Details

sample153.0ms

Algorithm

intervals

Results

68.0ms	51×	body	1280	valid
27.0ms	138×	body	80	valid
26.0ms	36×	body	640	valid
12.0ms	21×	body	320	valid
4.0ms	10×	body	160	valid

simplify994.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.6b

localize34.0ms

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)))
6.6b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite139.0ms

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` `insert-posit16` `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 → 92

Calls

4 calls:

20.0ms	(/ U (* (* J 2) (cos (/ K 2))))
15.0ms	(* (cos (/ K 2)) (* -2 J))
28.0ms	(* (* J 2) (cos (/ K 2)))
73.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

series632.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ U (* (* J 2) (cos (/ K 2))))
88.0ms	(* (cos (/ K 2)) (* -2 J))
89.0ms	(* (* J 2) (cos (/ K 2)))
322.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

simplify4.9s

Counts

104 → 104

Iterations

Iter	Nodes
3	8613
2	1469
1	408
0	162

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (cos (* 1/2 K)) J))
0.1b	(* (cos (* 1/2 K)) J)
0.1b	(* (cos (/ K 2)) (* -2 J))
6.6b	(* (hypot 1 (* 1/2 (/ U (* (cos (* 1/2 K)) J)))) (* (cos (/ K 2)) (* -2 J)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-cbrt-cube` `add-exp-log`
20×	`pow1`
12×	`add-sqr-sqrt`
11×	`prod-exp` `cbrt-unprod`
10×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt`
9×	`associate-l`
5×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

12.0ms	(/ U (* (cos (* 1/2 K)) J))
20.0ms	(* (cos (* 1/2 K)) J)
19.0ms	(* (cos (/ K 2)) (* -2 J))
60.0ms	(* (hypot 1 (* 1/2 (/ U (* (cos (* 1/2 K)) J)))) (* (cos (/ K 2)) (* -2 J)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ U (* (cos (* 1/2 K)) J))
73.0ms	(* (cos (* 1/2 K)) J)
66.0ms	(* (cos (/ K 2)) (* -2 J))
367.0ms	(* (hypot 1 (* 1/2 (/ U (* (cos (* 1/2 K)) J)))) (* (cos (/ K 2)) (* -2 J)))

simplify2.6s

Counts

102 → 102

Iterations

Iter	Nodes
3	5692
2	1199
1	356
0	155

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize46.0ms

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)))
6.6b	(* (* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2))) (* -2 J))

rewrite137.0ms

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` `insert-posit16` `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 → 93

Calls

4 calls:

16.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2)))
31.0ms	(/ U (* (* J 2) (cos (/ K 2))))
38.0ms	(* (* J 2) (cos (/ K 2)))
51.0ms	(* (* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2))) (* -2 J))

series831.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2)))
123.0ms	(/ U (* (* J 2) (cos (/ K 2))))
68.0ms	(* (* J 2) (cos (/ K 2)))
388.0ms	(* (* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2))) (* -2 J))

simplify4.8s

Counts

105 → 105

Iterations

Iter	Nodes
3	8009
2	1448
1	401
0	160

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.5b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (/ K 2)) (* -2 J))
0.1b	(* (* J 2) (cos (/ K 2)))
0.7b	(/ 1 (/ (* (* J 2) (cos (/ K 2))) U))
6.6b	(* (hypot 1 (/ 1 (/ (* (* J 2) (cos (/ K 2))) U))) (* (cos (/ K 2)) (* -2 J)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-exp-log`
37×	`add-cbrt-cube`
33×	`times-frac`
24×	`pow1`
23×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
21×	`prod-exp`
17×	`div-exp`
15×	`cbrt-unprod`
12×	`pow-prod-down`
7×	`cbrt-undiv` `associate-/r` `associate-l*`
5×	`associate-r` `div-inv`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `associate-/l`
1×	`clear-num` `frac-2neg` `associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 129

Calls

4 calls:

32.0ms	(* (cos (/ K 2)) (* -2 J))
28.0ms	(* (* J 2) (cos (/ K 2)))
22.0ms	(/ 1 (/ (* (* J 2) (cos (/ K 2))) U))
72.0ms	(* (hypot 1 (/ 1 (/ (* (* J 2) (cos (/ K 2))) U))) (* (cos (/ K 2)) (* -2 J)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (cos (/ K 2)) (* -2 J))
55.0ms	(* (* J 2) (cos (/ K 2)))
135.0ms	(/ 1 (/ (* (* J 2) (cos (/ K 2))) U))
285.0ms	(* (hypot 1 (/ 1 (/ (* (* J 2) (cos (/ K 2))) U))) (* (cos (/ K 2)) (* -2 J)))

simplify15.7s

Counts

141 → 141

Iterations

Iter	Nodes
3	11166
2	1988
1	560
0	223

prune1.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.5b

regimes439.0ms

Accuracy

0% (3.5b remaining)

Error of 7.2b against oracle of 3.7b and baseline of 7.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	22
1	22
0	16

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.1s	1517×	body	1280	valid
1.7s	1275×	body	640	valid
1.0s	4295×	body	80	valid
473.0ms	627×	body	320	valid
128.0ms	291×	body	160	valid