Details

sample206.0ms

Algorithm

intervals

Results

21.0ms	198×	body	80	valid
13.0ms	23×	body	2560	valid
7.0ms	16×	body	1280	valid
5.0ms	7×	body	5120	valid
2.0ms	5×	body	640	valid
2.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify782.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
5	44
4	42
3	35
2	27
1	19
0	12

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize25.0ms

Local error

Found 1 expressions with local error:

0.9b	(- (hypot re im) re)

rewrite19.0ms

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×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

15.0ms

(- (hypot re im) re)

series129.0ms

Counts

1 → 3

Calls

1 calls:

129.0ms

(- (hypot re im) re)

simplify3.4s

Counts

31 → 31

Iterations

Iter	Nodes
done	5115
5	3569
4	1349
3	619
2	237
1	130
0	61

prune202.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 12.1b

localize30.0ms

Local error

Found 1 expressions with local error:

14.2b

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

1.0ms

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

series253.0ms

Counts

1 → 3

Calls

1 calls:

253.0ms

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

simplify3.3s

Counts

13 → 13

Iterations

Iter	Nodes
done	5000
5	4960
4	1418
3	455
2	135
1	52
0	28

prune108.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 12.1b

localize28.0ms

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))
14.0b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `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))

series672.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (hypot re im))
195.0ms	(cbrt (hypot re im))
153.0ms	(cbrt (hypot re im))
178.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

simplify2.0s

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
4	1845
3	564
2	193
1	88
0	51

prune475.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 12.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
14.0b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))
14.0b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`

Counts

4 → 46

Calls

4 calls:

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

series650.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (hypot re im))
126.0ms	(cbrt (hypot re im))
211.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))
165.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

simplify2.2s

Counts

58 → 58

Iterations

Iter	Nodes
done	5001
4	1845
3	564
2	193
1	88
0	51

prune503.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 12.1b

regimes290.0ms

Accuracy

0% (0.2b remaining)

Error of 13.1b against oracle of 12.9b and baseline of 13.1b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

923.0ms	6033×	body	80	valid
399.0ms	677×	body	2560	valid
289.0ms	479×	body	1280	valid
157.0ms	313×	body	5120	valid
120.0ms	274×	body	640	valid
27.0ms	142×	body	320	valid
10.0ms	82×	body	160	valid