Details

sample123.0ms

Algorithm

intervals

Results

38.0ms	46×	body	1280	valid
24.0ms	42×	body	640	valid
19.0ms	132×	body	80	valid
9.0ms	21×	body	320	valid
5.0ms	15×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	34	24
2	71	24
3	132	24
4	189	24
5	300	24
6	731	24
7	2462	24
done	5000	24

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite405.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-cbrt-cube`
16×	`*-un-lft-identity`
15×	`pow1`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `prod-exp`
9×	`cbrt-unprod`
8×	`sqrt-prod`
7×	`unpow-prod-down` `associate-r`
6×	`times-frac` `div-exp` `pow-prod-down`
4×	`sqrt-div` `pow-exp` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/l*`
2×	`flip3-+` `associate-*r/` `flip-+` `div-inv` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l` `clear-num` `associate-/r` `-commutative` `sqr-pow`

Counts

4 → 90

Calls

4 calls:

39.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
44.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
202.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
114.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series876.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
217.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
272.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
254.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.3s

Counts

102 → 102

Iterations

Useful iterations: 2 (375.0ms)

Iter	Nodes	Cost
0	214	2168
1	531	1954
2	1953	1735
done	5001	1735

prune421.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.5b	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
8.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite396.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
25×	`add-cbrt-cube`
18×	`pow1`
14×	`prod-exp`
12×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `cbrt-unprod`
10×	`add-cube-cbrt`
8×	`pow-prod-down`
7×	`unpow-prod-down`
6×	`times-frac` `div-exp`
4×	`sqrt-div` `associate-*r/` `pow-exp` `sqrt-prod` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/l*`
2×	`flip3-+` `flip-+` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `clear-num` `associate-/r` `-commutative` `distribute-lft-out` `sqr-pow`

Counts

4 → 87

Calls

4 calls:

29.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
31.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
239.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
94.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series802.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
184.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
263.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
240.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.3s

Counts

99 → 99

Iterations

Useful iterations: 2 (379.0ms)

Iter	Nodes	Cost
0	212	2138
1	522	1929
2	1843	1679
done	5001	1679

prune478.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
0.2b	(pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)
6.5b	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))))
8.5b	(sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))

rewrite356.0ms

Algorithm

rewrite-expression-head

Rules

63×	`times-frac`
38×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
36×	`add-cube-cbrt`
35×	`add-exp-log`
25×	`unpow-prod-down` `add-cbrt-cube`
18×	`pow1`
10×	`div-exp` `prod-exp`
9×	`cbrt-unprod` `div-inv`
8×	`pow-prod-down`
7×	`associate-/l*`
5×	`cbrt-undiv`
4×	`sqrt-div` `associate-*r/` `pow-exp` `sqrt-prod` `add-log-exp`
3×	`pow-unpow` `associate-/r*`
2×	`flip3-+` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `clear-num` `*-commutative` `associate-/l/` `distribute-lft-out` `sqr-pow`

Counts

4 → 130

Calls

4 calls:

21.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
16.0ms	(pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)
209.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))))
99.0ms	(sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))

series836.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
202.0ms	(pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)
283.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))))
206.0ms	(sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))

simplify1.3s

Counts

142 → 142

Iterations

Useful iterations: 2 (453.0ms)

Iter	Nodes	Cost
0	298	3126
1	720	2885
2	2193	2633
done	5000	2633

prune705.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.1b

localize26.0ms

Local error

Found 4 expressions with local error:

6.4b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.4b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite405.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

109.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
104.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
99.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
90.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

380.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
354.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
206.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
253.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.6s

Counts

88 → 88

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	97	1968
1	192	1666
2	420	1604
3	1118	1598
4	3445	1592
done	5000	1580

prune461.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.1b

regimes407.0ms

Accuracy

-20% (6.8b remaining)

Error of 18.9b against oracle of 12.1b and baseline of 17.7b

bsearch210.0ms

Steps

Iters	Range		Point
9	-1.488607050460361e+122	-5.449253800430163e+114	-1.4686792642946565e+122
4	-4.94194543027164e+213	-3.284918449488842e+213	-3.44026472893723e+213

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	33	76
1	46	53
done	46	53

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.7s	1528×	body	1280	valid
1.2s	1234×	body	640	valid
637.0ms	4294×	body	80	valid
251.0ms	610×	body	320	valid
123.0ms	335×	body	160	valid