Details

sample39.0ms

Algorithm

intervals

Results

11.0ms	205×	body	80	valid
6.0ms	20×	body	2560	valid
3.0ms	12×	body	1280	valid
1.0ms	8×	body	640	valid
1.0ms	5×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	12	15
1	24	10
2	30	10
3	32	10
done	32	10

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (+ re (hypot re im)) 2.0))
1.2b	(+ re (hypot re im))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-*l/` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `pow1/2` `pow-prod-down` `sum-log` `sqrt-prod` `distribute-lft-out`

Counts

2 → 32

Calls

2 calls:

30.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
6.0ms	(+ re (hypot re im))

series340.0ms

Counts

2 → 6

Calls

2 calls:

247.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
93.0ms	(+ re (hypot re im))

simplify2.2s

Counts

38 → 38

Iterations

Useful iterations: 3 (774.0ms)

Iter	Nodes	Cost
0	75	354
1	173	325
2	588	302
3	3575	295
done	5000	295

prune207.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 10.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
12.1b	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt re)
2.0ms	(cbrt re)
2.0ms	(cbrt re)
1.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

series1.2s

Counts

4 → 12

Calls

4 calls:

266.0ms	(cbrt re)
271.0ms	(cbrt re)
327.0ms	(cbrt re)
292.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

simplify3.0s

Counts

61 → 61

Iterations

Useful iterations: 3 (142.0ms)

Iter	Nodes	Cost
0	42	372
1	65	360
2	158	286
3	581	244
4	2880	244
done	5001	244

prune273.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 10.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
12.0b	(fma (* (cbrt re) (cbrt re)) (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re))) (hypot re im))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt re)
1.0ms	(cbrt re)
1.0ms	(cbrt re)
0.0ms	(fma (* (cbrt re) (cbrt re)) (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re))) (hypot re im))

series1.2s

Counts

4 → 12

Calls

4 calls:

290.0ms	(cbrt re)
309.0ms	(cbrt re)
329.0ms	(cbrt re)
283.0ms	(fma (* (cbrt re) (cbrt re)) (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re))) (hypot re im))

simplify918.0ms

Counts

61 → 61

Iterations

Useful iterations: 3 (181.0ms)

Iter	Nodes	Cost
0	44	489
1	73	477
2	191	331
3	875	244
done	5000	244

prune383.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 10.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
12.0b	(fma (* (cbrt re) (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re)))) (cbrt re) (hypot re im))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt re)
1.0ms	(cbrt re)
1.0ms	(cbrt re)
0.0ms	(fma (* (cbrt re) (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re)))) (cbrt re) (hypot re im))

series1.3s

Counts

4 → 12

Calls

4 calls:

275.0ms	(cbrt re)
348.0ms	(cbrt re)
348.0ms	(cbrt re)
308.0ms	(fma (* (cbrt re) (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re)))) (cbrt re) (hypot re im))

simplify1.1s

Counts

61 → 61

Iterations

Useful iterations: 3 (200.0ms)

Iter	Nodes	Cost
0	45	489
1	75	477
2	204	353
3	924	244
done	5001	244

prune337.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 10.6b

regimes75.0ms

Accuracy

0% (0.1b remaining)

Error of 12.7b against oracle of 12.5b and baseline of 12.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	10
1	12	10
done	12	10

end0.0ms

sample2.1s

Algorithm

intervals

Results

670.0ms	503×	body	1280	valid
443.0ms	6130×	body	80	valid
396.0ms	667×	body	2560	valid
158.0ms	257×	body	5120	valid
65.0ms	239×	body	640	valid
27.0ms	143×	body	320	valid
7.0ms	61×	body	160	valid