Details

analyze127.0ms (7.5%)

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)

sample833.0ms (49.1%)

Symmetry

(sort re im)

Results

792.0ms

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`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

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 (0.7%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(hypot.f64 re im)

rewrite29.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

329×	`log1p-expm1-u_binary64`
329×	`expm1-log1p-u_binary64`
294×	`add-log-exp_binary64`
293×	`add-exp-log_binary64`
288×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	79	4
2	919	4

Stop Event

1×	node limit

Counts

1 → 38

Calls

1 calls:

28.0ms

(hypot.f64 re im)

simplify27.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

529×	`cancel-sign-sub-inv_binary64`
527×	`fma-neg_binary64`
262×	`distribute-rgt-neg-in_binary64`
259×	`distribute-lft-neg-in_binary64`
245×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	51	488
1	165	470
2	521	454
3	2342	454

Stop Event

1×	node limit

Counts

62 → 68

prune30.0ms (1.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	2	69

Error

Counts

69 → 2

Alt Table

Status	Error	Program
▶	1.5b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 re im))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 re im))) 3))
✓	0.0b	(hypot.f64 re im)

Compiler

Compiled 849 to 469 computations (44.8% saved)

localize6.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (hypot.f64 re im)))
✓	0.5b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 re im))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 re im))) 3))
✓	0.6b	(cbrt.f64 (hypot.f64 re im))
✓	0.7b	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 re im))) 3)

series111.0ms (6.5%)

Counts

4 → 80

Calls

4 calls:

53.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 re im))) 3)
26.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 re im)))
19.0ms	(cbrt.f64 (hypot.f64 re im))
12.0ms	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 re im))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 re im))) 3))

rewrite40.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

630×	`log1p-expm1-u_binary64`
630×	`expm1-log1p-u_binary64`
314×	`log-prod_binary64`
128×	`log-pow_binary64`
127×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	189	23
2	1951	23

Stop Event

1×	node limit

Counts

4 → 108

Calls

4 calls:

38.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 re im)))
38.0ms	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 re im))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 re im))) 3))
38.0ms	(cbrt.f64 (hypot.f64 re im))
38.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 re im))) 3)

simplify49.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

724×	`times-frac_binary64`
414×	`cancel-sign-sub-inv_binary64`
216×	`fma-neg_binary64`
200×	`distribute-rgt-neg-in_binary64`
199×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	245	2382
1	742	2332
2	2477	2326

Stop Event

1×	node limit

Counts

188 → 214

prune204.0ms (12%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	374	0	374
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	374	2	376

Error

Counts

376 → 2

Alt Table

Status	Error	Program
✓	1.5b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 re im))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 re im))) 3))
✓	0.0b	(hypot.f64 re im)

Compiler

Compiled 9093 to 5194 computations (42.9% saved)

regimes175.0ms (10.3%)

Accuracy

Total 0.0b remaining (25%)

Threshold costs 0.0b (25%)

Counts

29 → 1

Compiler

Compiled 2354 to 1620 computations (31.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4

Stop Event

1×

saturated

end42.0ms (2.5%)

Remove: (sort re im)
Compiler: Compiled 42 to 25 computations (40.5% saved)

Details

analyze127.0ms (7.5%)

sample833.0ms (49.1%)

simplify6.0ms (0.3%)

prune3.0ms (0.2%)

localize2.0ms (0.1%)

series11.0ms (0.7%)

rewrite29.0ms (1.7%)

simplify27.0ms (1.6%)

prune30.0ms (1.8%)

localize6.0ms (0.4%)

series111.0ms (6.5%)

rewrite40.0ms (2.4%)

simplify49.0ms (2.9%)

prune204.0ms (12%)

regimes175.0ms (10.3%)

simplify2.0ms (0.1%)

end42.0ms (2.5%)

Profiling