Details

sample163.0ms

Algorithm

intervals

Results

65.0ms	53×	body	1280	valid
40.0ms	48×	body	640	valid
26.0ms	131×	body	80	valid
10.0ms	14×	body	320	valid
4.0ms	10×	body	160	valid

simplify968.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	2043
4	623
3	190
2	83
1	34
0	17

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.4b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* J 2) (cos (/ K 2))))
0.1b	(* (cos (/ K 2)) (* -2 J))
0.1b	(* (* J 2) (cos (/ K 2)))
7.3b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite153.0ms

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` `add-cube-cbrt`
7×	`associate-l`
5×	`associate-r`
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`

Counts

4 → 88

Calls

4 calls:

26.0ms	(/ U (* (* J 2) (cos (/ K 2))))
27.0ms	(* (cos (/ K 2)) (* -2 J))
34.0ms	(* (* J 2) (cos (/ K 2)))
63.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

series579.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ U (* (* J 2) (cos (/ K 2))))
65.0ms	(* (cos (/ K 2)) (* -2 J))
71.0ms	(* (* J 2) (cos (/ K 2)))
300.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

simplify4.5s

Counts

100 → 100

Iterations

Iter	Nodes
3	8588
2	1471
1	410
0	158

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2)))
0.1b	(/ U (* (* J 2) (cos (/ K 2))))
0.1b	(* (* J 2) (cos (/ K 2)))
7.4b	(* (* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2))) (* -2 J))

rewrite93.0ms

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:

13.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2)))
26.0ms	(/ U (* (* J 2) (cos (/ K 2))))
20.0ms	(* (* J 2) (cos (/ K 2)))
31.0ms	(* (* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2))) (* -2 J))

series789.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2)))
111.0ms	(/ U (* (* J 2) (cos (/ K 2))))
80.0ms	(* (* J 2) (cos (/ K 2)))
334.0ms	(* (* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2))) (* -2 J))

simplify5.1s

Counts

101 → 101

Iterations

Iter	Nodes
3	8015
2	1457
1	403
0	156

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.7b

localize84.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J))))
7.3b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
7.3b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
7.3b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`associate-l`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `*-commutative`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 80

Calls

4 calls:

22.0ms	(cbrt (* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J))))
33.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
66.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
46.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

series1.5s

Counts

4 → 12

Calls

4 calls:

456.0ms	(cbrt (* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J))))
325.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
358.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
376.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

simplify1.6s

Counts

92 → 92

Iterations

Iter	Nodes
3	3466
2	837
1	265
0	110

prune1.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.7b

localize97.0ms

Local error

Found 4 expressions with local error:

7.3b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
7.3b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
7.3b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
7.3b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

40×	`pow1` `add-cbrt-cube` `add-exp-log`
24×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`associate-l`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-r` `*-commutative` `log1p-expm1-u` `add-log-exp`

Counts

4 → 92

Calls

4 calls:

31.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
59.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
37.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
40.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

series1.4s

Counts

4 → 12

Calls

4 calls:

359.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
344.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
342.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
336.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

simplify1.2s

Counts

104 → 104

Iterations

Iter	Nodes
3	2797
2	600
1	169
0	68

prune2.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.7b

regimes420.0ms

Accuracy

0% (3.9b remaining)

Error of 7.9b against oracle of 3.9b and baseline of 7.9b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	20
1	20
0	15

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.1s	1536×	body	1280	valid
1.2s	643×	body	320	valid
1.1s	4244×	body	80	valid
1.1s	1255×	body	640	valid
157.0ms	323×	body	160	valid