Details

sample202.0ms

Algorithm

intervals

Results

108.0ms	63×	body	1280	valid
36.0ms	44×	body	640	valid
28.0ms	126×	body	80	valid
10.0ms	17×	body	320	valid
3.0ms	6×	body	160	valid

simplify899.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.2b

localize35.0ms

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)))
6.2b	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite99.0ms

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:

14.0ms	(/ U (* (* J 2) (cos (/ K 2))))
24.0ms	(* (cos (/ K 2)) (* -2 J))
15.0ms	(* (* J 2) (cos (/ K 2)))
45.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

series577.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ U (* (* J 2) (cos (/ K 2))))
66.0ms	(* (cos (/ K 2)) (* -2 J))
75.0ms	(* (* J 2) (cos (/ K 2)))
329.0ms	(* (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

simplify4.9s

Counts

104 → 104

Iterations

Iter	Nodes
3	8613
2	1469
1	408
0	162

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* J 2) (cos (/ K 2)))
0.1b	(* (sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2)))))) (* (sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J))))
6.2b	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
6.2b	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
23×	`add-cbrt-cube` `add-exp-log`
13×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
7×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative`

Counts

4 → 83

Calls

4 calls:

15.0ms	(* (* J 2) (cos (/ K 2)))
106.0ms	(* (sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2)))))) (* (sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J))))
1.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
1.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

series930.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (* J 2) (cos (/ K 2)))
371.0ms	(* (sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2)))))) (* (sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J))))
278.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
219.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

simplify3.1s

Counts

95 → 95

Iterations

Iter	Nodes
3	5725
2	1126
1	320
0	129

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.4b

localize89.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))) (* (sqrt (sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))) (* (sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J)))))
6.2b	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
6.2b	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
6.2b	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

rewrite352.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1`
24×	`add-cbrt-cube` `add-exp-log`
18×	`sqrt-prod`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
13×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
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 → 84

Calls

4 calls:

343.0ms	(* (sqrt (sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))) (* (sqrt (sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))) (* (sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J)))))
2.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
2.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
2.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

308.0ms	(* (sqrt (sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))) (* (sqrt (sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))) (* (sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J)))))
225.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
303.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
286.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

simplify3.9s

Counts

96 → 96

Iterations

Iter	Nodes
3	6469
2	1133
1	312
0	121

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.4b

localize84.0ms

Local error

Found 4 expressions with local error:

6.2b	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
6.2b	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
6.2b	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
6.2b	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

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

series896.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
227.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
260.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))
199.0ms	(sqrt (hypot 1 (/ U (* (* J 2) (cos (/ K 2))))))

simplify5.5s

Counts

76 → 76

Iterations

Iter	Nodes
10	6468
9	1462
8	504
7	235
6	131
5	92
4	72
3	64
2	59
1	46
0	34

prune1.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 2.4b

regimes337.0ms

Accuracy

0% (3.6b remaining)

Error of 7.3b against oracle of 3.7b and baseline of 7.3b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	20
1	20
0	15

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.8s	1538×	body	1280	valid
1.3s	1243×	body	640	valid
1.1s	4354×	body	80	valid
476.0ms	591×	body	320	valid
119.0ms	275×	body	160	valid