Details

sample90.0ms

Algorithm

intervals

Results

31.0ms	57×	body	1280	valid
15.0ms	42×	body	640	valid
12.0ms	132×	body	80	valid
5.0ms	16×	body	320	valid
2.0ms	9×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3236
5	492
4	208
3	135
2	71
1	34
0	17

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
0.3b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.7b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.3b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
20×	`pow1`
18×	`add-cbrt-cube`
15×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `prod-exp`
11×	`add-cube-cbrt`
10×	`associate-r`
9×	`pow-prod-down` `cbrt-unprod`
8×	`sqrt-prod`
7×	`unpow-prod-down`
4×	`sqrt-div` `pow-exp` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp`
2×	`flip3-+` `associate-l` `associate-r/` `-commutative` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `sqr-pow`

Counts

4 → 85

Calls

4 calls:

28.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
26.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
161.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
63.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series823.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
199.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
330.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
234.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	2368
1	508
0	192

prune725.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(* J (cos (/ K 2.0)))
0.3b	(pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)
6.7b	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))))
11.3b	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

rewrite293.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
22×	`times-frac`
20×	`pow1`
19×	`add-sqr-sqrt`
18×	`*-un-lft-identity` `add-cbrt-cube`
17×	`unpow-prod-down`
16×	`add-cube-cbrt`
11×	`prod-exp`
9×	`pow-prod-down` `cbrt-unprod`
6×	`div-exp`
5×	`pow-exp`
4×	`sqrt-div` `associate-r` `associate-l` `associate-*r/` `sqrt-prod` `add-log-exp`
3×	`pow-unpow`
2×	`flip3-+` `*-commutative` `flip-+` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `distribute-lft-out` `unswap-sqr` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

12.0ms	(* J (cos (/ K 2.0)))
26.0ms	(pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)
171.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))))
78.0ms	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

series778.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* J (cos (/ K 2.0)))
184.0ms	(pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)
306.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))))
207.0ms	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

simplify1.2s

Counts

105 → 105

Iterations

Iter	Nodes
done	5002
2	2385
1	708
0	254

prune711.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.9b

localize59.0ms

Local error

Found 4 expressions with local error:

6.7b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.7b	(sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
11.3b	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
11.3b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite352.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `sqrt-pow1` `add-cube-cbrt`
6×	`rem-sqrt-square` `pow1/2`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

73.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
103.0ms	(sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
106.0ms	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
67.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

360.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
367.0ms	(sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
223.0ms	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
227.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.0s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
3	2031
2	699
1	272
0	141

prune751.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.9b

localize89.0ms

Local error

Found 4 expressions with local error:

6.7b	(sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
11.3b	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
11.3b	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
11.3b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
17×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
10×	`sqrt-div`
9×	`pow1` `add-cube-cbrt`
7×	`sqrt-pow1`
5×	`rem-sqrt-square` `pow1/2`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 70

Calls

4 calls:

72.0ms	(sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
92.0ms	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
68.0ms	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
55.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

394.0ms	(sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
319.0ms	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
247.0ms	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
196.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify968.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
3	1891
2	638
1	252
0	126

prune836.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 12.9b

regimes611.0ms

Accuracy

-15.9% (6.3b remaining)

Error of 19.6b against oracle of 13.3b and baseline of 18.7b

bsearch203.0ms

Steps

Iters	Range		Point
4	2.531710311300539e-234	4.502409745627338e-234	2.839632097914101e-234
7	-3.42525405092622e-189	-1.411644986557304e-191	-1.4549404577459228e-191

simplify5.0ms

Iterations

Iter	Nodes
done	45
1	45
0	33

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.6s	1503×	body	1280	valid
1.1s	4264×	body	80	valid
926.0ms	1300×	body	640	valid
278.0ms	632×	body	320	valid
145.0ms	306×	body	160	valid