Details

analyze131.0ms (7.3%)

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
37.5%	62.4%	0.1%	6
56.2%	43.7%	0.1%	7
65.6%	34.3%	0.1%	8
76.5%	23.4%	0.1%	9
82%	18%	0.1%	10
87.8%	12.1%	0.1%	11
90.7%	9.2%	0.1%	12
93.8%	6.1%	0.1%	13
95.3%	4.6%	0.1%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample1.0s (56.6%)

Symmetry

(sort re im)

Results

983.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`hypot-def_binary64`
2×	`fma-def_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4
2	12	4
3	12	4

prune3.0ms (0.2%)

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(hypot.f64 re im)

Compiler

Compiled 23 to 13 computations (43.5% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)

series11.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(hypot.f64 re im)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(hypot.f64 re im)

simplify52.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

943×	`fma-neg_binary64`
529×	`cancel-sign-sub-inv_binary64`
273×	`associate-/r/_binary64`
262×	`distribute-rgt-neg-in_binary64`
259×	`distribute-lft-neg-in_binary64`

Counts

34 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	64	568
1	177	541
2	507	525
3	2142	525
4	4490	525
5	5063	525

prune19.0ms (1.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	2	43

Error

Counts

43 → 2

Alt Table

Status	Error	Program
✓	0.0b	(hypot.f64 re im)
▶	1.3b	(.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))

Compiler

Compiled 577 to 339 computations (41.2% saved)

localize5.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))
✓	0.5b	(*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im)))
✓	0.5b	(cbrt.f64 (hypot.f64 re im))

series96.0ms (5.3%)

Counts

3 → 72

Calls

3 calls:

44.0ms	(*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im)))
38.0ms	(cbrt.f64 (hypot.f64 re im))
13.0ms	(.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))

rewrite21.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

11.0ms	(.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))
4.0ms	(*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im)))
1.0ms	(cbrt.f64 (hypot.f64 re im))

simplify106.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

647×	`fma-def_binary64`
626×	`fma-neg_binary64`
314×	`cancel-sign-sub-inv_binary64`
188×	`associate-r_binary64`
188×	`unswap-sqr_binary64`

Counts

165 → 195

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	3284
1	656	3131
2	1928	2968
3	4753	2968
4	5183	2968

prune178.0ms (9.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	415	0	415
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	415	2	417

Error

Counts

417 → 2

Alt Table

Status	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	1.3b	(.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))

Compiler

Compiled 9814 to 4079 computations (58.4% saved)

regimes106.0ms (5.9%)

Accuracy

Total 0.0b remaining (16.7%)

Threshold costs 0.0b (16.7%)

Counts

15 → 1

Compiler

Compiled 1107 to 671 computations (39.4% saved)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	4	4

end40.0ms (2.2%)

Remove: (sort re im)
Compiler: Compiled 41 to 21 computations (48.8% saved)

Details

analyze131.0ms (7.3%)

sample1.0s (56.6%)

simplify6.0ms (0.3%)

prune3.0ms (0.2%)

localize2.0ms (0.1%)

series11.0ms (0.6%)

rewrite1.0ms (0%)

simplify52.0ms (2.9%)

prune19.0ms (1.1%)

localize5.0ms (0.3%)

series96.0ms (5.3%)

rewrite21.0ms (1.2%)

simplify106.0ms (5.9%)

prune178.0ms (9.9%)

regimes106.0ms (5.9%)

simplify1.0ms (0.1%)

end40.0ms (2.2%)

Profiling