Details

sample160.0ms

Algorithm

intervals

Results

28.0ms	195×	body	80	valid
15.0ms	18×	body	2560	valid
11.0ms	16×	body	1280	valid
10.0ms	11×	body	5120	valid
6.0ms	11×	body	640	valid
1.0ms	3×	body	160	valid
0.0ms	2×	body	320	valid

simplify185.0ms

Counts

1 → 1

Iterations

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

prune61.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.7b

localize37.0ms

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)

rewrite48.0ms

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:

0.0ms	(hypot re im)
18.0ms	(sqrt (* (- (hypot re im) re) 2.0))
14.0ms	(- (hypot re im) re)

series726.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(hypot re im)
429.0ms	(sqrt (* (- (hypot re im) re) 2.0))
243.0ms	(- (hypot re im) re)

simplify2.1s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
3	1780
2	568
1	247
0	118

prune352.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.3b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.4b	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
0.7b	(- (hypot re im) re)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 77

Calls

3 calls:

0.0ms	(hypot re im)
33.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
10.0ms	(- (hypot re im) re)

series473.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(hypot re im)
314.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
85.0ms	(- (hypot re im) re)

simplify2.0s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
3	2082
2	718
1	310
0	144

prune403.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.3b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
32×	`sqrt-div`
31×	`sqrt-prod`
26×	`add-cube-cbrt`
25×	`pow1`
18×	`prod-diff`
14×	`flip3--` `flip--`
12×	`swap-sqr` `associate-*l/`
11×	`sqrt-pow1`
9×	`pow1/2`
8×	`frac-times` `associate-r` `associate-l` `distribute-lft-out--` `add-log-exp`
6×	`add-cbrt-cube` `fma-neg` `pow-prod-down` `add-exp-log` `difference-of-squares`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`pow-sqr`
2×	`sub-neg` `diff-log`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 149

Calls

4 calls:

79.0ms	(sqrt (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 2.0))
37.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
5.0ms	(- (hypot re im) re)
5.0ms	(- (hypot re im) re)

series567.0ms

Counts

4 → 12

Calls

4 calls:

314.0ms	(sqrt (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 2.0))
85.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
88.0ms	(- (hypot re im) re)
80.0ms	(- (hypot re im) re)

simplify2.6s

Counts

161 → 161

Iterations

Iter	Nodes
done	5002
3	2096
2	800
1	399
0	191

prune702.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 12.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
7.2b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`pow1`
19×	`sqrt-prod`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1`
9×	`pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`prod-diff` `pow-sqr`
2×	`flip3--` `sqrt-div` `associate-*l/` `flip--`
1×	`pow2` `hypot-udef` `sub-neg` `rem-square-sqrt` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares`

Counts

4 → 99

Calls

4 calls:

0.0ms	(hypot re im)
32.0ms	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
18.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
28.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series479.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(hypot re im)
266.0ms	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
62.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
78.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify2.2s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
3	2313
2	800
1	335
0	156

prune504.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 12.3b

regimes185.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.0s	6080×	body	80	valid
599.0ms	677×	body	2560	valid
567.0ms	279×	body	640	valid
283.0ms	479×	body	1280	valid
262.0ms	269×	body	5120	valid
45.0ms	126×	body	320	valid
22.0ms	90×	body	160	valid