Details

sample153.0ms

Algorithm

intervals

Results

62.0ms	52×	body	1280	valid
32.0ms	42×	body	640	valid
26.0ms	133×	body	80	valid
11.0ms	20×	body	320	valid
4.0ms	9×	body	160	valid

simplify960.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	2043
4	623
3	190
2	83
1	34
0	17

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.6b

localize47.0ms

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)))
7.6b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite111.0ms

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 (* (* J 2) (cos (/ K 2))))
16.0ms	(* (cos (/ K 2)) (* -2 J))
21.0ms	(* (* J 2) (cos (/ K 2)))
58.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

series555.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ U (* (* J 2) (cos (/ K 2))))
87.0ms	(* (cos (/ K 2)) (* -2 J))
57.0ms	(* (* J 2) (cos (/ K 2)))
291.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

simplify4.8s

Counts

104 → 104

Iterations

Iter	Nodes
3	8613
2	1469
1	408
0	162

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2)))
0.1b	(/ U (* (* J 2) (cos (/ K 2))))
0.1b	(* (* J 2) (cos (/ K 2)))
7.6b	(* (* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2))) (* -2 J))

rewrite112.0ms

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:

15.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2)))
30.0ms	(/ U (* (* J 2) (cos (/ K 2))))
21.0ms	(* (* J 2) (cos (/ K 2)))
44.0ms	(* (* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2))) (* -2 J))

series761.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2)))
113.0ms	(/ U (* (* J 2) (cos (/ K 2))))
58.0ms	(* (* J 2) (cos (/ K 2)))
355.0ms	(* (* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (cos (/ K 2))) (* -2 J))

simplify4.5s

Counts

105 → 105

Iterations

Iter	Nodes
3	8009
2	1448
1	401
0	160

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* J 2) (cos (/ K 2)))
0.1b	(* (* J 2) (cos (/ K 2)))
7.6b	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
7.6b	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

rewrite40.0ms

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:

16.0ms	(* (* J 2) (cos (/ K 2)))
21.0ms	(* (* J 2) (cos (/ K 2)))
1.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
1.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

series634.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (* J 2) (cos (/ K 2)))
67.0ms	(* (* J 2) (cos (/ K 2)))
258.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
233.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

simplify2.8s

Counts

86 → 86

Iterations

Iter	Nodes
4	3468
3	1118
2	363
1	143
0	71

prune1.1s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 4.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* J 2) (cos (/ K 2))))
0.5b	(cbrt (* (* J 2) (cos (/ K 2))))
7.6b	(sqrt (hypot 1 (/ U (* (* (cbrt (* (* J 2) (cos (/ K 2)))) (cbrt (* (* J 2) (cos (/ K 2))))) (cbrt (* (* J 2) (cos (/ K 2))))))))
7.6b	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

17.0ms	(cbrt (* (* J 2) (cos (/ K 2))))
14.0ms	(cbrt (* (* J 2) (cos (/ K 2))))
1.0ms	(sqrt (hypot 1 (/ U (* (* (cbrt (* (* J 2) (cos (/ K 2)))) (cbrt (* (* J 2) (cos (/ K 2))))) (cbrt (* (* J 2) (cos (/ K 2))))))))
1.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

205.0ms	(cbrt (* (* J 2) (cos (/ K 2))))
195.0ms	(cbrt (* (* J 2) (cos (/ K 2))))
420.0ms	(sqrt (hypot 1 (/ U (* (* (cbrt (* (* J 2) (cos (/ K 2)))) (cbrt (* (* J 2) (cos (/ K 2))))) (cbrt (* (* J 2) (cos (/ K 2))))))))
627.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

simplify6.0s

Counts

68 → 68

Iterations

Iter	Nodes
5	6869
4	1901
3	555
2	239
1	144
0	90

prune1.1s

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 4.0b

regimes522.0ms

Accuracy

0% (4.0b remaining)

Error of 7.7b against oracle of 3.7b and baseline of 7.7b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	20
1	20
0	15

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.0s	1468×	body	1280	valid
1.3s	1283×	body	640	valid
1.2s	4306×	body	80	valid
895.0ms	630×	body	320	valid
629.0ms	316×	body	160	valid