Details

sample199.0ms

Algorithm

intervals

Results

70.0ms	198×	body	80	valid
17.0ms	24×	body	2560	valid
9.0ms	11×	body	5120	valid
6.0ms	11×	body	1280	valid
2.0ms	5×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	3×	body	160	valid

simplify454.0ms

Counts

1 → 1

Iterations

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

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.6b

localize83.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* (- (hypot re im) re) 2.0))
0.7b	(- (hypot re im) re)

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`prod-diff`
6×	`pow1`
5×	`add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3--` `sqrt-div` `associate-*l/` `flip--`
1×	`hypot-udef` `sub-neg` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 56

Calls

3 calls:

2.0ms	(hypot re im)
42.0ms	(sqrt (* (- (hypot re im) re) 2.0))
35.0ms	(- (hypot re im) re)

series531.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(hypot re im)
334.0ms	(sqrt (* (- (hypot re im) re) 2.0))
126.0ms	(- (hypot re im) re)

simplify4.7s

Counts

65 → 65

Iterations

Iter	Nodes
done	5002
3	1783
2	567
1	247
0	118

prune765.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.4b

localize122.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (* (- (hypot re im) re) 2.0))
0.4b	(* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (* (- (hypot re im) re) 2.0))))
0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

76×	`sqrt-pow1`
64×	`pow1`
42×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
27×	`sqrt-prod`
26×	`sqrt-div` `add-cube-cbrt`
23×	`pow-prod-down`
19×	`pow1/2`
18×	`prod-diff`
16×	`associate-*l/`
14×	`pow-prod-up`
9×	`flip3--` `swap-sqr` `flip--`
8×	`pow-sqr` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log`
4×	`expm1-log1p-u` `frac-times` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
2×	`sub-neg` `diff-log` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 156

Calls

4 calls:

21.0ms	(sqrt (* (- (hypot re im) re) 2.0))
239.0ms	(* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (* (- (hypot re im) re) 2.0))))
17.0ms	(- (hypot re im) re)
18.0ms	(- (hypot re im) re)

series920.0ms

Counts

4 → 12

Calls

4 calls:

345.0ms	(sqrt (* (- (hypot re im) re) 2.0))
353.0ms	(* (sqrt (sqrt (* (- (hypot re im) re) 2.0))) (sqrt (sqrt (* (- (hypot re im) re) 2.0))))
122.0ms	(- (hypot re im) re)
100.0ms	(- (hypot re im) re)

simplify5.8s

Counts

168 → 168

Iterations

Iter	Nodes
done	5001
3	2710
2	935
1	390
0	184

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.4b

localize291.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 116

Calls

4 calls:

31.0ms	(- (hypot re im) re)
31.0ms	(- (hypot re im) re)
31.0ms	(- (hypot re im) re)
30.0ms	(- (hypot re im) re)

series410.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (hypot re im) re)
100.0ms	(- (hypot re im) re)
95.0ms	(- (hypot re im) re)
128.0ms	(- (hypot re im) re)

simplify5.3s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
4	1796
3	651
2	239
1	130
0	62

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 11.4b

localize572.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)
0.7b	(- (hypot re im) re)
13.8b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 98

Calls

4 calls:

15.0ms	(- (hypot re im) re)
23.0ms	(- (hypot re im) re)
14.0ms	(- (hypot re im) re)
1.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

series683.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (hypot re im) re)
133.0ms	(- (hypot re im) re)
121.0ms	(- (hypot re im) re)
338.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- re))

simplify4.3s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
4	1687
3	669
2	274
1	154
0	77

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 11.4b

regimes391.0ms

Accuracy

0% (0.2b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.0b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

722.0ms	282×	body	5120	valid
613.0ms	6088×	body	80	valid
340.0ms	616×	body	2560	valid
283.0ms	510×	body	1280	valid
133.0ms	274×	body	640	valid
37.0ms	155×	body	320	valid
12.0ms	75×	body	160	valid