Details

sample194.0ms

Algorithm

intervals

Results

60.0ms	45×	body	1280	valid
52.0ms	39×	body	640	valid
34.0ms	138×	body	80	valid
15.0ms	21×	body	320	valid
7.0ms	13×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5025
5	4486
4	782
3	215
2	81
1	36
0	17

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* -2 J) (cos (/ K 2)))
0.2b	(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
8.3b	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
9.7b	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
20×	`pow1`
18×	`add-cbrt-cube`
15×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `prod-exp`
11×	`add-cube-cbrt`
10×	`associate-r`
9×	`pow-prod-down` `cbrt-unprod`
8×	`sqrt-prod`
7×	`unpow-prod-down`
4×	`sqrt-div` `pow-exp` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp`
2×	`flip3-+` `associate-l` `associate-r/` `-commutative` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 90

Calls

4 calls:

32.0ms	(* (* -2 J) (cos (/ K 2)))
27.0ms	(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
89.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
149.0ms	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

series531.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* -2 J) (cos (/ K 2)))
126.0ms	(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
168.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
189.0ms	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

simplify1.8s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1519
1	485
0	179

prune627.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (cos (/ K 2)) 2) J)
0.2b	(* (/ U (* (* (cos (/ K 2)) 2) J)) (/ U (* (* (cos (/ K 2)) 2) J)))
8.3b	(sqrt (+ (* (/ U (* (* (cos (/ K 2)) 2) J)) (/ U (* (* (cos (/ K 2)) 2) J))) 1))
9.7b	(* (* -2 J) (* (sqrt (+ (* (/ U (* (* (cos (/ K 2)) 2) J)) (/ U (* (* (cos (/ K 2)) 2) J))) 1)) (cos (/ K 2))))

rewrite679.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-cbrt-cube` `add-exp-log`
51×	`prod-exp` `cbrt-unprod`
29×	`pow1`
24×	`cbrt-undiv` `div-exp`
17×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac` `pow-prod-down`
11×	`associate-r`
9×	`associate-l`
7×	`swap-sqr`
4×	`sqrt-div` `insert-posit16` `div-inv` `add-log-exp`
3×	`associate-l/` `associate-r/` `*-commutative` `sqrt-prod`
2×	`flip3-+` `flip-+`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up` `unswap-sqr`

Counts

4 → 131

Calls

4 calls:

31.0ms	(* (* (cos (/ K 2)) 2) J)
112.0ms	(* (/ U (* (* (cos (/ K 2)) 2) J)) (/ U (* (* (cos (/ K 2)) 2) J)))
176.0ms	(sqrt (+ (* (/ U (* (* (cos (/ K 2)) 2) J)) (/ U (* (* (cos (/ K 2)) 2) J))) 1))
356.0ms	(* (* -2 J) (* (sqrt (+ (* (/ U (* (* (cos (/ K 2)) 2) J)) (/ U (* (* (cos (/ K 2)) 2) J))) 1)) (cos (/ K 2))))

series601.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (* (cos (/ K 2)) 2) J)
159.0ms	(* (/ U (* (* (cos (/ K 2)) 2) J)) (/ U (* (* (cos (/ K 2)) 2) J)))
124.0ms	(sqrt (+ (* (/ U (* (* (cos (/ K 2)) 2) J)) (/ U (* (* (cos (/ K 2)) 2) J))) 1))
223.0ms	(* (* -2 J) (* (sqrt (+ (* (/ U (* (* (cos (/ K 2)) 2) J)) (/ U (* (* (cos (/ K 2)) 2) J))) 1)) (cos (/ K 2))))

simplify3.0s

Counts

143 → 143

Iterations

Iter	Nodes
done	5003
2	3237
1	712
0	237

prune691.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.0b

localize65.0ms

Local error

Found 4 expressions with local error:

8.3b	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
8.3b	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
9.8b	(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
9.8b	(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

rewrite374.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `sqrt-pow1` `add-cube-cbrt`
6×	`rem-sqrt-square` `pow1/2`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `distribute-lft-out` `add-log-exp`

Counts

4 → 80

Calls

4 calls:

71.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
80.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
103.0ms	(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
119.0ms	(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

series827.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
160.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
278.0ms	(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
242.0ms	(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

simplify2.1s

Counts

92 → 92

Iterations

Iter	Nodes
done	5004
3	1614
2	439
1	178
0	92

prune818.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
8.3b	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
9.7b	(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

rewrite607.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
29×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
13×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`sqrt-prod`
7×	`associate-r`
6×	`cbrt-prod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
2×	`flip3-+` `pow1/3` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 78

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
71.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
533.0ms	(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

series675.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (cos (/ K 2)))
187.0ms	(cbrt (cos (/ K 2)))
164.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
192.0ms	(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

simplify2.0s

Counts

90 → 90

Iterations

Iter	Nodes
done	5006
2	1460
1	379
0	147

prune552.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 8.0b

regimes723.0ms

Accuracy

83.1% (1.4b remaining)

Error of 9.7b against oracle of 8.2b and baseline of 16.6b

bsearch4.0ms

simplify23.0ms

Iterations

Iter	Nodes
done	48
1	48
0	32

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.5s	1479×	body	1280	valid
1.3s	1250×	body	640	valid
1.1s	4309×	body	80	valid
847.0ms	625×	body	320	valid
193.0ms	337×	body	160	valid