Details

sample93.0ms

Algorithm

intervals

Results

26.0ms	39×	body	1280	valid
23.0ms	48×	body	640	valid
18.0ms	139×	body	80	valid
8.0ms	22×	body	320	valid
2.0ms	8×	body	160	valid

simplify2.4s

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: 17.8b

localize53.0ms

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)
8.5b	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
9.2b	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite360.0ms

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)))
38.0ms	(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
209.0ms	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
89.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series543.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (* -2 J) (cos (/ K 2)))
155.0ms	(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
175.0ms	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
141.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify1.5s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1535
1	482
0	179

prune625.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.5b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ U (* 2 J)) (cos (/ K 2)))
0.2b	(* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2))))
8.6b	(* (* -2 J) (* (sqrt (+ (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2)))) 1)) (cos (/ K 2))))
9.2b	(sqrt (+ (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2)))) 1))

rewrite378.0ms

Algorithm

rewrite-expression-head

Rules

157×	`times-frac`
105×	`add-cbrt-cube` `add-exp-log`
90×	`add-sqr-sqrt`
77×	`*-un-lft-identity` `add-cube-cbrt`
45×	`cbrt-undiv` `div-exp`
33×	`prod-exp` `cbrt-unprod`
26×	`associate-r` `associate-l`
25×	`swap-sqr`
24×	`pow1`
21×	`div-inv`
9×	`pow-prod-down`
7×	`associate-/l*`
4×	`sqrt-div` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `associate-l/` `associate-*r/` `sqrt-prod`
2×	`flip3-+` `*-commutative` `flip-+`
1×	`pow2` `frac-times` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up` `associate-/l/`

Counts

4 → 218

Calls

4 calls:

24.0ms	(/ (/ U (* 2 J)) (cos (/ K 2)))
94.0ms	(* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2))))
161.0ms	(* (* -2 J) (* (sqrt (+ (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2)))) 1)) (cos (/ K 2))))
85.0ms	(sqrt (+ (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2)))) 1))

series569.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (/ U (* 2 J)) (cos (/ K 2)))
119.0ms	(* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2))))
220.0ms	(* (* -2 J) (* (sqrt (+ (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2)))) 1)) (cos (/ K 2))))
131.0ms	(sqrt (+ (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2)))) 1))

simplify2.9s

Counts

230 → 230

Iterations

Iter	Nodes
done	5003
2	4921
1	1197
0	350

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.9b

localize92.0ms

Local error

Found 4 expressions with local error:

8.9b	(cbrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
9.2b	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
9.2b	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
9.2b	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite359.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
16×	`sqrt-prod`
12×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`sqrt-div`
7×	`cbrt-prod` `pow1`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `distribute-lft-out` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 69

Calls

4 calls:

64.0ms	(cbrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
80.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
77.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
137.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series794.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(cbrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
178.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
163.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
170.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify2.2s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
3	1337
2	404
1	171
0	91

prune724.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.9b

localize87.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
8.5b	(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
9.2b	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite815.0ms

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:

2.0ms	(cbrt (cos (/ K 2)))
2.0ms	(cbrt (cos (/ K 2)))
740.0ms	(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
68.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series754.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt (cos (/ K 2)))
166.0ms	(cbrt (cos (/ K 2)))
233.0ms	(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
177.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify2.1s

Counts

90 → 90

Iterations

Iter	Nodes
done	5004
2	1441
1	376
0	147

prune566.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 8.9b

regimes880.0ms

Accuracy

92.6% (0.6b remaining)

Error of 9.6b against oracle of 9.0b and baseline of 17.3b

bsearch3.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	35
1	35
0	24

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.1s	1417×	body	1280	valid
944.0ms	4462×	body	80	valid
738.0ms	1186×	body	640	valid
244.0ms	597×	body	320	valid
88.0ms	339×	body	160	valid