Details

sample123.0ms

Algorithm

intervals

Results

31.0ms	45×	body	1280	valid
17.0ms	138×	body	80	valid
17.0ms	39×	body	640	valid
8.0ms	21×	body	320	valid
3.0ms	13×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5038
5	4827
4	843
3	216
2	85
1	36
0	17

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2 (cos (/ K 2))) J))
0.1b	(* (cos (/ K 2)) (* -2 J))
0.1b	(* (* 2 (cos (/ K 2))) J)
9.7b	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

rewrite147.0ms

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:

33.0ms	(/ U (* (* 2 (cos (/ K 2))) J))
30.0ms	(* (cos (/ K 2)) (* -2 J))
21.0ms	(* (* 2 (cos (/ K 2))) J)
60.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

series578.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ U (* (* 2 (cos (/ K 2))) J))
54.0ms	(* (cos (/ K 2)) (* -2 J))
68.0ms	(* (* 2 (cos (/ K 2))) J)
345.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

simplify1.8s

Counts

104 → 104

Iterations

Iter	Nodes
done	5001
2	1590
1	418
0	164

prune672.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2)))
0.1b	(/ U (* (* 2 (cos (/ K 2))) J))
0.1b	(* (* 2 (cos (/ K 2))) J)
9.7b	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))

rewrite95.0ms

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:

8.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2)))
21.0ms	(/ U (* (* 2 (cos (/ K 2))) J))
32.0ms	(* (* 2 (cos (/ K 2))) J)
33.0ms	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))

series798.0ms

Counts

4 → 12

Calls

4 calls:

275.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2)))
122.0ms	(/ U (* (* 2 (cos (/ K 2))) J))
88.0ms	(* (* 2 (cos (/ K 2))) J)
312.0ms	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))

simplify1.6s

Counts

105 → 105

Iterations

Iter	Nodes
done	5002
2	1593
1	419
0	165

prune612.0ms

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	(* (cos (/ K 2)) (* -2 J))
0.2b	(* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J)))
9.8b	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
9.8b	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
9×	`-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `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-r` `*-commutative`

Counts

4 → 80

Calls

4 calls:

17.0ms	(* (cos (/ K 2)) (* -2 J))
46.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J)))
1.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
1.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

series917.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (cos (/ K 2)) (* -2 J))
350.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J)))
250.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
243.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

simplify2.6s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
3	3247
2	724
1	234
0	105

prune599.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.5b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J)))
9.7b	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))
9.7b	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))
9.7b	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

16.0ms	(cbrt (* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J)))
25.0ms	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))
49.0ms	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))
51.0ms	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))

series1.4s

Counts

4 → 12

Calls

4 calls:

392.0ms	(cbrt (* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J)))
305.0ms	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))
352.0ms	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))
381.0ms	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))

simplify3.6s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
3	3879
2	846
1	267
0	110

prune755.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

regimes420.0ms

Accuracy

-5.7% (4.3b remaining)

Error of 8.1b against oracle of 3.8b and baseline of 7.9b

bsearch165.0ms

Steps

Iters	Range		Point
10	4.5767912825291445e+246	4.205015792487067e+261	1.0984957296591846e+254

simplify6.0ms

Iterations

Iter	Nodes
done	29
1	29
0	21

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.4s	1479×	body	1280	valid
1.4s	4309×	body	80	valid
807.0ms	1250×	body	640	valid
403.0ms	625×	body	320	valid
100.0ms	337×	body	160	valid