Details

sample168.0ms

Algorithm

intervals

Results

78.0ms	55×	body	1280	valid
30.0ms	141×	body	80	valid
26.0ms	32×	body	640	valid
13.0ms	23×	body	320	valid
2.0ms	5×	body	160	valid

simplify599.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2024
4	782
3	215
2	81
1	36
0	17

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize42.0ms

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))))
8.7b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
9.0b	(* (* (cos (/ K 2)) (* -2 J)) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))

rewrite493.0ms

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-r`
12×	`times-frac`
11×	`associate-l`
10×	`pow-prod-down`
7×	`swap-sqr`
6×	`sqrt-prod`
4×	`sqrt-div` `insert-posit16` `div-inv` `add-log-exp`
3×	`associate-r/` `-commutative`
2×	`flip3-+` `flip-+`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `associate-*l/` `pow-sqr` `pow-prod-up` `unswap-sqr`

Counts

4 → 133

Calls

4 calls:

24.0ms	(* (cos (/ K 2)) (* 2 J))
110.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
134.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
221.0ms	(* (* (cos (/ K 2)) (* -2 J)) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))

series518.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (cos (/ K 2)) (* 2 J))
104.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
108.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
252.0ms	(* (* (cos (/ K 2)) (* -2 J)) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))

simplify639.0ms

Counts

145 → 145

Iterations

Iter	Nodes
done	2001
1	708
0	236

prune751.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (/ K 2)) (* (* -2 J) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
0.2b	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
8.7b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
9.0b	(* (* -2 J) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))

rewrite652.0ms

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-r`
12×	`times-frac`
11×	`associate-l`
10×	`pow-prod-down`
7×	`swap-sqr` `associate-*r/`
6×	`sqrt-div` `sqrt-prod`
4×	`insert-posit16` `div-inv` `add-log-exp`
3×	`flip3-+` `*-commutative` `flip-+`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `associate-*l/` `pow-sqr` `pow-prod-up` `unswap-sqr`

Counts

4 → 135

Calls

4 calls:

264.0ms	(* (cos (/ K 2)) (* (* -2 J) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
93.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
100.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
191.0ms	(* (* -2 J) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))

series618.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(* (cos (/ K 2)) (* (* -2 J) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
133.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
103.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
159.0ms	(* (* -2 J) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))

simplify627.0ms

Counts

147 → 147

Iterations

Iter	Nodes
done	2001
1	710
0	236

prune658.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.6b

localize53.0ms

Local error

Found 4 expressions with local error:

9.9b	(sqrt (* (cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)) (cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
15.5b	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
15.5b	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
15.5b	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

rewrite363.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
12×	`pow1`
9×	`cbrt-prod` `sqrt-pow1` `flip3-+` `pow1/3` `flip-+`
8×	`sqrt-div`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`frac-times` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 70

Calls

4 calls:

155.0ms	(sqrt (* (cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)) (cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
91.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
60.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
55.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series1.1s

Counts

4 → 12

Calls

4 calls:

266.0ms	(sqrt (* (cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)) (cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
251.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
253.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
291.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

simplify705.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	2004
2	493
1	210
0	115

prune698.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.6b

localize93.0ms

Local error

Found 4 expressions with local error:

9.3b	(cbrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
9.9b	(sqrt (* (* (cbrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))) (cbrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))) (cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
15.5b	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
15.5b	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

rewrite869.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-div`
60×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
14×	`associate-*l/`
12×	`cbrt-prod`
10×	`pow1`
8×	`add-sqr-sqrt` `-un-lft-identity` `associate-r/` `add-cube-cbrt`
6×	`pow1/3`
5×	`pow-prod-down`
4×	`sqrt-pow1` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `insert-posit16` `add-log-exp`
1×	`pow1/2`

Counts

4 → 85

Calls

4 calls:

58.0ms	(cbrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
670.0ms	(sqrt (* (* (cbrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))) (cbrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))) (cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
63.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
76.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series1.0s

Counts

4 → 12

Calls

4 calls:

247.0ms	(cbrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
262.0ms	(sqrt (* (* (cbrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))) (cbrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))) (cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
260.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
241.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

simplify995.0ms

Counts

97 → 97

Iterations

Iter	Nodes
done	2004
2	704
1	374
0	207

prune925.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 10.6b

regimes559.0ms

Accuracy

-5.2% (8.3b remaining)

Error of 18.3b against oracle of 10.1b and baseline of 17.9b

bsearch361.0ms

Steps

Iters	Range		Point
9	6.663106274387195e-199	1.6002496888159529e-193	6.925182500906958e-195
9	1.489357378424865e-235	2.5924312970512867e-230	1.32384858102125e-232

simplify16.0ms

Iterations

Iter	Nodes
done	44
3	44
2	43
1	39
0	25

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.5s	1552×	body	1280	valid
1.5s	4320×	body	80	valid
1.2s	1180×	body	640	valid
496.0ms	649×	body	320	valid
189.0ms	301×	body	160	valid