Details

analyze7.0ms (0.2%)

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 8 computations (20% saved)

sample1.4s (35.8%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify117.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1333×	`fma-def_binary64`
773×	`distribute-rgt-out_binary64`
559×	`hypot-def_binary64`
453×	`associate-l_binary64`
451×	`count-2_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	4
2	25	4
3	46	4
4	98	4
5	245	4
6	763	4
7	1382	4
8	2673	4
9	3450	4
10	4144	4
11	4482	4
12	4395	4
13	4766	4
14	4993	4
15	4742	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 12 computations (40% saved)

localize2.0ms (0%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(hypot.f64 x x)

rewrite67.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

438×	`log1p-udef_binary64`
249×	`log1p-expm1-u_binary64`
249×	`expm1-log1p-u_binary64`
229×	`add-cbrt-cube_binary64`
228×	`add-cube-cbrt_binary64`

Counts

1 → 41

Calls

1 calls:

66.0ms

(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

simplify11.0ms (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

53 → 44

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

prune21.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	39	5	44
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	6	45

Error

0.0b

Counts

45 → 6

Alt Table

Status	Error	Program
	26.9b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	33.2b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	32.5b	(*.f64 (sqrt.f64 2) x)
▶	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

Compiler

Compiled 476 to 228 computations (52.1% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series18.0ms (0.5%)

Counts

2 → 0

Calls

2 calls:

12.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
6.0ms	(sqrt.f64 (hypot.f64 x x))

rewrite75.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

688×	`log1p-udef_binary64`
386×	`log1p-expm1-u_binary64`
386×	`expm1-log1p-u_binary64`
339×	`pow1_binary64`
273×	`unpow-prod-down_binary64`

Counts

2 → 89

Calls

2 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	106	10
2	1032	10
3	4509	10
4	5547	10

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune62.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	132	7	139

Error

0.0b

Counts

139 → 7

Alt Table

Status	Error	Program
	26.9b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	33.2b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	32.5b	(*.f64 (sqrt.f64 2) x)
▶	0.3b	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

Compiler

Compiled 1579 to 843 computations (46.6% saved)

localize9.0ms (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)
✓	0.2b	(pow.f64 (hypot.f64 x x) 3/4)
✓	0.3b	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))

series359.0ms (9.3%)

Counts

3 → 36

Calls

3 calls:

178.0ms	(pow.f64 (hypot.f64 x x) 3/4)
173.0ms	(pow.f64 (hypot.f64 x x) 1/4)
8.0ms	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))

rewrite75.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
304×	`log-prod_binary64`
121×	`expm1-udef_binary64`
121×	`log1p-udef_binary64`

Counts

3 → 66

Calls

3 calls:

73.0ms	(pow.f64 (hypot.f64 x x) 1/4)
73.0ms	(pow.f64 (hypot.f64 x x) 3/4)
73.0ms	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	157	18
2	1595	18
3	4966	18
4	4816	18

simplify70.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

765×	`fma-def_binary64`
658×	`fma-neg_binary64`
406×	`associate-l_binary64`
367×	`associate-r_binary64`
240×	`unswap-sqr_binary64`

Counts

102 → 79

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	464
1	74	464
2	122	416
3	274	320
4	632	312
5	1478	312
6	4008	312
7	4950	312
8	4978	312

prune192.0ms (5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	163	4	167
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	165	9	174

Error

0.0b

Counts

174 → 9

Alt Table

Status	Error	Program
	1.0b	(.f64 (pow.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 3) (cbrt.f64 (hypot.f64 x x))) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
	32.5b	(*.f64 (sqrt.f64 2) x)
	26.9b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	0.6b	(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3)) (pow.f64 (hypot.f64 x x) 3/4))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	1.3b	(.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3)) 3/4))
▶	0.6b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 3) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

Compiler

Compiled 2770 to 1449 computations (47.7% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (hypot.f64 x x) 3/4)
✓	0.3b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 3) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
✓	0.6b	(cbrt.f64 (hypot.f64 x x))
✓	0.8b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)

series406.0ms (10.5%)

Counts

3 → 36

Calls

3 calls:

221.0ms	(cbrt.f64 (hypot.f64 x x))
181.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
4.0ms	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 3) 1/4) (pow.f64 (hypot.f64 x x) 3/4))

rewrite102.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

728×	`log1p-expm1-u_binary64`
728×	`expm1-log1p-u_binary64`
144×	`expm1-udef_binary64`
144×	`log1p-udef_binary64`
95×	`add-log-exp_binary64`

Counts

3 → 76

Calls

3 calls:

101.0ms	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 3) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
101.0ms	(cbrt.f64 (hypot.f64 x x))
101.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	223	14
2	1930	14
3	4977	14
4	4959	14
5	4764	14

simplify95.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

708×	`associate-l_binary64`
577×	`associate-r_binary64`
408×	`unswap-sqr_binary64`
401×	`fma-def_binary64`
250×	`fma-neg_binary64`

Counts

112 → 77

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	28	648
1	75	648
2	123	612
3	347	276
4	1065	264
5	4300	264
6	4996	264
7	4869	264

prune252.0ms (6.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	104	10	114

Error

0.0b

Counts

114 → 10

Alt Table

Status	Error	Program
	1.0b	(.f64 (pow.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 3) (cbrt.f64 (hypot.f64 x x))) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
	32.5b	(*.f64 (sqrt.f64 2) x)
	26.9b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
	0.6b	(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3)) (pow.f64 (hypot.f64 x x) 3/4))
	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	15.6b	(pow.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (hypot.f64 x x)) 3/4)
	1.3b	(.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3)) 3/4))
✓	0.6b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 3) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

Compiler

Compiled 1999 to 1137 computations (43.1% saved)

regimes236.0ms (6.1%)

Accuracy

Total 0.1b remaining (86.9%)

Threshold costs 0.1b (86.9%)

Counts

53 → 1

Compiler

Compiled 3002 to 1938 computations (35.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end268.0ms (7%)

Compiler: Compiled 133 to 83 computations (37.6% saved)

Details

analyze7.0ms (0.2%)

sample1.4s (35.8%)

simplify117.0ms (3%)

prune3.0ms (0.1%)

localize2.0ms (0%)

series3.0ms (0.1%)

rewrite67.0ms (1.7%)

simplify11.0ms (0.3%)

prune21.0ms (0.5%)

localize4.0ms (0.1%)

series18.0ms (0.5%)

rewrite75.0ms (1.9%)

simplify6.0ms (0.2%)

prune62.0ms (1.6%)

localize9.0ms (0.2%)

series359.0ms (9.3%)

rewrite75.0ms (1.9%)

simplify70.0ms (1.8%)

prune192.0ms (5%)

localize12.0ms (0.3%)

series406.0ms (10.5%)

rewrite102.0ms (2.6%)

simplify95.0ms (2.5%)

prune252.0ms (6.5%)

regimes236.0ms (6.1%)

simplify2.0ms (0%)

end268.0ms (7%)

Profiling