Details

sample107.0ms

Algorithm

intervals

Results

11.0ms	195×	body	80	valid
6.0ms	22×	body	2560	valid
2.0ms	11×	body	1280	valid
2.0ms	13×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	6×	body	160	valid
0.0ms	3×	body	320	valid

simplify95.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (14.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
1.3b	(- (hypot re im) re)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 38

Calls

2 calls:

1.0ms	(hypot re im)
19.0ms	(- (hypot re im) re)

series178.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(hypot re im)
108.0ms	(- (hypot re im) re)

simplify3.5s

Counts

44 → 44

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	69	463
1	130	370
2	224	300
3	683	256
4	2191	247
done	5001	246

prune174.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
14.9b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 30

Calls

3 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series345.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(hypot re im)
67.0ms	(hypot re im)
202.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify3.1s

Counts

39 → 39

Iterations

Useful iterations: 5 (1.7s)

Iter	Nodes	Cost
0	39	304
1	64	232
2	150	198
3	383	198
4	980	198
5	3255	196
done	5000	196

prune288.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 13.0b

localize21.0ms

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))
14.7b	(fma (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (sqrt (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 (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (sqrt (hypot re im)) (- re))

series761.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(cbrt (hypot re im))
207.0ms	(cbrt (hypot re im))
164.0ms	(cbrt (hypot re im))
245.0ms	(fma (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))) (sqrt (hypot re im)) (- re))

simplify3.7s

Counts

61 → 61

Iterations

Useful iterations: 5 (2.0s)

Iter	Nodes	Cost
0	57	681
1	105	670
2	225	511
3	544	469
4	1380	403
5	4358	401
done	5000	401

prune440.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 13.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (sqrt (hypot re im)))
0.6b	(cbrt (sqrt (hypot re im)))
14.7b	(fma (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))) (sqrt (hypot re im)) (- re))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod`
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 → 55

Calls

4 calls:

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

series735.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(cbrt (hypot re im))
177.0ms	(cbrt (sqrt (hypot re im)))
189.0ms	(cbrt (sqrt (hypot re im)))
204.0ms	(fma (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))) (sqrt (hypot re im)) (- re))

simplify1.8s

Counts

67 → 67

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	87	882
1	163	861
2	351	651
3	808	642
4	2210	642
done	5000	640

prune473.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.0b

regimes173.0ms

Accuracy

0% (0.3b remaining)

Error of 14.0b against oracle of 13.7b and baseline of 14.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.0s	5957×	body	80	valid
351.0ms	706×	body	2560	valid
187.0ms	507×	body	1280	valid
146.0ms	260×	body	5120	valid
81.0ms	319×	body	640	valid
29.0ms	173×	body	320	valid
13.0ms	78×	body	160	valid