Details

analyze452.0ms (15.8%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample1.8s (61.5%)

Alt Table

Status	Error	Program
▶	39.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Results

772.0ms	6230×	body	128	valid
360.0ms	582×	body	4096	valid
314.0ms	634×	body	2048	valid
169.0ms	425×	body	1024	valid
81.0ms	265×	body	512	valid
30.0ms	120×	body	256	valid

Compiler

Compiled 87 to 62 computations (28.7% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 re re) (.f64 im im))
✓	0.5b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
✓	31.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series32.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

13.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
12.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
6.0ms	(+.f64 (.f64 re re) (.f64 im im))

rewrite56.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

909×	`log1p-expm1-u_binary64`
909×	`expm1-log1p-u_binary64`
102×	`egg-rr`
88×	`add-sqr-sqrt_binary64`
84×	`add-log-exp_binary64`

Counts

3 → 102

Calls

3 calls:

53.0ms	(+.f64 (.f64 re re) (.f64 im im))
53.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
53.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	179	18
2	2259	18
3	5449	18
0	0	0
1	0	0

prune108.0ms (3.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	170	4	174
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	171	4	175

Error

6.7b

Counts

175 → 4

Alt Table

Status	Error	Program
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	49.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	12.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (hypot.f64 re im) re))))
	45.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1 im))))

Compiler

Compiled 3223 to 2213 computations (31.3% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.5b	(+.f64 (hypot.f64 re im) re)

series25.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(+.f64 (hypot.f64 re im) re)
12.0ms	(hypot.f64 re im)

rewrite97.0ms (3.4%)

Algorithm

2×	batch-egg-rewrite

Rules

569×	`log1p-expm1-u_binary64`
569×	`expm1-log1p-u_binary64`
506×	`prod-diff_binary64`
389×	`fma-udef_binary64`
191×	`fma-def_binary64`

Counts

2 → 56

Calls

2 calls:

95.0ms	(hypot.f64 re im)
95.0ms	(+.f64 (hypot.f64 re im) re)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	110	11
2	1412	11
3	4851	11
4	4781	11
5	4963	11
0	0	0
1	0	0

prune55.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	104	4	108

Error

6.7b

Counts

108 → 4

Alt Table

Status	Error	Program
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	49.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	12.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (hypot.f64 re im) re))))
▶	45.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1 im))))

Compiler

Compiled 1941 to 1319 computations (32% saved)

localize6.0ms (0.2%)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Error

6.7b

Counts

4 → 4

Alt Table

Status	Error	Program
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	49.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	12.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (hypot.f64 re im) re))))
✓	45.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1 im))))

Compiler

Compiled 66 to 56 computations (15.2% saved)

localize4.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

6.7b

Counts

4 → 4

Alt Table

Status	Error	Program
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	49.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	12.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (hypot.f64 re im) re))))
✓	45.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1 im))))

Compiler

Compiled 44 to 37 computations (15.9% saved)

regimes166.0ms (5.8%)

Accuracy

Total 2.7b remaining (26.8%)

Threshold costs 0b (0%)

Counts

17 → 2

Compiler

Compiled 1834 to 1455 computations (20.7% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	58
1	37	58
2	37	58

end73.0ms (2.6%)

Compiler: Compiled 124 to 97 computations (21.8% saved)

Details

analyze452.0ms (15.8%)

sample1.8s (61.5%)

localize11.0ms (0.4%)

series32.0ms (1.1%)

rewrite56.0ms (1.9%)

prune108.0ms (3.8%)

localize7.0ms (0.2%)

series25.0ms (0.9%)

rewrite97.0ms (3.4%)

prune55.0ms (1.9%)

localize6.0ms (0.2%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

prune2.0ms (0.1%)

regimes166.0ms (5.8%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end73.0ms (2.6%)

Profiling