Details

sample197.0ms

Algorithm

intervals

Results

85.0ms	55×	body	1280	valid
36.0ms	141×	body	80	valid
31.0ms	32×	body	640	valid
19.0ms	23×	body	320	valid
2.0ms	5×	body	160	valid

simplify892.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
4	843
3	216
2	85
1	36
0	17

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2 J) (cos (/ K 2))))
0.1b	(* (cos (/ K 2)) (* -2 J))
0.1b	(* (* 2 J) (cos (/ K 2)))
9.0b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite103.0ms

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:

16.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
29.0ms	(* (cos (/ K 2)) (* -2 J))
17.0ms	(* (* 2 J) (cos (/ K 2)))
41.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

series532.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
68.0ms	(* (cos (/ K 2)) (* -2 J))
56.0ms	(* (* 2 J) (cos (/ K 2)))
308.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

simplify700.0ms

Counts

104 → 104

Iterations

Iter	Nodes
done	2027
2	1564
1	413
0	161

prune551.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J)))
0.2b	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J))))
9.1b	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
9.1b	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

43.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J)))
136.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J))))
1.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
1.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

302.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J)))
326.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J))))
251.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
269.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

simplify960.0ms

Counts

101 → 101

Iterations

Iter	Nodes
done	2018
2	940
1	270
0	114

prune567.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J))))
9.0b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
9.0b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
9.0b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite170.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `*-commutative`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 84

Calls

4 calls:

26.0ms	(cbrt (* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J))))
63.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
36.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
43.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

series1.6s

Counts

4 → 12

Calls

4 calls:

523.0ms	(cbrt (* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J))))
406.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
269.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))
388.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

simplify778.0ms

Counts

96 → 96

Iterations

Iter	Nodes
done	2001
2	855
1	268
0	111

prune840.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))
0.1b	(/ U (* (* 2 J) (cos (/ K 2))))
0.1b	(* (* 2 J) (cos (/ K 2)))
6.8b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

54.0ms	(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))
15.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
28.0ms	(* (* 2 J) (cos (/ K 2)))
151.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))

series668.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))
134.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
90.0ms	(* (* 2 J) (cos (/ K 2)))
373.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))

simplify1.1s

Counts

113 → 113

Iterations

Iter	Nodes
done	2003
2	1892
1	482
0	179

prune569.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.5b

regimes400.0ms

Accuracy

0% (4.1b remaining)

Error of 8.0b against oracle of 3.9b and baseline of 8.0b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	22
1	22
0	15

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.5s	1552×	body	1280	valid
1.6s	4320×	body	80	valid
1.2s	1180×	body	640	valid
485.0ms	649×	body	320	valid
163.0ms	301×	body	160	valid