Details

sample38.0ms

Algorithm

intervals

Results

9.0ms	203×	body	80	valid
6.0ms	18×	body	2560	valid
4.0ms	19×	body	1280	valid
1.0ms	8×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify35.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.4b

localize7.0ms

Local error

Found 1 expressions with local error:

0.5b	(- (hypot re im) re)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 28

Calls

1 calls:

8.0ms

(- (hypot re im) re)

series75.0ms

Counts

1 → 3

Calls

1 calls:

75.0ms

(- (hypot re im) re)

simplify2.2s

Counts

31 → 31

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	61	403
1	121	318
2	211	257
3	669	222
4	2214	195
done	5002	194

prune68.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.2b

localize11.0ms

Local error

Found 1 expressions with local error:

13.0b

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series138.0ms

Counts

1 → 3

Calls

1 calls:

138.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify2.4s

Counts

13 → 13

Iterations

Useful iterations: 5 (631.0ms)

Iter	Nodes	Cost
0	26	184
1	49	116
2	118	94
3	315	94
4	813	94
5	2245	92
done	5000	92

prune42.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 12.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
12.8b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

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

series473.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (hypot re im))
112.0ms	(cbrt (hypot re im))
112.0ms	(cbrt (hypot re im))
139.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

simplify2.3s

Counts

61 → 61

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	51	580
1	87	570
2	169	423
3	388	381
4	1097	381
5	4130	381
done	5000	381

prune197.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt (hypot re im)))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
12.8b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (- re))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`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` `sqrt-prod`
1×	`fma-udef`

Counts

4 → 52

Calls

4 calls:

2.0ms	(cbrt (sqrt (hypot re im)))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
0.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (- re))

series465.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(cbrt (sqrt (hypot re im)))
108.0ms	(cbrt (hypot re im))
107.0ms	(cbrt (hypot re im))
135.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (- re))

simplify1.4s

Counts

64 → 64

Iterations

Useful iterations: 3 (135.0ms)

Iter	Nodes	Cost
0	81	726
1	145	711
2	299	636
3	711	627
4	2140	627
done	5002	627

prune220.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 12.1b

regimes135.0ms

Accuracy

0% (0.2b remaining)

Error of 13.3b against oracle of 13.0b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample681.0ms

Algorithm

intervals

Results

194.0ms	6051×	body	80	valid
126.0ms	698×	body	2560	valid
70.0ms	469×	body	1280	valid
63.0ms	276×	body	5120	valid
29.0ms	254×	body	640	valid
15.0ms	171×	body	320	valid
5.0ms	81×	body	160	valid