Details

sample112.0ms

Algorithm

intervals

Results

35.0ms	47×	body	1280	valid
24.0ms	34×	body	640	valid
20.0ms	147×	body	80	valid
7.0ms	17×	body	320	valid
3.0ms	11×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5025
5	4486
4	782
3	215
2	81
1	36
0	17

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (cos (/ K 2)))
0.3b	(* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J)))
8.8b	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
8.9b	(sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1))

rewrite424.0ms

Algorithm

rewrite-expression-head

Rules

145×	`add-cbrt-cube` `add-exp-log`
97×	`times-frac`
61×	`cbrt-undiv` `div-exp`
51×	`prod-exp` `cbrt-unprod`
50×	`add-sqr-sqrt`
47×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-r`
21×	`pow1`
18×	`associate-l`
17×	`swap-sqr`
9×	`div-inv`
7×	`pow-prod-down`
6×	`sqrt-prod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-r/` `associate-/l*`
2×	`flip3-+` `*-commutative` `flip-+`
1×	`pow2` `frac-times` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `associate-*l/` `pow-sqr` `pow-prod-up` `unswap-sqr`

Counts

4 → 190

Calls

4 calls:

8.0ms	(/ U (cos (/ K 2)))
91.0ms	(* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J)))
208.0ms	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
103.0ms	(sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1))

series476.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ U (cos (/ K 2)))
112.0ms	(* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J)))
182.0ms	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
111.0ms	(sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1))

simplify3.1s

Counts

202 → 202

Iterations

Iter	Nodes
done	5000
2	4866
1	1037
0	333

prune949.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.7b

localize40.0ms

Local error

Found 4 expressions with local error:

8.8b	(sqrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
8.8b	(sqrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
8.9b	(sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1))
8.9b	(sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1))

rewrite366.0ms

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:

84.0ms	(sqrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
100.0ms	(sqrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
97.0ms	(sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1))
83.0ms	(sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1))

series860.0ms

Counts

4 → 12

Calls

4 calls:

316.0ms	(sqrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
277.0ms	(sqrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
116.0ms	(sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1))
151.0ms	(sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1))

simplify2.0s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
3	2188
2	501
1	181
0	92

prune721.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.7b

localize76.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J)))
8.8b	(sqrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
8.9b	(sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1))
17.9b	(pow (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1) 1/4)

rewrite433.0ms

Algorithm

rewrite-expression-head

Rules

135×	`add-exp-log`
134×	`add-cbrt-cube`
88×	`times-frac`
60×	`cbrt-undiv` `div-exp`
46×	`add-sqr-sqrt`
45×	`prod-exp` `cbrt-unprod`
41×	`*-un-lft-identity` `add-cube-cbrt`
17×	`swap-sqr` `associate-r` `associate-l`
15×	`pow1`
13×	`sqrt-prod`
8×	`div-inv`
6×	`sqrt-div`
5×	`sqrt-pow1`
4×	`insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `unpow-prod-down` `pow1/2`
2×	`flip3-+` `flip-+`
1×	`pow2` `frac-times` `pow-to-exp` `pow-pow` `pow-plus` `pow-prod-down` `associate-l/` `pow-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr` `sqr-pow`

Counts

4 → 175

Calls

4 calls:

92.0ms	(* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J)))
92.0ms	(sqrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
112.0ms	(sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1))
129.0ms	(pow (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1) 1/4)

series836.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J)))
247.0ms	(sqrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
153.0ms	(sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1))
294.0ms	(pow (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1) 1/4)

simplify3.2s

Counts

187 → 187

Iterations

Iter	Nodes
done	5004
2	4472
1	1013
0	342

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.7b

localize79.0ms

Local error

Found 4 expressions with local error:

8.9b	(sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1))
9.1b	(cbrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
9.1b	(cbrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
9.1b	(cbrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
12×	`add-sqr-sqrt` `sqrt-prod`
11×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-div`
6×	`cbrt-div`
5×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 67

Calls

4 calls:

108.0ms	(sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1))
57.0ms	(cbrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
64.0ms	(cbrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
51.0ms	(cbrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))

series956.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1))
270.0ms	(cbrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
296.0ms	(cbrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))
252.0ms	(cbrt (sqrt (+ (* (/ (/ U (cos (/ K 2))) (* 2 J)) (/ (/ U (cos (/ K 2))) (* 2 J))) 1)))

simplify2.8s

Counts

79 → 79

Iterations

Iter	Nodes
done	5004
3	2005
2	461
1	174
0	91

prune675.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 12.7b

regimes487.0ms

Accuracy

0% (4.6b remaining)

Error of 17.0b against oracle of 12.4b and baseline of 17.0b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	24
1	24
0	17

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.6s	1519×	body	1280	valid
1.1s	1262×	body	640	valid
812.0ms	4242×	body	80	valid
410.0ms	647×	body	320	valid
123.0ms	332×	body	160	valid