Details

sample166.0ms

Algorithm

intervals

Results

54.0ms	44×	body	640	valid
49.0ms	49×	body	1280	valid
25.0ms	129×	body	80	valid
16.0ms	27×	body	320	valid
2.0ms	7×	body	160	valid

simplify994.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2093
5	2093
4	843
3	216
2	85
1	36
0	17

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2 J) (cos (/ K 2))))
0.2b	(* (cos (/ K 2)) (* -2 J))
0.2b	(* (* 2 J) (cos (/ K 2)))
5.7b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite119.0ms

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:

29.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
31.0ms	(* (cos (/ K 2)) (* -2 J))
17.0ms	(* (* 2 J) (cos (/ K 2)))
40.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

series611.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
66.0ms	(* (cos (/ K 2)) (* -2 J))
71.0ms	(* (* 2 J) (cos (/ K 2)))
354.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

simplify1.4s

Counts

104 → 104

Iterations

Iter	Nodes
done	2090
3	2090
2	1564
1	413
0	161

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2 J) (cos (/ K 2)))
0.2b	(* (* 2 J) (cos (/ K 2)))
5.7b	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
5.7b	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 74

Calls

4 calls:

40.0ms	(* (* 2 J) (cos (/ K 2)))
31.0ms	(* (* 2 J) (cos (/ K 2)))
3.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
3.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

series590.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (* 2 J) (cos (/ K 2)))
59.0ms	(* (* 2 J) (cos (/ K 2)))
235.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
235.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

simplify1.2s

Counts

86 → 86

Iterations

Iter	Nodes
done	2003
4	2003
3	1348
2	403
1	144
0	70

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.6b

localize80.0ms

Local error

Found 4 expressions with local error:

5.7b	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
5.9b	(cbrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
5.9b	(cbrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
5.9b	(cbrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

2.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
1.0ms	(cbrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
1.0ms	(cbrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
2.0ms	(cbrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

241.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
381.0ms	(cbrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
385.0ms	(cbrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
358.0ms	(cbrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

simplify999.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	2000
4	2000
3	606
2	216
1	107
0	64

prune1.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 2.6b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
5.7b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1` `add-exp-log`
23×	`add-cbrt-cube`
22×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-l`
1×	`associate-r` `*-commutative`

Counts

4 → 78

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
195.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

series803.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt (cos (/ K 2)))
127.0ms	(cbrt (cos (/ K 2)))
148.0ms	(cbrt (cos (/ K 2)))
339.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

simplify1.2s

Counts

90 → 90

Iterations

Iter	Nodes
done	2000
3	2000
2	1283
1	327
0	123

prune1.3s

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 2.6b

regimes572.0ms

Accuracy

0% (3.9b remaining)

Error of 7.3b against oracle of 3.4b and baseline of 7.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	22
1	22
0	15

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.1s	1402×	body	1280	valid
1.7s	1282×	body	640	valid
1.6s	4329×	body	80	valid
600.0ms	656×	body	320	valid
162.0ms	340×	body	160	valid