Details

sample94.0ms

Algorithm

intervals

Results

31.0ms	47×	body	1280	valid
18.0ms	147×	body	80	valid
16.0ms	34×	body	640	valid
6.0ms	17×	body	320	valid
2.0ms	11×	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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.8b

localize38.0ms

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)
8.8b	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

rewrite135.0ms

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:

31.0ms	(/ U (* (* 2 (cos (/ K 2))) J))
22.0ms	(* (cos (/ K 2)) (* -2 J))
30.0ms	(* (* 2 (cos (/ K 2))) J)
48.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ U (* (* 2 (cos (/ K 2))) J))
67.0ms	(* (cos (/ K 2)) (* -2 J))
69.0ms	(* (* 2 (cos (/ K 2))) J)
336.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

simplify1.6s

Counts

104 → 104

Iterations

Iter	Nodes
done	5001
2	1590
1	418
0	164

prune626.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J))))
0.2b	(* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J)))
8.8b	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.8b	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

rewrite249.0ms

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:

176.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J))))
63.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J)))
3.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
3.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

series1.1s

Counts

4 → 12

Calls

4 calls:

319.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J))))
301.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J)))
235.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
275.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

simplify1.8s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	945
1	273
0	115

prune649.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize82.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))) (* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J))))
8.8b	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.8b	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.8b	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
18×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
13×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
9×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate-r` `*-commutative`

Counts

4 → 81

Calls

4 calls:

218.0ms	(* (sqrt (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))) (* (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))))
3.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

series1.4s

Counts

4 → 12

Calls

4 calls:

670.0ms	(* (sqrt (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))) (* (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J))))
228.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
280.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
240.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

simplify2.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	5002
2	1103
1	319
0	132

prune719.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))) (* (cos (/ K 2)) (* -2 J)))
8.8b	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.8b	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.8b	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

94.0ms	(* (sqrt (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))) (* (cos (/ K 2)) (* -2 J)))
3.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
3.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
3.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

series1.4s

Counts

4 → 12

Calls

4 calls:

614.0ms	(* (sqrt (sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))) (* (cos (/ K 2)) (* -2 J)))
295.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
263.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
237.0ms	(sqrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

simplify2.9s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
3	3613
2	821
1	255
0	113

prune620.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.2b

regimes552.0ms

Accuracy

0% (4.2b remaining)

Error of 8.1b against oracle of 3.9b and baseline of 8.1b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	28
1	28
0	19

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	1519×	body	1280	valid
976.0ms	4242×	body	80	valid
787.0ms	647×	body	320	valid
734.0ms	1262×	body	640	valid
123.0ms	332×	body	160	valid