Details

sample111.0ms

Algorithm

intervals

Results

43.0ms	46×	body	1280	valid
20.0ms	45×	body	640	valid
18.0ms	144×	body	80	valid
5.0ms	15×	body	320	valid
1.0ms	6×	body	160	valid

simplify4.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	636
1	34	636
2	72	636
3	135	636
4	209	636
5	495	636
6	3226	636
done	5000	636

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize57.0ms

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)
8.5b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.9b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite313.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
20×	`pow1`
18×	`add-cbrt-cube`
17×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`prod-exp`
11×	`add-cube-cbrt`
10×	`associate-r`
9×	`pow-prod-down` `cbrt-unprod`
8×	`unpow-prod-down` `sqrt-prod`
4×	`expm1-log1p-u` `sqrt-div` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp` `hypot-def`
2×	`flip3-+` `associate-l` `associate-r/` `-commutative` `flip-+` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 96

Calls

4 calls:

27.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
32.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
182.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
68.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series772.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
213.0ms	(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))))
214.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.9s

Counts

108 → 108

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	200	53644
1	519	50768
2	2432	50038
done	5000	50038

prune833.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.9b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
8.5b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
23×	`pow1`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
9×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-l` `-commutative` `associate-/l`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Counts

4 → 88

Calls

4 calls:

22.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
14.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
19.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
61.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series930.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
65.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
57.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
682.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify2.5s

Counts

100 → 100

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	194	39918
1	499	37315
2	3021	36600
done	5000	36520

prune770.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.8b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
8.6b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
23×	`pow1`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `-commutative` `associate-/l`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

6.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
14.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
14.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
34.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

573.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
96.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
54.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
743.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

simplify2.2s

Counts

101 → 101

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	207	50291
1	536	47363
2	3024	45528
done	5001	45528

prune632.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
0.1b	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
0.1b	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
8.6b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
27×	`add-cbrt-cube` `add-exp-log`
24×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
10×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down`
7×	`associate-/l*`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`*-commutative`
1×	`hypot-udef` `clear-num` `frac-2neg` `unswap-sqr` `associate-/l/`

Counts

4 → 104

Calls

4 calls:

0.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
6.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
12.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
21.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

557.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
579.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
128.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
625.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

simplify2.5s

Counts

116 → 116

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	258	66507
1	639	61880
2	3108	60984
done	5000	60584

prune723.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.8b

regimes594.0ms

Accuracy

0% (0.3b remaining)

Error of 8.1b against oracle of 7.8b and baseline of 8.1b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	692
1	24	692
done	24	692

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.3s	1296×	body	640	valid
1.2s	1520×	body	1280	valid
1.1s	4242×	body	80	valid
249.0ms	623×	body	320	valid
85.0ms	324×	body	160	valid