Details

sample144.0ms

Algorithm

intervals

Results

62.0ms	49×	body	1280	valid
29.0ms	44×	body	640	valid
22.0ms	129×	body	80	valid
13.0ms	27×	body	320	valid
2.0ms	7×	body	160	valid

simplify880.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	2043
4	623
3	190
2	83
1	34
0	17

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.7b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* J 2) (cos (/ K 2))))
0.2b	(* (cos (/ K 2)) (* -2 J))
0.2b	(* (* J 2) (cos (/ K 2)))
5.7b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
23×	`pow1`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l`
5×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `-commutative` `associate-/l`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Counts

4 → 92

Calls

4 calls:

14.0ms	(/ U (* (* J 2) (cos (/ K 2))))
23.0ms	(* (cos (/ K 2)) (* -2 J))
15.0ms	(* (* J 2) (cos (/ K 2)))
34.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

series544.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ U (* (* J 2) (cos (/ K 2))))
54.0ms	(* (cos (/ K 2)) (* -2 J))
63.0ms	(* (* J 2) (cos (/ K 2)))
315.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

simplify4.3s

Counts

104 → 104

Iterations

Iter	Nodes
3	8613
2	1469
1	408
0	162

prune544.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* J 2) (cos (/ K 2)))
0.2b	(* (* J 2) (cos (/ K 2)))
5.7b	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
5.7b	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 74

Calls

4 calls:

27.0ms	(* (* J 2) (cos (/ K 2)))
15.0ms	(* (* J 2) (cos (/ K 2)))
1.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
1.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

series598.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (* J 2) (cos (/ K 2)))
74.0ms	(* (* J 2) (cos (/ K 2)))
228.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
234.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

simplify2.9s

Counts

86 → 86

Iterations

Iter	Nodes
4	3468
3	1118
2	363
1	143
0	71

prune532.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.6b

localize55.0ms

Local error

Found 4 expressions with local error:

5.7b	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
5.9b	(cbrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
5.9b	(cbrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
5.9b	(cbrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

1.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
1.0ms	(cbrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
1.0ms	(cbrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
1.0ms	(cbrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

227.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
290.0ms	(cbrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
364.0ms	(cbrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
388.0ms	(cbrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

simplify637.0ms

Counts

70 → 70

Iterations

Iter	Nodes
4	2013
3	497
2	194
1	106
0	64

prune608.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 2.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
5.7b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1` `add-exp-log`
23×	`add-cbrt-cube`
22×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-l`
1×	`associate-r` `*-commutative`

Counts

4 → 78

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
170.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

series754.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (cos (/ K 2)))
151.0ms	(cbrt (cos (/ K 2)))
153.0ms	(cbrt (cos (/ K 2)))
347.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

simplify2.9s

Counts

90 → 90

Iterations

Iter	Nodes
3	5929
2	1260
1	325
0	124

prune466.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 2.6b

regimes373.0ms

Accuracy

0% (3.9b remaining)

Error of 7.3b against oracle of 3.4b and baseline of 7.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	20
1	20
0	15

end0.0ms

sample6.1s

Algorithm

intervals

Results

1.9s	1282×	body	640	valid
1.7s	1402×	body	1280	valid
1.4s	4329×	body	80	valid
471.0ms	656×	body	320	valid
219.0ms	340×	body	160	valid