Details

sample216.0ms

Algorithm

intervals

Results

97.0ms	49×	body	1280	valid
41.0ms	44×	body	640	valid
30.0ms	129×	body	80	valid
18.0ms	27×	body	320	valid
3.0ms	7×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
5	2067
4	616
3	185
2	79
1	34
0	17

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* J 2) (cos (/ K 2)))
0.2b	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
5.7b	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
9.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite698.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

16.0ms	(* (* J 2) (cos (/ K 2)))
105.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
399.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
174.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series590.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (* J 2) (cos (/ K 2)))
155.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
225.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
153.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify1.2s

Counts

145 → 145

Iterations

Iter	Nodes
2	3067
1	664
0	231

prune709.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.4b

localize54.0ms

Local error

Found 4 expressions with local error:

5.7b	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
9.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite988.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

429.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
217.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
206.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
134.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series719.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
162.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
162.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
156.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify2.2s

Counts

87 → 87

Iterations

Iter	Nodes
3	4507
2	868
1	247
0	102

prune649.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.4b

localize90.0ms

Local error

Found 4 expressions with local error:

9.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite574.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

150.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
128.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
127.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
168.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series526.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
146.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
127.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
111.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify8.8s

Counts

76 → 76

Iterations

Iter	Nodes
4	13617
3	1344
2	251
1	94
0	48

prune638.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.4b

localize143.0ms

Local error

Found 4 expressions with local error:

9.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite668.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

177.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
162.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
142.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
185.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series533.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
127.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
140.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
157.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify8.9s

Counts

76 → 76

Iterations

Iter	Nodes
4	13617
3	1344
2	251
1	94
0	48

prune808.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.4b

regimes522.0ms

Accuracy

17.2% (7.1b remaining)

Error of 15.7b against oracle of 8.6b and baseline of 17.2b

bsearch211.0ms

Steps

Iters	Range		Point
1	1.4494688608278896e-204	1.5476579372038662e-204	1.4740161299218837e-204
8	-2.1299395721749067e-207	-1.2247130479564265e-210	-3.3576117535859503e-209

simplify10.0ms

Iterations

Iter	Nodes
2	33
1	33
0	24

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.5s	1402×	body	1280	valid
1.9s	1282×	body	640	valid
1.0s	4329×	body	80	valid
528.0ms	656×	body	320	valid
146.0ms	340×	body	160	valid