Details

sample76.0ms

Algorithm

intervals

Results

31.0ms	193×	body	80	valid
8.0ms	18×	body	2560	valid
7.0ms	19×	body	1280	valid
4.0ms	7×	body	5120	valid
3.0ms	9×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	32
3	32
2	30
1	24
0	12

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.6b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.9b	(+ (hypot re im) re)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `*-un-lft-identity`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`+-commutative` `hypot-udef` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

3 → 42

Calls

3 calls:

0.0ms	(hypot re im)
13.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
9.0ms	(+ (hypot re im) re)

series486.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(hypot re im)
294.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
103.0ms	(+ (hypot re im) re)

simplify2.1s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
3	3673
2	612
1	187
0	86

prune384.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.4b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`pow1`
19×	`sqrt-prod`
12×	`*-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` `log1p-expm1-u` `unswap-sqr`
3×	`pow-sqr`
2×	`flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`pow2` `+-commutative` `hypot-udef` `sum-log` `rem-square-sqrt` `fma-def` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 90

Calls

4 calls:

0.0ms	(hypot re im)
13.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
10.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
10.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series484.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(hypot re im)
268.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
53.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
82.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1169
1	291
0	129

prune613.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.3b

localize74.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.4b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
8.4b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
36×	`sqrt-prod`
34×	`pow1`
20×	`*-un-lft-identity` `add-cube-cbrt`
16×	`sqrt-pow1` `pow1/2` `swap-sqr`
12×	`associate-r` `associate-l`
10×	`pow-prod-up`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp` `unswap-sqr`
6×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `fma-def` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 130

Calls

4 calls:

20.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
20.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
17.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
18.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series291.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
73.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
69.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
81.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify6.0s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
3	4590
2	655
1	182
0	80

prune940.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
15.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef` `sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

4 → 43

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
7.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series612.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(hypot re im)
67.0ms	(hypot re im)
304.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
189.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.8s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
3	2477
2	481
1	149
0	74

prune345.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 13.3b

regimes321.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.0s	6031×	body	80	valid
428.0ms	695×	body	2560	valid
190.0ms	447×	body	1280	valid
160.0ms	300×	body	5120	valid
80.0ms	293×	body	640	valid
28.0ms	151×	body	320	valid
11.0ms	83×	body	160	valid