Details

sample59.0ms

Algorithm

intervals

Results

15.0ms	193×	body	80	valid
15.0ms	30×	body	2560	valid
4.0ms	11×	body	1280	valid
3.0ms	5×	body	5120	valid
3.0ms	9×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify56.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.3b

localize18.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* (+ re (hypot re im)) 2.0))
0.6b	(+ re (hypot re im))

rewrite19.0ms

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:

9.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
9.0ms	(+ re (hypot re im))

series335.0ms

Counts

2 → 6

Calls

2 calls:

267.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
68.0ms	(+ re (hypot re im))

simplify2.2s

Counts

38 → 38

Iterations

Useful iterations: 3 (742.0ms)

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

prune152.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 13.9b

localize14.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
0.6b	(+ re (hypot re im))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

38.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
6.0ms	(+ re (hypot re im))

series377.0ms

Counts

2 → 6

Calls

2 calls:

282.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
94.0ms	(+ re (hypot re im))

simplify855.0ms

Counts

58 → 58

Iterations

Useful iterations: done (852.0ms)

Iter	Nodes	Cost
0	99	619
1	233	584
2	996	548
done	5000	539

prune229.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 13.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
15.1b	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

rewrite7.0ms

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:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

291.0ms	(cbrt re)
270.0ms	(cbrt re)
266.0ms	(cbrt re)
300.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

simplify3.0s

Counts

61 → 61

Iterations

Useful iterations: 3 (112.0ms)

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

prune279.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 13.9b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
15.0b	(fma (* (cbrt re) (cbrt re)) (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re))) (hypot re im))

rewrite8.0ms

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:

2.0ms	(cbrt re)
2.0ms	(cbrt re)
2.0ms	(cbrt re)
1.0ms	(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:

309.0ms	(cbrt re)
320.0ms	(cbrt re)
289.0ms	(cbrt re)
297.0ms	(fma (* (cbrt re) (cbrt re)) (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re))) (hypot re im))

simplify955.0ms

Counts

61 → 61

Iterations

Useful iterations: 3 (190.0ms)

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

prune336.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 13.9b

regimes93.0ms

Accuracy

0% (0.2b remaining)

Error of 12.3b against oracle of 12.1b and baseline of 12.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.0s

Algorithm

intervals

Results

972.0ms	6164×	body	80	valid
285.0ms	652×	body	2560	valid
190.0ms	269×	body	5120	valid
145.0ms	469×	body	1280	valid
57.0ms	244×	body	640	valid
24.0ms	143×	body	320	valid
7.0ms	59×	body	160	valid