Details

sample183.0ms

Algorithm

intervals

Results

58.0ms	49×	body	1280	valid
56.0ms	44×	body	640	valid
29.0ms	129×	body	80	valid
20.0ms	27×	body	320	valid
3.0ms	7×	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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos (/ K 2)) (* 2 J))
0.2b	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
5.7b	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
9.1b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

rewrite829.0ms

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))
89.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
252.0ms	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
457.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series517.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (cos (/ K 2)) (* 2 J))
106.0ms	(* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J))))
203.0ms	(* (* J (* -2 (cos (/ K 2)))) (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))

simplify1.2s

Counts

145 → 145

Iterations

Iter	Nodes
done	2009
2	2009
1	705
0	236

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.7b

localize76.0ms

Local error

Found 4 expressions with local error:

5.7b	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
9.1b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
9.1b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
9.1b	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

rewrite720.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

264.0ms	(* (* J (* -2 (cos (/ K 2)))) (sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1)))
156.0ms	(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))
158.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series612.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (* 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))
135.0ms	(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))

simplify1.3s

Counts

87 → 87

Iterations

Iter	Nodes
done	2000
3	2000
2	893
1	250
0	97

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.7b

localize115.0ms

Local error

Found 4 expressions with local error:

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

rewrite709.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

191.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
165.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
188.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
164.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series500.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
145.0ms	(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))
120.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

simplify1.5s

Counts

76 → 76

Iterations

Iter	Nodes
done	2067
4	2067
3	1148
2	261
1	95
0	48

prune1.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.7b

localize144.0ms

Local error

Found 4 expressions with local error:

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

rewrite549.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

115.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
136.0ms	(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))
159.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

series568.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(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))
142.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))
119.0ms	(sqrt (+ (* (/ U (* (cos (/ K 2)) (* 2 J))) (/ U (* (cos (/ K 2)) (* 2 J)))) 1))

simplify1.5s

Counts

76 → 76

Iterations

Iter	Nodes
done	2067
4	2067
3	1148
2	261
1	95
0	48

prune1.9s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 9.7b

regimes492.0ms

Accuracy

0% (4.8b remaining)

Error of 17.2b against oracle of 12.4b and baseline of 17.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	25
1	25
0	17

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.7s	1402×	body	1280	valid
1.4s	1282×	body	640	valid
1.2s	4329×	body	80	valid
518.0ms	656×	body	320	valid
152.0ms	340×	body	160	valid