Details

sample169.0ms

Algorithm

intervals

Results

75.0ms	49×	body	1280	valid
33.0ms	39×	body	640	valid
30.0ms	141×	body	80	valid
12.0ms	20×	body	320	valid
3.0ms	7×	body	160	valid

simplify680.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	2059
4	626
3	192
2	85
1	36
0	17

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.2b

localize27.0ms

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)))
6.1b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite153.0ms

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 (* (* J 2) (cos (/ K 2))))
32.0ms	(* (cos (/ K 2)) (* -2 J))
21.0ms	(* (* J 2) (cos (/ K 2)))
66.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ U (* (* J 2) (cos (/ K 2))))
53.0ms	(* (cos (/ K 2)) (* -2 J))
61.0ms	(* (* J 2) (cos (/ K 2)))
395.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

simplify4.7s

Counts

104 → 104

Iterations

Iter	Nodes
3	8580
2	1465
1	410
0	162

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.6b

localize46.0ms

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)))
6.1b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

rewrite190.0ms

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)))
186.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

series744.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(cbrt (cos (/ K 2)))
123.0ms	(cbrt (cos (/ K 2)))
152.0ms	(cbrt (cos (/ K 2)))
352.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

simplify3.1s

Counts

90 → 90

Iterations

Iter	Nodes
3	6104
2	1263
1	326
0	124

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.6b

localize57.0ms

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)))
6.1b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (log (exp (cbrt (cos (/ K 2)))))) (* (cbrt (cos (/ K 2))) (* -2 J))))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1` `add-exp-log`
26×	`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:

2.0ms	(cbrt (cos (/ K 2)))
2.0ms	(cbrt (cos (/ K 2)))
2.0ms	(cbrt (cos (/ K 2)))
217.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (log (exp (cbrt (cos (/ K 2)))))) (* (cbrt (cos (/ K 2))) (* -2 J))))

series770.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (cos (/ K 2)))
141.0ms	(cbrt (cos (/ K 2)))
136.0ms	(cbrt (cos (/ K 2)))
337.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (log (exp (cbrt (cos (/ K 2)))))) (* (cbrt (cos (/ K 2))) (* -2 J))))

simplify3.6s

Counts

90 → 90

Iterations

Iter	Nodes
3	6542
2	1403
1	353
0	129

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.6b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
0.6b	(expm1 (cbrt (cos (/ K 2))))
6.1b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (log1p (expm1 (cbrt (cos (/ K 2))))) (* -2 J))))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1` `add-exp-log`
27×	`add-cbrt-cube`
22×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`associate-l`
2×	`pow1/3`
1×	`expm1-log1p` `associate-r` `*-commutative` `expm1-udef`

Counts

4 → 76

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
0.0ms	(expm1 (cbrt (cos (/ K 2))))
193.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (log1p (expm1 (cbrt (cos (/ K 2))))) (* -2 J))))

series1.1s

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (cos (/ K 2)))
122.0ms	(cbrt (cos (/ K 2)))
294.0ms	(expm1 (cbrt (cos (/ K 2))))
551.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (log1p (expm1 (cbrt (cos (/ K 2))))) (* -2 J))))

simplify4.3s

Counts

88 → 88

Iterations

Iter	Nodes
3	7391
2	1570
1	408
0	150

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.6b

regimes574.0ms

Accuracy

0% (3.8b remaining)

Error of 7.5b against oracle of 3.7b and baseline of 7.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	22
1	22
0	15

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.2s	1499×	body	1280	valid
1.4s	4296×	body	80	valid
1.4s	1279×	body	640	valid
505.0ms	635×	body	320	valid
162.0ms	295×	body	160	valid