

Threshold costs 0.1b (70.6%)

Counts

56 → 1

Compiler

Compiled 2377 to 1750 computations (26.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end84.0ms (1.9%)

Compiler: Compiled 80 to 54 computations (32.5% saved)

Details

analyze4.0ms (0.1%)

sample741.0ms (16.4%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize2.0ms (0%)

series4.0ms (0.1%)

rewrite141.0ms (3.1%)

simplify12.0ms (0.3%)

prune105.0ms (2.3%)

localize4.0ms (0.1%)

series26.0ms (0.6%)

rewrite156.0ms (3.5%)

simplify6.0ms (0.1%)

prune69.0ms (1.5%)

localize7.0ms (0.2%)

series629.0ms (13.9%)

rewrite171.0ms (3.8%)

simplify86.0ms (1.9%)

prune94.0ms (2.1%)

localize12.0ms (0.3%)

series1.5s (32.8%)

rewrite272.0ms (6%)

simplify116.0ms (2.6%)

prune96.0ms (2.1%)

regimes187.0ms (4.1%)

simplify2.0ms (0%)

end84.0ms (1.9%)

Profiling