Details

sample55.0ms

Algorithm

intervals

Results

18.0ms	48×	body	1280	valid
10.0ms	39×	body	640	valid
9.0ms	142×	body	80	valid
3.0ms	19×	body	320	valid
1.0ms	8×	body	160	valid

simplify2.4s

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	271	24
6	654	24
7	2067	24
done	5001	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

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)
6.7b	(* (* (* -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)))

rewrite101.0ms

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:

6.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
9.0ms	(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)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
133.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
185.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
141.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.1s

Counts

97 → 97

Iterations

Useful iterations: 2 (221.0ms)

Iter	Nodes	Cost
0	193	2013
1	455	1800
2	1525	1613
done	5000	1613

prune289.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.7b

localize21.0ms

Local error

Found 4 expressions with local error:

6.6b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.6b	(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)))

rewrite95.0ms

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))))
25.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
22.0ms	(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:

222.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
219.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
143.0ms	(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)))

simplify1.3s

Counts

88 → 88

Iterations

Useful iterations: 4 (660.0ms)

Iter	Nodes	Cost
0	97	1968
1	192	1666
2	419	1604
3	1043	1598
4	3326	1592
done	5001	1592

prune348.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.7b

localize24.0ms

Local error

Found 4 expressions with local error:

2.0b	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
2.0b	(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
16.2b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.2b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
14×	`pow1`
13×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
7×	`sqrt-prod`
6×	`cbrt-div` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`flip3-+` `pow1/3` `associate-l` `flip-+` `distribute-lft-out`
2×	`rem-sqrt-square` `sqrt-pow1` `sqrt-div`
1×	`pow1/2` `associate-r` `*-commutative`

Counts

4 → 70

Calls

4 calls:

26.0ms	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
17.0ms	(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
11.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
12.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series763.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
101.0ms	(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
221.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
219.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.8s

Counts

82 → 82

Iterations

Useful iterations: 3 (788.0ms)

Iter	Nodes	Cost
0	156	2277
1	355	2140
2	1090	1854
3	4725	1796
done	5000	1796

prune355.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.7b

localize22.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (fabs (* (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))) (* (* -2.0 J) (cos (/ K 2.0))))
16.2b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.2b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.2b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`flip3-+` `pow1/3` `associate-l` `flip-+` `distribute-lft-out`
1×	`associate-r` `*-commutative`

Counts

4 → 63

Calls

4 calls:

18.0ms	(* (fabs (* (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))) (* (* -2.0 J) (cos (/ K 2.0))))
11.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
11.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series935.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (fabs (* (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))) (* (* -2.0 J) (cos (/ K 2.0))))
212.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
218.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
407.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.8s

Counts

75 → 75

Iterations

Useful iterations: 3 (758.0ms)

Iter	Nodes	Cost
0	132	2668
1	321	2050
2	1028	1748
3	4558	1724
done	5000	1724

prune330.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 12.7b

regimes257.0ms

Accuracy

87.7% (0.7b remaining)

Error of 12.7b against oracle of 12.0b and baseline of 17.4b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	32	118
1	45	99
done	45	99

end0.0ms

sample1.5s

Algorithm

intervals

Results

569.0ms	1513×	body	1280	valid
313.0ms	1218×	body	640	valid
296.0ms	4355×	body	80	valid
113.0ms	593×	body	320	valid
42.0ms	323×	body	160	valid