Details

sample157.0ms

Algorithm

intervals

Results

63.0ms	39×	body	1280	valid
34.0ms	41×	body	640	valid
29.0ms	152×	body	80	valid
11.0ms	18×	body	320	valid
2.0ms	6×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5038
5	4827
4	843
3	216
2	85
1	36
0	17

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2 (cos (/ K 2))) J))
0.1b	(* (cos (/ K 2)) (* -2 J))
0.1b	(* (* 2 (cos (/ K 2))) J)
9.1b	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

rewrite153.0ms

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:

15.0ms	(/ U (* (* 2 (cos (/ K 2))) J))
30.0ms	(* (cos (/ K 2)) (* -2 J))
32.0ms	(* (* 2 (cos (/ K 2))) J)
76.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

series619.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ U (* (* 2 (cos (/ K 2))) J))
87.0ms	(* (cos (/ K 2)) (* -2 J))
69.0ms	(* (* 2 (cos (/ K 2))) J)
361.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

simplify1.8s

Counts

104 → 104

Iterations

Iter	Nodes
done	5001
2	1590
1	418
0	164

prune602.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2 (cos (/ K 2))) J))
0.1b	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2)))
0.1b	(* (* 2 (cos (/ K 2))) J)
9.1b	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
23×	`pow1`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r`
5×	`associate-l`
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` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

22.0ms	(/ U (* (* 2 (cos (/ K 2))) J))
7.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2)))
17.0ms	(* (* 2 (cos (/ K 2))) J)
28.0ms	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))

series783.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ U (* (* 2 (cos (/ K 2))) J))
279.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2)))
84.0ms	(* (* 2 (cos (/ K 2))) J)
317.0ms	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))

simplify1.6s

Counts

105 → 105

Iterations

Iter	Nodes
done	5005
2	1581
1	425
0	165

prune638.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J)))
0.2b	(* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J))))
9.0b	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
9.0b	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

43.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J)))
151.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J))))
2.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
3.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

series1.3s

Counts

4 → 12

Calls

4 calls:

362.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J)))
405.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J))))
295.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
259.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

simplify1.9s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	941
1	272
0	115

prune708.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))) (sqrt (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))))
9.0b	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
9.0b	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
9.0b	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

75×	`sqrt-prod`
52×	`add-sqr-sqrt`
35×	`sqrt-pow1`
30×	`pow1`
19×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 126

Calls

4 calls:

27.0ms	(* (sqrt (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))) (sqrt (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))))
3.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
2.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
2.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

series1.1s

Counts

4 → 12

Calls

4 calls:

268.0ms	(* (sqrt (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))) (sqrt (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))))
258.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
276.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
260.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

simplify5.6s

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
5	4330
4	1128
3	575
2	349
1	170
0	94

prune693.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 4.7b

regimes873.0ms

Accuracy

0.2% (4.1b remaining)

Error of 7.8b against oracle of 3.8b and baseline of 7.9b

bsearch246.0ms

Steps

Iters	Range		Point
4	2.7009210918123233e-278	4.740316911388573e-278	2.7346568877506468e-278
9	-8.649692897985271e-279	-5.517962605111487e-286	-1.3819507464850254e-285

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	22

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.4s	1389×	body	1280	valid
1.3s	1246×	body	640	valid
1.1s	4416×	body	80	valid
543.0ms	632×	body	320	valid
228.0ms	319×	body	160	valid