Details

sample62.0ms

Algorithm

intervals

Results

21.0ms	58×	body	1280	valid
13.0ms	50×	body	640	valid
8.0ms	121×	body	80	valid
5.0ms	14×	body	320	valid
2.0ms	13×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	34	24
2	71	24
3	127	24
4	169	24
5	285	24
6	666	24
7	2094	24
done	5000	24

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.0b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite100.0ms

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-r/` `associate-l` `-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:

7.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
8.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
55.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
27.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
136.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
197.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
150.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.4s

Counts

97 → 97

Iterations

Useful iterations: 2 (227.0ms)

Iter	Nodes	Cost
0	193	2013
1	455	1804
2	1533	1613
done	5001	1613

prune303.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.0b	(* (* -2.0 J) (* (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cos (/ K 2.0))))
9.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

7.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
9.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
50.0ms	(* (* -2.0 J) (* (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cos (/ K 2.0))))
23.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
139.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
222.0ms	(* (* -2.0 J) (* (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cos (/ K 2.0))))
148.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.3s

Counts

94 → 94

Iterations

Useful iterations: 2 (224.0ms)

Iter	Nodes	Cost
0	200	1999
1	497	1791
2	1570	1573
done	5000	1573

prune290.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* -2.0 J) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (cos (/ K 2.0)))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.0b	(* (* -2.0 J) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite147.0ms

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`
6×	`sqrt-div`
4×	`associate-*r/` `pow-exp` `add-log-exp`
3×	`pow-unpow` `flip3-+` `times-frac` `div-exp` `flip-+`
2×	`associate-l` `associate-l/` `-commutative` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `sqr-pow`

Counts

4 → 87

Calls

4 calls:

70.0ms	(* (* (* -2.0 J) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (cos (/ K 2.0)))
9.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
40.0ms	(* (* -2.0 J) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
25.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series647.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(* (* (* -2.0 J) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (cos (/ K 2.0)))
132.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
171.0ms	(* (* -2.0 J) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
145.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.4s

Counts

99 → 99

Iterations

Useful iterations: 2 (230.0ms)

Iter	Nodes	Cost
0	196	2318
1	470	2047
2	1552	1841
done	5000	1841

prune297.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.4b

localize21.0ms

Local error

Found 4 expressions with local error:

6.0b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.0b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite97.0ms

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:

23.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
26.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
23.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
23.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series723.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
217.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
140.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
146.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.5s

Counts

88 → 88

Iterations

Useful iterations: 4 (684.0ms)

Iter	Nodes	Cost
0	97	1968
1	192	1674
2	419	1608
3	1056	1602
4	3439	1596
done	5001	1596

prune336.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.4b

regimes285.0ms

Accuracy

14.1% (8.4b remaining)

Error of 16.5b against oracle of 8.0b and baseline of 17.8b

bsearch163.0ms

Steps

Iters	Range		Point
9	1.953506508507719e-177	6.247390229845809e-171	2.5022959607105417e-175
7	-7.02045258805284e-223	-4.31564945894888e-225	-1.1414993822869651e-223

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	29	98
1	41	57
done	41	57

end0.0ms

sample1.5s

Algorithm

intervals

Results

557.0ms	1491×	body	1280	valid
327.0ms	1302×	body	640	valid
287.0ms	4278×	body	80	valid
115.0ms	618×	body	320	valid
43.0ms	314×	body	160	valid