Details

analyze542.0ms (11.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample2.1s (45.4%)

Results

903.0ms	6320×	body	128	valid
424.0ms	634×	body	2048	valid
413.0ms	517×	body	4096	valid
194.0ms	428×	body	1024	valid
74.0ms	220×	body	512	valid
32.0ms	137×	body	256	valid

Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify29.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

203×	`fma-def_binary64`
142×	`fma-neg_binary64`
51×	`distribute-rgt-in_binary64`
42×	`cancel-sign-sub-inv_binary64`
28×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

prune4.0ms (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

11.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
✓	0.8b	(-.f64 (hypot.f64 re im) re)

series43.0ms (0.9%)

Counts

2 → 32

Calls

2 calls:

31.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
11.0ms	(-.f64 (hypot.f64 re im) re)

rewrite54.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

811×	`log1p-expm1-u_binary64`
811×	`expm1-log1p-u_binary64`
410×	`prod-diff_binary64`
85×	`add-sqr-sqrt_binary64`
81×	`add-log-exp_binary64`

Counts

2 → 74

Calls

2 calls:

52.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
52.0ms	(-.f64 (hypot.f64 re im) re)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	172	19
2	2053	19
3	5735	19

simplify45.0ms (1%)

Algorithm

1×	egg-herbie

Rules

529×	`fma-def_binary64`
374×	`associate-l_binary64`
337×	`associate-/l*_binary64`
311×	`times-frac_binary64`
237×	`associate-/r*_binary64`

Counts

106 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	1017
1	419	994
2	1385	945
3	5001	945

prune85.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	113	6	119
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	113	7	120

Error

0.2b

Counts

120 → 7

Alt Table

Status	Error	Program
	55.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	54.4b	(.f64 1/2 (+.f64 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (-.f64 (.f64 1/32 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2))) (.f64 1/256 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2)))))) (.f64 (/.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) -1/16))))
	50.0b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	43.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (+.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 re)) (-.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 re))))))
	27.5b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
▶	11.7b	(.f64 1/2 (pow.f64 (pow.f64 (.f64 (-.f64 (hypot.f64 re im) re) 2) 1/4) 2))

Compiler

Compiled 2837 to 1941 computations (31.6% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 (-.f64 (hypot.f64 re im) re) 2) 1/4)
✓	0.4b	(pow.f64 (pow.f64 (*.f64 (-.f64 (hypot.f64 re im) re) 2) 1/4) 2)
	0.8b	(-.f64 (hypot.f64 re im) re)

series73.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

42.0ms	(pow.f64 (pow.f64 (*.f64 (-.f64 (hypot.f64 re im) re) 2) 1/4) 2)
31.0ms	(pow.f64 (*.f64 (-.f64 (hypot.f64 re im) re) 2) 1/4)

rewrite50.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

468×	`log-prod_binary64`
410×	`prod-diff_binary64`
204×	`fma-def_binary64`
182×	`expm1-udef_binary64`
182×	`log1p-udef_binary64`

Counts

2 → 56

Calls

2 calls:

49.0ms	(pow.f64 (*.f64 (-.f64 (hypot.f64 re im) re) 2) 1/4)
49.0ms	(pow.f64 (pow.f64 (*.f64 (-.f64 (hypot.f64 re im) re) 2) 1/4) 2)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	226	25
2	2468	25
3	4975	25

simplify73.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

834×	`associate-/r*_binary64`
643×	`fma-def_binary64`
332×	`associate-/r/_binary64`
241×	`cancel-sign-sub-inv_binary64`
163×	`unswap-sqr_binary64`

Counts

104 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	264	2943
1	677	2871
2	2207	2535
3	5768	2535

prune205.0ms (4.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	216	3	219
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	219	7	226

Error

0.1b

Counts

226 → 7

Alt Table

Status	Error	Program
	50.0b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
	49.9b	(.f64 1/2 (pow.f64 (.f64 (sqrt.f64 im) (pow.f64 (/.f64 1 re) 1/4)) 2))
	55.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
▶	11.6b	(.f64 1/2 (.f64 (pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2) (pow.f64 (pow.f64 2 1/4) 2)))
	52.0b	(.f64 1/2 (pow.f64 (fma.f64 (.f64 (/.f64 (.f64 im im) (.f64 re re)) (.f64 (sqrt.f64 im) (pow.f64 (/.f64 1 re) 1/4))) -1/16 (.f64 (sqrt.f64 im) (pow.f64 (/.f64 1 re) 1/4))) 2))
	54.4b	(.f64 1/2 (+.f64 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (-.f64 (.f64 1/32 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2))) (.f64 1/256 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 im 5)) (sqrt.f64 1/2)))))) (.f64 (/.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) -1/16))))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 6692 to 4933 computations (26.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2) (pow.f64 (pow.f64 2 1/4) 2))
✓	0.4b	(pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2)
	0.8b	(-.f64 (hypot.f64 re im) re)
✓	1.0b	(pow.f64 (pow.f64 2 1/4) 2)

series63.0ms (1.4%)

Counts

3 → 32

Calls

3 calls:

