Details

sample132.0ms

Algorithm

intervals

Results

18.0ms	194×	body	80	valid
9.0ms	16×	body	5120	valid
7.0ms	17×	body	1280	valid
7.0ms	14×	body	2560	valid
3.0ms	10×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	3×	body	160	valid

simplify128.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (72.0ms)

Iter	Nodes	Cost
0	12	15
1	19	10
2	28	10
3	36	10
4	43	10
5	45	10
done	45	10

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.3b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.6b	(- (hypot re im) re)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `hypot-udef` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 38

Calls

2 calls:

0.0ms	(hypot re im)
9.0ms	(- (hypot re im) re)

series195.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(hypot re im)
106.0ms	(- (hypot re im) re)

simplify1.6s

Counts

44 → 44

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	69	463
1	140	373
2	349	309
3	1568	274
done	5000	247

prune229.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (- (hypot re im) re))
0.6b	(- (hypot re im) re)
0.6b	(- (hypot re im) re)
0.6b	(- (hypot re im) re)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
5×	`cbrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 101

Calls

4 calls:

4.0ms	(cbrt (- (hypot re im) re))
7.0ms	(- (hypot re im) re)
10.0ms	(- (hypot re im) re)
14.0ms	(- (hypot re im) re)

series515.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(cbrt (- (hypot re im) re))
81.0ms	(- (hypot re im) re)
107.0ms	(- (hypot re im) re)
78.0ms	(- (hypot re im) re)

simplify2.7s

Counts

113 → 113

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	114	1462
1	240	1206
2	698	1000
3	2957	885
done	5000	798

prune724.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
0.6b	(- (hypot re im) re)
0.6b	(- (hypot re im) re)
14.7b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`prod-diff`
8×	`add-log-exp`
6×	`fma-neg`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`pow1/3` `fma-udef`

Counts

4 → 79

Calls

4 calls:

2.0ms	(cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
14.0ms	(- (hypot re im) re)
14.0ms	(- (hypot re im) re)
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series701.0ms

Counts

4 → 12

Calls

4 calls:

310.0ms	(cbrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
87.0ms	(- (hypot re im) re)
102.0ms	(- (hypot re im) re)
201.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify2.8s

Counts

91 → 91

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	134	1323
1	305	960
2	1032	802
3	4885	725
done	5000	725

prune632.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.6b	(- (hypot re im) re)
14.6b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))
14.7b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `fma-neg`
2×	`fma-udef`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 61

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
7.0ms	(- (hypot re im) re)
0.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series669.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt (hypot re im))
86.0ms	(- (hypot re im) re)
193.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))
203.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify3.5s

Counts

73 → 73

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	120	931
1	245	762
2	817	538
3	4522	482
done	5000	482

prune688.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.1b

regimes165.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	11	10
done	11	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

589.0ms	297×	body	640	valid
564.0ms	6078×	body	80	valid
327.0ms	673×	body	2560	valid
224.0ms	478×	body	1280	valid
137.0ms	276×	body	5120	valid
23.0ms	129×	body	320	valid
12.0ms	69×	body	160	valid