Details

sample123.0ms

Algorithm

intervals

Results

35.0ms	48×	body	1280	valid
22.0ms	26×	body	320	valid
22.0ms	46×	body	640	valid
16.0ms	128×	body	80	valid
2.0ms	8×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3236
5	492
4	208
3	135
2	71
1	34
0	17

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize38.0ms

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)
6.6b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite312.0ms

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

28.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
33.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
179.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
66.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series815.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
220.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
301.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
227.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	2368
1	508
0	192

prune718.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.2b

localize72.0ms

Local error

Found 4 expressions with local error:

6.7b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.7b	(sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
10.1b	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
10.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `sqrt-pow1` `add-cube-cbrt`
6×	`rem-sqrt-square` `pow1/2`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

88.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
72.0ms	(sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
55.0ms	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
70.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

321.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
353.0ms	(sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
222.0ms	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
214.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify913.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
3	2031
2	699
1	272
0	141

prune973.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.2b

localize124.0ms

Local error

Found 4 expressions with local error:

6.7b	(sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
10.1b	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
16.0b	(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
16.0b	(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

63.0ms	(sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
88.0ms	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
28.0ms	(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
53.0ms	(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

333.0ms	(sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
241.0ms	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
308.0ms	(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
367.0ms	(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

simplify932.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
3	1709
2	536
1	222
0	114

prune1.0s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 12.2b

localize141.0ms

Local error

Found 4 expressions with local error:

10.1b	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* (cos (/ K 2.0)) J)) 2.0)))
12.3b	(cbrt (pow (sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* (cos (/ K 2.0)) J)) 2.0)))) 3))
16.0b	(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
16.0b	(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

34×	`cbrt-prod`
26×	`sqrt-prod`
24×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
10×	`unpow-prod-down` `cube-prod`
6×	`cbrt-div` `sqrt-div`
5×	`pow1` `distribute-lft-out`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `add-log-exp`
3×	`pow1/3`
2×	`cube-div`
1×	`cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 81

Calls

4 calls:

64.0ms	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* (cos (/ K 2.0)) J)) 2.0)))
90.0ms	(cbrt (pow (sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* (cos (/ K 2.0)) J)) 2.0)))) 3))
54.0ms	(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
44.0ms	(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

210.0ms	(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* (cos (/ K 2.0)) J)) 2.0)))
339.0ms	(cbrt (pow (sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* (cos (/ K 2.0)) J)) 2.0)))) 3))
348.0ms	(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
371.0ms	(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

simplify1.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	1662
1	401
0	169

prune1.1s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 12.2b

regimes879.0ms

Accuracy

91.7% (0.4b remaining)

Error of 13.4b against oracle of 12.9b and baseline of 18.2b

bsearch5.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	44
1	44
0	32

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.9s	1509×	body	1280	valid
1.2s	4309×	body	80	valid
722.0ms	1244×	body	640	valid
225.0ms	618×	body	320	valid
87.0ms	325×	body	160	valid