Details

sample31.0ms

Algorithm

intervals

Results

8.0ms	27×	body	2560	valid
6.0ms	184×	body	80	valid
3.0ms	13×	body	5120	valid
2.0ms	15×	body	1280	valid
2.0ms	14×	body	640	valid
0.0ms	3×	body	320	valid

simplify27.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(- (hypot re im) re)

rewrite8.0ms

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:

7.0ms

(- (hypot re im) re)

series64.0ms

Counts

1 → 3

Calls

1 calls:

64.0ms

(- (hypot re im) re)

simplify2.1s

Counts

31 → 31

Iterations

Useful iterations: done (2.1s)

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

prune65.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.6b

localize10.0ms

Local error

Found 1 expressions with local error:

17.7b

(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))

series140.0ms

Counts

1 → 3

Calls

1 calls:

140.0ms

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

simplify2.3s

Counts

13 → 13

Iterations

Useful iterations: 5 (596.0ms)

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

prune41.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 14.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
17.4b	(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))

series461.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (hypot re im))
106.0ms	(cbrt (hypot re im))
106.0ms	(cbrt (hypot re im))
139.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

simplify2.4s

Counts

61 → 61

Iterations

Useful iterations: 3 (69.0ms)

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

prune212.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 14.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
17.4b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (sqrt (cbrt (hypot re im))) (sqrt (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))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (- re))

series471.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(cbrt (hypot re im))
111.0ms	(cbrt (hypot re im))
110.0ms	(cbrt (hypot re im))
140.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (- re))

simplify1.1s

Counts

61 → 61

Iterations

Useful iterations: 4 (265.0ms)

Iter	Nodes	Cost
0	53	671
1	93	570
2	195	423
3	453	381
4	1409	375
done	5000	375

prune214.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 14.6b

regimes103.0ms

Accuracy

0% (0.2b remaining)

Error of 13.0b against oracle of 12.8b and baseline of 13.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample685.0ms

Algorithm

intervals

Results

195.0ms	6038×	body	80	valid
130.0ms	694×	body	2560	valid
74.0ms	512×	body	1280	valid
65.0ms	298×	body	5120	valid
28.0ms	244×	body	640	valid
12.0ms	138×	body	320	valid
4.0ms	76×	body	160	valid