Details

sample133.0ms

Algorithm

intervals

Results

41.0ms	47×	body	1280	valid
25.0ms	39×	body	640	valid
22.0ms	138×	body	80	valid
12.0ms	25×	body	320	valid
3.0ms	7×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	34	24
2	72	24
3	136	24
4	214	24
5	498	24
6	3356	24
done	5002	24

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* 2.0 J) (cos (/ K 2.0)))
0.4b	(* (* -2.0 J) (cos (/ K 2.0)))
5.2b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.8b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite508.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
23×	`add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt`
13×	`-un-lft-identity` `associate-r*`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt`
8×	`sqrt-prod`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `*-commutative` `hypot-def`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`unpow-prod-down` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqr-pow`

Counts

4 → 90

Calls

4 calls:

41.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
42.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
254.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
165.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
84.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
267.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
188.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.0s

Counts

102 → 102

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	145	1894
1	372	1713
2	2252	1484
done	5001	1478

prune545.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.4b	(* (* 2.0 J) (cos (/ K 2.0)))
0.4b	(* (* -2.0 J) (cos (/ K 2.0)))
5.2b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

40.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
42.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
41.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
102.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series1.0s

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
74.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
84.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
729.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify2.3s

Counts

100 → 100

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	193	1843
1	497	1816
2	3042	1449
done	5000	1447

prune656.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize52.0ms

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))))
0.4b	(* (* 2.0 J) (cos (/ K 2.0)))
5.5b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
23×	`pow1`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
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×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

9.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
23.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
33.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
33.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

706.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
147.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
61.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
725.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

simplify1.7s

Counts

101 → 101

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	206	2273
1	534	2248
2	3049	1773
done	5000	1772

prune632.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.4b

localize36.0ms

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))))
0.2b	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
5.5b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
27×	`add-exp-log` `add-cbrt-cube`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
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` `frac-2neg` `clear-num` `associate-/l/` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

0.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
19.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
32.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
36.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

series2.2s

Counts

4 → 12

Calls

4 calls:

625.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
661.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
137.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
735.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

simplify1.4s

Counts

116 → 116

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	250	2841
1	623	2768
2	3044	2304
done	5001	2303

prune560.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 5.4b

regimes518.0ms

Accuracy

0% (0.3b remaining)

Error of 7.9b against oracle of 7.6b and baseline of 7.9b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	26
1	24	26
done	24	26

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.2s	1529×	body	1280	valid
1.0s	4302×	body	80	valid
675.0ms	1263×	body	640	valid
433.0ms	328×	body	160	valid
186.0ms	581×	body	320	valid