Details

sample55.0ms

Algorithm

intervals

Results

19.0ms	54×	body	1280	valid
9.0ms	143×	body	80	valid
8.0ms	34×	body	640	valid
3.0ms	18×	body	320	valid
1.0ms	7×	body	160	valid

simplify46.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	13
1	74	13
2	138	13
3	203	13
4	368	13
5	1361	13
6	5001	13
done	5001	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize20.0ms

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)
7.1b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.9b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite246.0ms

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:

17.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
22.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
142.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
61.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
143.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
198.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
149.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify56.0ms

Counts

97 → 97

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	453	1006
1	1965	898
2	5001	898
done	5001	898

prune296.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.7b

localize20.0ms

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)
7.1b	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
8.9b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite223.0ms

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/` `associate-r*` `pow-exp` `sqrt-prod` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp`
2×	`flip3-+` `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:

19.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
20.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
120.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
61.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
140.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
201.0ms	(* (* -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)))

simplify58.0ms

Counts

94 → 94

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	488	987
1	2021	866
2	5002	866
done	5002	866

prune270.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.7b

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
2.4b	(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
14.1b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.1b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

58.0ms	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
26.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
32.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
29.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series779.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
85.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
230.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
233.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify42.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	347	1291
1	1206	1104
2	5001	1096
done	5001	1096

prune377.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.7b

localize26.0ms

Local error

Found 4 expressions with local error:

14.1b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.1b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.1b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.1b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod` `*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 56

Calls

4 calls:

30.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
29.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
30.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
32.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series928.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
230.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
231.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
232.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify45.0ms

Counts

68 → 68

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	150	968
1	344	900
2	1231	884
3	5002	872
done	5002	872

prune402.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 11.7b

regimes367.0ms

Accuracy

84.8% (0.8b remaining)

Error of 13.6b against oracle of 12.8b and baseline of 18.2b

bsearch3.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	50
1	45	50
done	45	50

end0.0ms

sample1.6s

Algorithm

intervals

Results

561.0ms	1581×	body	1280	valid
305.0ms	1245×	body	640	valid
274.0ms	4274×	body	80	valid
112.0ms	598×	body	320	valid
37.0ms	305×	body	160	valid