Details

sample221.0ms

Algorithm

intervals

Results

76.0ms	49×	body	1280	valid
47.0ms	41×	body	640	valid
38.0ms	135×	body	80	valid
29.0ms	21×	body	320	valid
6.0ms	10×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* J 2) (cos (/ K 2)))
0.2b	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
8.3b	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
8.7b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite787.0ms

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:

32.0ms	(* (* J 2) (cos (/ K 2)))
132.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
444.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
175.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series1.1s

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (* J 2) (cos (/ K 2)))
184.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
738.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
149.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify1.3s

Counts

145 → 145

Iterations

Iter	Nodes
2	3067
1	664
0	231

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.5b

localize81.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* J 2) (cos (/ K 2)))
0.2b	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* 2 (* (cos (* 1/2 K)) J))))
8.3b	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* 2 (* (cos (* 1/2 K)) J)))) 1)) (* (cos (/ K 2)) (* -2 J)))
8.7b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* 2 (* (cos (* 1/2 K)) J)))) 1))

rewrite742.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

15.0ms	(* (* J 2) (cos (/ K 2)))
204.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* 2 (* (cos (* 1/2 K)) J))))
355.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* 2 (* (cos (* 1/2 K)) J)))) 1)) (* (cos (/ K 2)) (* -2 J)))
165.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* 2 (* (cos (* 1/2 K)) J)))) 1))

series644.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (* J 2) (cos (/ K 2)))
161.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* 2 (* (cos (* 1/2 K)) J))))
225.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* 2 (* (cos (* 1/2 K)) J)))) 1)) (* (cos (/ K 2)) (* -2 J)))
170.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* 2 (* (cos (* 1/2 K)) J)))) 1))

simplify1.7s

Counts

134 → 134

Iterations

Iter	Nodes
2	3775
1	721
0	249

prune2.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.5b

localize57.0ms

Local error

Found 4 expressions with local error:

8.3b	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
8.3b	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
8.7b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
8.7b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite721.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

189.0ms	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
191.0ms	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
165.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
174.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series942.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
302.0ms	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
184.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
175.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify22.1s

Counts

88 → 88

Iterations

Iter	Nodes
4	15942
3	1864
2	449
1	182
0	92

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.5b

localize76.0ms

Local error

Found 4 expressions with local error:

8.3b	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
8.7b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
8.7b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
8.7b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite880.0ms

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:

367.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
167.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
158.0ms	(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))

series733.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
161.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
150.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
176.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify2.3s

Counts

87 → 87

Iterations

Iter	Nodes
3	4507
2	868
1	247
0	102

prune1.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 8.5b

regimes669.0ms

Accuracy

16.2% (7.1b remaining)

Error of 15.6b against oracle of 8.5b and baseline of 17.0b

bsearch380.0ms

Steps

Iters	Range		Point
5	1.1954967650485863e-170	2.58594990464841e-170	1.920732154664696e-170
9	-8.1282947335980755e-202	-9.690005947286085e-207	-1.7519438251008617e-206

simplify14.0ms

Iterations

Iter	Nodes
2	43
1	43
0	30

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.6s	1479×	body	1280	valid
1.7s	4304×	body	80	valid
1.4s	1281×	body	640	valid
610.0ms	610×	body	320	valid
179.0ms	328×	body	160	valid