Details

sample151.0ms

Algorithm

intervals

Results

28.0ms	195×	body	80	valid
16.0ms	18×	body	2560	valid
11.0ms	16×	body	1280	valid
10.0ms	11×	body	5120	valid
6.0ms	11×	body	640	valid
1.0ms	2×	body	320	valid
1.0ms	3×	body	160	valid

simplify73.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.7b

localize17.0ms

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)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 71

Calls

3 calls:

0.0ms	(hypot re im)
59.0ms	(sqrt (* (- (hypot re im) re) 2.0))
9.0ms	(- (hypot re im) re)

series683.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(hypot re im)
538.0ms	(sqrt (* (- (hypot re im) re) 2.0))
85.0ms	(- (hypot re im) re)

simplify2.1s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
3	1829
2	619
1	286
0	144

prune377.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* (- (hypot re im) re) (sqrt 2.0)))
0.3b	(* (sqrt (* (- (hypot re im) re) (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.3b	(* (- (hypot re im) re) (sqrt 2.0))
0.7b	(- (hypot re im) re)

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
81×	`add-sqr-sqrt`
36×	`associate-l`
34×	`*-un-lft-identity`
27×	`associate-r`
26×	`add-cube-cbrt` `unswap-sqr`
16×	`pow1`
9×	`prod-diff`
8×	`add-cbrt-cube` `associate-*l/` `add-exp-log`
7×	`pow-prod-down`
6×	`sqrt-pow1` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `*-commutative` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`rem-sqrt-square` `pow1/2` `fma-neg`
2×	`prod-exp` `cbrt-unprod`
1×	`sub-neg` `sqrt-unprod` `diff-log`

Counts

4 → 156

Calls

4 calls:

43.0ms	(sqrt (* (- (hypot re im) re) (sqrt 2.0)))
174.0ms	(* (sqrt (* (- (hypot re im) re) (sqrt 2.0))) (sqrt (sqrt 2.0)))
46.0ms	(* (- (hypot re im) re) (sqrt 2.0))
14.0ms	(- (hypot re im) re)

series871.0ms

Counts

4 → 12

Calls

4 calls:

376.0ms	(sqrt (* (- (hypot re im) re) (sqrt 2.0)))
238.0ms	(* (sqrt (* (- (hypot re im) re) (sqrt 2.0))) (sqrt (sqrt 2.0)))
160.0ms	(* (- (hypot re im) re) (sqrt 2.0))
97.0ms	(- (hypot re im) re)

simplify2.9s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
3	4498
2	1315
1	502
0	223

prune854.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.2b

localize21.0ms

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)

rewrite465.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 216

Calls

4 calls:

362.0ms	(sqrt (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 2.0))
63.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
13.0ms	(- (hypot re im) re)
12.0ms	(- (hypot re im) re)

series585.0ms

Counts

4 → 12

Calls

4 calls:

303.0ms	(sqrt (* (* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re))) 2.0))
79.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
92.0ms	(- (hypot re im) re)
111.0ms	(- (hypot re im) re)

simplify2.2s

Counts

228 → 228

Iterations

Iter	Nodes
done	5002
3	2775
2	1067
1	531
0	260

prune964.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.2b

localize38.0ms

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)

rewrite996.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 249

Calls

4 calls:

1.0ms	(hypot re im)
424.0ms	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
20.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
534.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series461.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot re im)
252.0ms	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
73.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
85.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify2.6s

Counts

261 → 261

Iterations

Iter	Nodes
done	5001
3	2790
2	1098
1	502
0	242

prune603.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 12.2b

regimes294.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.8s

Algorithm

intervals

Results

935.0ms	677×	body	2560	valid
860.0ms	6080×	body	80	valid
306.0ms	269×	body	5120	valid
295.0ms	479×	body	1280	valid
122.0ms	279×	body	640	valid
79.0ms	126×	body	320	valid
18.0ms	90×	body	160	valid