Details

sample189.0ms

Algorithm

intervals

Results

86.0ms	51×	body	1280	valid
36.0ms	41×	body	640	valid
28.0ms	135×	body	80	valid
8.0ms	16×	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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.0b

localize40.0ms

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	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
11.5b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

rewrite544.0ms

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:

26.0ms	(* (cos (/ K 2)) (* 2 J))
133.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
236.0ms	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
144.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series541.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (cos (/ K 2)) (* 2 J))
134.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
214.0ms	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
124.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

simplify1.2s

Counts

145 → 145

Iterations

Iter	Nodes
done	2009
2	2009
1	705
0	236

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.2b

localize73.0ms

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	(* J (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
11.5b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

rewrite573.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-cbrt-cube` `add-exp-log`
49×	`prod-exp` `cbrt-unprod`
26×	`pow1`
24×	`cbrt-undiv` `div-exp`
18×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-l`
12×	`times-frac`
10×	`pow-prod-down`
9×	`associate-r`
7×	`swap-sqr`
5×	`associate-*r/`
4×	`sqrt-div` `insert-posit16` `div-inv` `add-log-exp`
3×	`*-commutative` `sqrt-prod`
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 → 130

Calls

4 calls:

29.0ms	(* (cos (/ K 2)) (* 2 J))
136.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
281.0ms	(* J (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
122.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series537.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (cos (/ K 2)) (* 2 J))
151.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
174.0ms	(* J (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
123.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

simplify1.1s

Counts

142 → 142

Iterations

Iter	Nodes
done	2003
2	2003
1	696
0	237

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.1b

localize75.0ms

Local error

Found 4 expressions with local error:

8.3b	(sqrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
8.3b	(sqrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
11.5b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
11.5b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

rewrite547.0ms

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:

123.0ms	(sqrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
154.0ms	(sqrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
130.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
138.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series831.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(sqrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
261.0ms	(sqrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
139.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
135.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

simplify1.2s

Counts

88 → 88

Iterations

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

prune1.5s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.1b

localize72.0ms

Local error

Found 4 expressions with local error:

8.3b	(* J (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
11.5b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
11.5b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
11.5b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

rewrite710.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

291.0ms	(* J (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))
134.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
135.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
149.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series636.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(* J (* (* -2 (cos (/ K 2))) (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))
159.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
122.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

simplify1.3s

Counts

84 → 84

Iterations

Iter	Nodes
done	2001
3	2001
2	848
1	240
0	98

prune1.4s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 13.1b

regimes586.0ms

Accuracy

0% (5.1b remaining)

Error of 17.9b against oracle of 12.8b and baseline of 17.9b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	25
1	25
0	17

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.1s	1280×	body	640	valid
2.0s	1481×	body	1280	valid
1.0s	4310×	body	80	valid
483.0ms	605×	body	320	valid
163.0ms	328×	body	160	valid