Details

sample54.0ms

Algorithm

intervals

Results

15.0ms	202×	body	80	valid
9.0ms	19×	body	2560	valid
5.0ms	12×	body	1280	valid
3.0ms	11×	body	640	valid
3.0ms	6×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify32.0ms

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

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize9.0ms

Local error

Found 1 expressions with local error:

0.8b	(+ re (hypot re im))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity`
3×	`fma-def` `add-log-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`

Counts

1 → 17

Calls

1 calls:

6.0ms

(+ re (hypot re im))

series99.0ms

Counts

1 → 3

Calls

1 calls:

99.0ms

(+ re (hypot re im))

simplify1.3s

Counts

20 → 20

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	31	133
1	75	127
2	170	117
3	429	117
4	1222	117
done	5001	117

prune62.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 11.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
13.1b	(fma (* (cbrt re) (cbrt re)) (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 re) (hypot re im))

series1.1s

Counts

4 → 12

Calls

4 calls:

293.0ms	(cbrt re)
263.0ms	(cbrt re)
284.0ms	(cbrt re)
274.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

simplify2.9s

Counts

61 → 61

Iterations

Useful iterations: 3 (166.0ms)

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

prune265.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 11.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt re)
0.6b	(cbrt re)
0.6b	(cbrt re)
13.1b	(fma (* (cbrt re) (cbrt re)) (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (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 (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re))) (hypot re im))

series1.2s

Counts

4 → 12

Calls

4 calls:

294.0ms	(cbrt re)
332.0ms	(cbrt re)
287.0ms	(cbrt re)
288.0ms	(fma (* (cbrt re) (cbrt re)) (* (* (cbrt (cbrt re)) (cbrt (cbrt re))) (cbrt (cbrt re))) (hypot re im))

simplify1.0s

Counts

61 → 61

Iterations

Useful iterations: 3 (152.0ms)

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

prune373.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 11.6b

localize26.0ms

Local error

Found 2 expressions with local error:

0.8b	(+ re (hypot re im))
3.2b	(expm1 (log1p (+ re (hypot re im))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

6.0ms	(+ re (hypot re im))
0.0ms	(expm1 (log1p (+ re (hypot re im))))

series266.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(+ re (hypot re im))
193.0ms	(expm1 (log1p (+ re (hypot re im))))

simplify1.1s

Counts

34 → 34

Iterations

Useful iterations: 3 (281.0ms)

Iter	Nodes	Cost
0	53	263
1	122	230
2	280	204
3	1167	196
done	5000	196

prune142.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 11.6b

regimes89.0ms

Accuracy

0% (0.2b remaining)

Error of 13.3b against oracle of 13.1b and baseline of 13.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	6025×	body	80	valid
335.0ms	696×	body	2560	valid
162.0ms	466×	body	1280	valid
147.0ms	290×	body	5120	valid
79.0ms	296×	body	640	valid
30.0ms	150×	body	320	valid
10.0ms	77×	body	160	valid