Details

sample191.0ms

Algorithm

intervals

Results

79.0ms	49×	body	1280	valid
34.0ms	140×	body	80	valid
32.0ms	31×	body	640	valid
19.0ms	26×	body	320	valid
5.0ms	10×	body	160	valid

simplify1.4s

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: 17.3b

localize38.0ms

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))))
7.8b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
9.4b	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))

rewrite631.0ms

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:

28.0ms	(* (cos (/ K 2)) (* 2 J))
145.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
140.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
316.0ms	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))

series594.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (cos (/ K 2)) (* 2 J))
174.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
152.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
180.0ms	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))

simplify1.5s

Counts

145 → 145

Iterations

Iter	Nodes
done	2000
2	2000
1	708
0	236

prune886.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.6b

localize65.0ms

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))))
7.8b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
9.4b	(* J (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))

rewrite619.0ms

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:

14.0ms	(* (cos (/ K 2)) (* 2 J))
112.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
151.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
339.0ms	(* J (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))

series583.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (cos (/ K 2)) (* 2 J))
155.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
145.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
210.0ms	(* J (* (* -2 (cos (/ K 2))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))))

simplify1.9s

Counts

142 → 142

Iterations

Iter	Nodes
done	2001
2	2001
1	699
0	237

prune858.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.6b

localize99.0ms

Local error

Found 4 expressions with local error:

10.8b	(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))))
14.8b	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
14.8b	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
14.8b	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

rewrite418.0ms

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:

173.0ms	(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))))
96.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
67.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
80.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series1.2s

Counts

4 → 12

Calls

4 calls:

301.0ms	(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))))
317.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
314.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
270.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

simplify1.7s

Counts

82 → 82

Iterations

Iter	Nodes
done	2004
3	2004
2	493
1	210
0	115

prune758.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 13.6b

localize98.0ms

Local error

Found 4 expressions with local error:

9.8b	(cbrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
10.8b	(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))))
14.8b	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
14.8b	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

rewrite382.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
12×	`cbrt-prod` `pow1`
10×	`sqrt-div`
9×	`sqrt-pow1` `flip3-+` `pow1/3` `flip-+`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`frac-times` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `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`

Counts

4 → 73

Calls

4 calls:

64.0ms	(cbrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
148.0ms	(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))))
81.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
86.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series1.1s

Counts

4 → 12

Calls

4 calls:

275.0ms	(cbrt (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
252.0ms	(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))))
290.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
288.0ms	(cbrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

simplify1.3s

Counts

85 → 85

Iterations

Iter	Nodes
done	2002
3	2002
2	573
1	242
0	142

prune825.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 13.6b

regimes376.0ms

Accuracy

0% (5.2b remaining)

Error of 16.9b against oracle of 11.7b and baseline of 16.9b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	25
1	25
0	17

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.2s	1514×	body	1280	valid
1.3s	1278×	body	640	valid
1.1s	4305×	body	80	valid
446.0ms	628×	body	320	valid
141.0ms	278×	body	160	valid