Details

sample135.0ms

Algorithm

intervals

Results

19.0ms	195×	body	80	valid
11.0ms	21×	body	2560	valid
8.0ms	11×	body	5120	valid
6.0ms	14×	body	1280	valid
3.0ms	10×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify116.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	45
5	45
4	43
3	36
2	28
1	19
0	12

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite19.0ms

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` `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 → 53

Calls

3 calls:

0.0ms	(hypot re im)
8.0ms	(sqrt (* (- (hypot re im) re) 2.0))
8.0ms	(- (hypot re im) re)

series455.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(hypot re im)
280.0ms	(sqrt (* (- (hypot re im) re) 2.0))
109.0ms	(- (hypot re im) re)

simplify2.4s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
3	4021
2	770
1	245
0	115

prune401.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.9b

localize45.0ms

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)))
5.7b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite85.0ms

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` `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 → 95

Calls

4 calls:

0.0ms	(hypot re im)
29.0ms	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
28.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
22.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series513.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(hypot re im)
279.0ms	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
65.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
90.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify1.3s

Counts

107 → 107

Iterations

Iter	Nodes
done	5001
2	1345
1	340
0	152

prune616.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.9b

localize58.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))))
0.6b	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
7.6b	(- (* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))))) re)

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
24×	`pow1`
19×	`cbrt-prod` `pow1/3`
18×	`add-cube-cbrt`
17×	`*-un-lft-identity`
12×	`sqrt-pow1` `associate-l` `pow-prod-up`
10×	`associate-r` `pow-prod-down`
8×	`add-exp-log`
7×	`swap-sqr` `sqrt-prod`
6×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `pow1/2` `pow-sqr` `log1p-expm1-u`
3×	`prod-diff`
2×	`prod-exp` `*-commutative` `cbrt-unprod`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `fma-neg` `sqrt-unprod` `diff-log` `flip--`

Counts

4 → 108

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
104.0ms	(* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))))
18.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
110.0ms	(- (* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))))) re)

series458.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(cbrt (hypot re im))
58.0ms	(* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)))))
154.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
89.0ms	(- (* (sqrt (hypot re im)) (sqrt (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))))) re)

simplify1.6s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	1434
1	369
0	166

prune863.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.9b

localize122.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(* (sqrt (hypot re im)) (sqrt (* (* (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) (cbrt (hypot re im)))))
0.6b	(* (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))
9.8b	(- (* (sqrt (hypot re im)) (sqrt (* (* (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) (cbrt (hypot re im))))) re)

rewrite2.7s

Algorithm

rewrite-expression-head

Rules

260×	`pow1`
234×	`sqrt-pow1`
197×	`pow-prod-up`
120×	`pow1/2`
105×	`pow1/3`
89×	`pow-sqr`
77×	`pow-prod-down`
18×	`pow-plus` `add-cbrt-cube` `add-exp-log`
13×	`pow2` `add-sqr-sqrt`
9×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
7×	`associate-l`
6×	`sqrt-unprod` `add-log-exp`
5×	`associate-r` `sqrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-prod` `prod-diff` `unswap-sqr`
2×	`*-commutative`
1×	`sub-neg` `rem-square-sqrt` `flip3--` `fma-neg` `diff-log` `swap-sqr` `flip--`

Counts

4 → 210

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.2s	(* (sqrt (hypot re im)) (sqrt (* (* (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) (cbrt (hypot re im)))))
115.0ms	(* (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))
1.4s	(- (* (sqrt (hypot re im)) (sqrt (* (* (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) (cbrt (hypot re im))))) re)

series501.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt (hypot re im))
64.0ms	(* (sqrt (hypot re im)) (sqrt (* (* (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) (cbrt (hypot re im)))))
163.0ms	(* (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))))
96.0ms	(- (* (sqrt (hypot re im)) (sqrt (* (* (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) (cbrt (hypot re im))))) re)

simplify2.0s

Counts

222 → 222

Iterations

Iter	Nodes
done	5000
2	2096
1	716
0	252

prune821.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.9b

regimes173.0ms

Accuracy

0% (0.2b remaining)

Error of 13.4b against oracle of 13.2b and baseline of 13.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.3s

Algorithm

intervals

Results

600.0ms	6008×	body	80	valid
487.0ms	176×	body	320	valid
321.0ms	734×	body	2560	valid
251.0ms	476×	body	1280	valid
188.0ms	291×	body	5120	valid
68.0ms	262×	body	640	valid
7.0ms	53×	body	160	valid