Details

sample168.0ms

Algorithm

intervals

Results

19.0ms	198×	body	80	valid
11.0ms	21×	body	2560	valid
7.0ms	16×	body	1280	valid
5.0ms	7×	body	5120	valid
4.0ms	9×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify101.0ms

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.2b	(- (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))
7.0ms	(- (hypot re im) re)

series458.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(hypot re im)
298.0ms	(sqrt (* (- (hypot re im) re) 2.0))
97.0ms	(- (hypot re im) re)

simplify2.2s

Counts

62 → 62

Iterations

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

prune370.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.9b

localize19.0ms

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)))
8.0b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite81.0ms

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)
35.0ms	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
21.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
21.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series530.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(hypot re im)
281.0ms	(sqrt (* (- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
66.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
102.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify1.4s

Counts

107 → 107

Iterations

Iter	Nodes
done	5001
2	1345
1	340
0	152

prune637.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (fabs (cbrt (hypot re im))) (sqrt (hypot re im)))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
5.8b	(- (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))) re)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `add-cbrt-cube` `associate-r` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`associate-l` `prod-diff`
2×	`pow1/3` `unswap-sqr`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--`

Counts

4 → 68

Calls

4 calls:

21.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (hypot re im)))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
44.0ms	(- (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))) re)

series691.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (hypot re im)))
176.0ms	(cbrt (hypot re im))
165.0ms	(cbrt (hypot re im))
188.0ms	(- (* (* (fabs (cbrt (hypot re im))) (sqrt (hypot re im))) (sqrt (cbrt (hypot re im)))) re)

simplify1.4s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1488
1	371
0	150

prune715.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.9b

localize81.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (fabs (cbrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
6.6b	(- (* (* (* (fabs (cbrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (sqrt (cbrt (hypot re im)))) re)

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log` `sqrt-prod`
6×	`cbrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow1/3`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `associate-l` `*-commutative` `flip--`

Counts

4 → 70

Calls

4 calls:

57.0ms	(* (* (fabs (cbrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
127.0ms	(- (* (* (* (fabs (cbrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (sqrt (cbrt (hypot re im)))) re)

series646.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (* (fabs (cbrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im))))
165.0ms	(cbrt (hypot re im))
168.0ms	(cbrt (hypot re im))
182.0ms	(- (* (* (* (fabs (cbrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (sqrt (cbrt (hypot re im)))) re)

simplify1.4s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1913
1	423
0	161

prune656.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.9b

regimes197.0ms

Accuracy

0% (0.2b remaining)

Error of 13.2b against oracle of 13.0b and baseline of 13.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.0s	6030×	body	80	valid
324.0ms	683×	body	2560	valid
267.0ms	487×	body	1280	valid
147.0ms	301×	body	5120	valid
116.0ms	245×	body	640	valid
32.0ms	175×	body	320	valid
10.0ms	79×	body	160	valid