Details

sample185.0ms

Algorithm

intervals

Results

75.0ms	45×	body	1280	valid
45.0ms	50×	body	640	valid
30.0ms	136×	body	80	valid
8.0ms	12×	body	320	valid
6.0ms	13×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2090
5	2090
4	782
3	215
2	81
1	36
0	17

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (cos (/ K 2)) (* 2 J)))
0.2b	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
7.2b	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
9.7b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

rewrite491.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-cbrt-cube` `add-exp-log`
49×	`prod-exp` `cbrt-unprod`
27×	`cbrt-undiv` `div-exp`
21×	`pow1`
20×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `add-cube-cbrt`
15×	`times-frac`
13×	`associate-r`
8×	`associate-l`
7×	`swap-sqr` `pow-prod-down`
6×	`sqrt-prod`
5×	`div-inv`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`associate-r/` `associate-/l`
2×	`flip3-+` `*-commutative` `flip-+`
1×	`pow2` `frac-times` `rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `associate-l/` `pow-sqr` `pow-prod-up` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

23.0ms	(/ U (* (cos (/ K 2)) (* 2 J)))
117.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
232.0ms	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
115.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series586.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ U (* (cos (/ K 2)) (* 2 J)))
114.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
232.0ms	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
141.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

simplify1.2s

Counts

150 → 150

Iterations

Iter	Nodes
done	2001
2	2001
1	701
0	236

prune827.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (cos (/ K 2)) (* 2 J)))
0.2b	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
7.2b	(* J (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
9.7b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

rewrite476.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-cbrt-cube` `add-exp-log`
49×	`prod-exp` `cbrt-unprod`
27×	`cbrt-undiv` `div-exp`
21×	`pow1`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
15×	`times-frac`
10×	`associate-l`
8×	`associate-r`
7×	`swap-sqr` `pow-prod-down`
5×	`associate-*r/` `div-inv`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3-+` `*-commutative` `flip-+`
1×	`pow2` `frac-times` `rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `associate-l/` `pow-sqr` `pow-prod-up` `unswap-sqr`

Counts

4 → 135

Calls

4 calls:

13.0ms	(/ U (* (cos (/ K 2)) (* 2 J)))
104.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
248.0ms	(* J (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
108.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series548.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ U (* (cos (/ K 2)) (* 2 J)))
147.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
164.0ms	(* J (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
140.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

simplify1.2s

Counts

147 → 147

Iterations

Iter	Nodes
done	2000
2	2000
1	692
0	237

prune960.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.7b

localize67.0ms

Local error

Found 4 expressions with local error:

7.2b	(sqrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
7.2b	(sqrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
9.7b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
9.7b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

rewrite574.0ms

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:

185.0ms	(sqrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
130.0ms	(sqrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
106.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
152.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series823.0ms

Counts

4 → 12

Calls

4 calls:

300.0ms	(sqrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
248.0ms	(sqrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
150.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
125.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

simplify1.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	2018
3	2018
2	492
1	182
0	92

prune656.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.7b

localize83.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt J)
3.2b	(* (cbrt J) (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
4.3b	(* (* (cbrt J) (cbrt J)) (* (cbrt J) (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))))
9.7b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

1.0ms	(cbrt J)
227.0ms	(* (cbrt J) (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
793.0ms	(* (* (cbrt J) (cbrt J)) (* (cbrt J) (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))))
172.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series920.0ms

Counts

4 → 12

Calls

4 calls:

259.0ms	(cbrt J)
316.0ms	(* (cbrt J) (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
217.0ms	(* (* (cbrt J) (cbrt J)) (* (cbrt J) (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))))
128.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

simplify1.4s

Counts

104 → 104

Iterations

Iter	Nodes
done	2005
3	2005
2	1627
1	433
0	160

prune489.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 10.7b

regimes531.0ms

Accuracy

-4.8% (5.2b remaining)

Error of 17.8b against oracle of 12.6b and baseline of 17.6b

bsearch282.0ms

Steps

Iters	Range		Point
8	9.129764230118176e-234	3.33100974052138e-231	9.21309517046108e-234
7	-1.370860344702447e-289	-1.836848574899269e-291	-5.409574867481547e-290

simplify8.0ms

Iterations

Iter	Nodes
done	47
1	47
0	31

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.3s	1464×	body	1280	valid
1.6s	1252×	body	640	valid
1.1s	4326×	body	80	valid
413.0ms	624×	body	320	valid
141.0ms	337×	body	160	valid