Details

sample127.0ms

Algorithm

intervals

Results

36.0ms	53×	body	1280	valid
29.0ms	127×	body	80	valid
22.0ms	41×	body	640	valid
9.0ms	25×	body	320	valid
3.0ms	10×	body	160	valid

simplify3.7s

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: 18.2b

localize67.0ms

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)
7.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite281.0ms

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:

29.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
16.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
154.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
79.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series800.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
197.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
297.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
230.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.2s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	2368
1	508
0	192

prune698.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize42.0ms

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)
7.4b	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
9.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite288.0ms

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` `pow-exp` `associate-*r/` `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:

14.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
28.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
161.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
82.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series859.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
238.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
304.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
233.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.9s

Counts

94 → 94

Iterations

Iter	Nodes
done	5002
2	2427
1	544
0	199

prune589.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
0.2b	(pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)
7.4b	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))))
9.6b	(sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))

rewrite746.0ms

Algorithm

rewrite-expression-head

Rules

63×	`times-frac`
38×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
36×	`add-cube-cbrt`
35×	`add-exp-log`
25×	`unpow-prod-down` `add-cbrt-cube`
18×	`pow1`
10×	`div-exp` `prod-exp`
9×	`cbrt-unprod` `div-inv`
8×	`pow-prod-down`
7×	`associate-/l*`
5×	`cbrt-undiv`
4×	`sqrt-div` `pow-exp` `associate-*r/` `sqrt-prod` `add-log-exp`
3×	`pow-unpow` `associate-/r*`
2×	`flip3-+` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `*-commutative` `distribute-lft-out` `sqr-pow` `associate-/l/`

Counts

4 → 130

Calls

4 calls:

12.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
16.0ms	(pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)
610.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))))
103.0ms	(sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))

series858.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
239.0ms	(pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)
256.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))))
230.0ms	(sqrt (+ 1.0 (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))

simplify2.4s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
2	3801
1	914
0	298

prune963.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.2b

localize62.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.4b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite316.0ms

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))))
85.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
62.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
78.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

370.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
303.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
236.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
201.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	1471
2	475
1	195
0	97

prune709.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.2b

regimes589.0ms

Accuracy

-1.4% (5.5b remaining)

Error of 18.0b against oracle of 12.5b and baseline of 18.0b

bsearch137.0ms

Steps

Iters	Range		Point
6	2.9613139026136572e+256	2.589187708518178e+257	1.5340647844779605e+257

simplify12.0ms

Iterations

Iter	Nodes
done	40
1	40
0	30

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.4s	1451×	body	1280	valid
1.2s	1263×	body	640	valid
785.0ms	4322×	body	80	valid
230.0ms	622×	body	320	valid
84.0ms	342×	body	160	valid