42.0ms	(pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2)
21.0ms	(*.f64 (pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2) (pow.f64 (pow.f64 2 1/4) 2))
0.0ms	(pow.f64 (pow.f64 2 1/4) 2)

rewrite60.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

527×	`log-prod_binary64`
410×	`prod-diff_binary64`
243×	`fma-def_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`

Counts

3 → 72

Calls

3 calls:

58.0ms	(*.f64 (pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2) (pow.f64 (pow.f64 2 1/4) 2))
58.0ms	(pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2)
58.0ms	(pow.f64 (pow.f64 2 1/4) 2)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	270	24
2	2743	24
3	5438	24

simplify68.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

579×	`associate-/l*_binary64`
478×	`fma-def_binary64`
460×	`associate-/r*_binary64`
256×	`cancel-sign-sub-inv_binary64`
248×	`fma-neg_binary64`

Counts

104 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	1697
1	520	1593
2	1612	1415
3	4898	1415
4	4975	1415

prune166.0ms (3.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	200	2	202
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	201	8	209

Error

0.0b

Counts

209 → 8

Alt Table

Status	Error	Program
	50.0b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
	49.9b	(.f64 1/2 (pow.f64 (.f64 (sqrt.f64 im) (pow.f64 (/.f64 1 re) 1/4)) 2))
	49.9b	(.f64 1/2 (.f64 (pow.f64 (*.f64 (sqrt.f64 im) (pow.f64 (/.f64 1/2 re) 1/4)) 2) (pow.f64 (pow.f64 2 1/4) 2)))
	55.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
✓	11.6b	(.f64 1/2 (.f64 (pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2) (pow.f64 (pow.f64 2 1/4) 2)))
	52.0b	(.f64 1/2 (pow.f64 (fma.f64 (.f64 (/.f64 (.f64 im im) (.f64 re re)) (.f64 (sqrt.f64 im) (pow.f64 (/.f64 1 re) 1/4))) -1/16 (.f64 (sqrt.f64 im) (pow.f64 (/.f64 1 re) 1/4))) 2))
▶	49.8b	(.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 re)) im))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 5706 to 4141 computations (27.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 1 re))
✓	0.1b	(*.f64 (sqrt.f64 (/.f64 1 re)) im)

series17.0ms (0.4%)

Counts

2 → 0

Calls

2 calls:

13.0ms	(*.f64 (sqrt.f64 (/.f64 1 re)) im)
4.0ms	(sqrt.f64 (/.f64 1 re))

rewrite44.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

543×	`log1p-expm1-u_binary64`
543×	`expm1-log1p-u_binary64`
453×	`unpow-prod-down_binary64`
296×	`log-prod_binary64`
161×	`pow2_binary64`

Counts

2 → 69

Calls

2 calls:

42.0ms	(sqrt.f64 (/.f64 1 re))
42.0ms	(*.f64 (sqrt.f64 (/.f64 1 re)) im)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	137	10
2	1474	10
3	5389	10

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune33.0ms (0.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	4	1	5
Picked	0	1	1
Done	0	2	2
Total	71	6	77

Error

0.0b

Counts

77 → 6

Alt Table

Status	Error	Program
✓	11.6b	(.f64 1/2 (.f64 (pow.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 1/4) 2) (pow.f64 (pow.f64 2 1/4) 2)))
	52.0b	(.f64 1/2 (pow.f64 (fma.f64 (.f64 (/.f64 (.f64 im im) (.f64 re re)) (.f64 (sqrt.f64 im) (pow.f64 (/.f64 1 re) 1/4))) -1/16 (.f64 (sqrt.f64 im) (pow.f64 (/.f64 1 re) 1/4))) 2))
✓	49.8b	(.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 re)) im))
	49.9b	(*.f64 1/2 (pow.f64 (sqrt.f64 (/.f64 im (sqrt.f64 re))) 2))
	49.8b	(*.f64 1/2 (/.f64 im (sqrt.f64 re)))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 916 to 652 computations (28.8% saved)

regimes721.0ms (15.6%)

Accuracy

Total 6.3b remaining (98.6%)

Threshold costs 0b (0%)

Counts

70 → 2

Compiler

Compiled 8760 to 7042 computations (19.6% saved)

bsearch2.0ms (0%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	50
1	34	50
2	39	50
3	41	50
4	42	50
5	42	50

end99.0ms (2.2%)

Compiler: Compiled 162 to 121 computations (25.3% saved)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

Details

analyze542.0ms (11.7%)

sample2.1s (45.4%)

simplify29.0ms (0.6%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series43.0ms (0.9%)

rewrite54.0ms (1.2%)

simplify45.0ms (1%)

prune85.0ms (1.8%)

localize10.0ms (0.2%)

series73.0ms (1.6%)

rewrite50.0ms (1.1%)

simplify73.0ms (1.6%)

prune205.0ms (4.4%)

localize13.0ms (0.3%)

series63.0ms (1.4%)

rewrite60.0ms (1.3%)

simplify68.0ms (1.5%)

prune166.0ms (3.6%)

localize5.0ms (0.1%)

series17.0ms (0.4%)

rewrite44.0ms (0.9%)

simplify6.0ms (0.1%)

prune33.0ms (0.7%)

regimes721.0ms (15.6%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end99.0ms (2.2%)

Profiling

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15