Details

sample128.0ms

Algorithm

intervals

Results

43.0ms	41×	body	640	valid
33.0ms	39×	body	1280	valid
24.0ms	152×	body	80	valid
8.0ms	18×	body	320	valid
2.0ms	6×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5025
5	4486
4	782
3	215
2	81
1	36
0	17

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* -2 J) (cos (/ K 2)))
0.2b	(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
8.9b	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
9.1b	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

rewrite307.0ms

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` `insert-posit16` `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` `unpow2` `sqr-pow`

Counts

4 → 90

Calls

4 calls:

22.0ms	(* (* -2 J) (cos (/ K 2)))
29.0ms	(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
88.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
166.0ms	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

series538.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (* -2 J) (cos (/ K 2)))
120.0ms	(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
133.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
203.0ms	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

simplify1.8s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1519
1	485
0	179

prune542.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.3b

localize55.0ms

Local error

Found 4 expressions with local error:

11.2b	(sqrt (* (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))
16.1b	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
16.1b	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
16.1b	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
13×	`*-un-lft-identity`
12×	`cbrt-prod` `pow1`
9×	`sqrt-pow1` `flip3-+` `pow1/3` `flip-+`
8×	`sqrt-div`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`frac-times` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`distribute-lft-out`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 73

Calls

4 calls:

64.0ms	(sqrt (* (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))
27.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
31.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
31.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series893.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(sqrt (* (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))
241.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
202.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
246.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify1.9s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
3	1280
2	418
1	209
0	115

prune894.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.3b

localize118.0ms

Local error

Found 4 expressions with local error:

16.1b	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
16.1b	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
16.1b	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
16.1b	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod` `*-un-lft-identity`
8×	`add-sqr-sqrt` `cbrt-div` `add-cube-cbrt`
4×	`pow1` `flip3-+` `add-cbrt-cube` `pow1/3` `add-exp-log` `flip-+` `insert-posit16` `distribute-lft-out` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

39.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
34.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
57.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
54.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

289.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
246.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
299.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
248.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify2.0s

Counts

72 → 72

Iterations

Iter	Nodes
done	5006
3	1151
2	339
1	141
0	69

prune872.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
8.9b	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
9.1b	(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

rewrite556.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
29×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
13×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`sqrt-prod`
7×	`associate-r`
6×	`cbrt-prod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
2×	`flip3-+` `pow1/3` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 78

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
88.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
466.0ms	(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

series649.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (cos (/ K 2)))
144.0ms	(cbrt (cos (/ K 2)))
164.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
200.0ms	(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

simplify1.8s

Counts

90 → 90

Iterations

Iter	Nodes
done	5006
2	1460
1	379
0	147

prune573.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.2b

regimes804.0ms

Accuracy

87.1% (0.6b remaining)

Error of 12.8b against oracle of 12.2b and baseline of 17.1b

bsearch5.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	40
1	40
0	27

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.3s	1389×	body	1280	valid
1.6s	4416×	body	80	valid
1.3s	1246×	body	640	valid
543.0ms	632×	body	320	valid
195.0ms	319×	body	160	valid