Details

Time bar (total: 22.8s)

sample105.0ms

Algorithm
intervals
Results
33.0ms49×body1280valid
19.0ms37×body640valid
18.0ms137×body80valid
10.0ms25×body320valid
2.0ms8×body160valid

simplify2.9s

Counts
1 → 1
Iterations
IterNodes
done5025
54486
4782
3215
281
136
017

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* -2 J) (cos (/ K 2)))
0.2b
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
7.9b
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
11.3b
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite401.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
18×add-cbrt-cube
15×*-un-lft-identity
12×add-sqr-sqrt prod-exp
11×add-cube-cbrt
10×associate-*r*
9×pow-prod-down cbrt-unprod
8×sqrt-prod
7×unpow-prod-down
4×sqrt-div pow-exp insert-posit16 add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*l* associate-*r/ *-commutative flip-+ distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv unpow2 sqr-pow
Counts
4 → 90
Calls
4 calls:
31.0ms
(* (* -2 J) (cos (/ K 2)))
36.0ms
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
219.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
113.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series580.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(* (* -2 J) (cos (/ K 2)))
159.0ms
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
209.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
143.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify1.7s

Counts
102 → 102
Iterations
IterNodes
done5000
21535
1482
0179

prune573.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.6b

localize74.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
7.9b
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
11.3b
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
11.3b
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite342.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-prod
18×*-un-lft-identity
16×add-sqr-sqrt
12×sqrt-div
10×pow1 sqrt-pow1 add-cube-cbrt
6×rem-sqrt-square pow1/2
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 distribute-lft-out add-log-exp
Counts
4 → 80
Calls
4 calls:
81.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
83.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
81.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
95.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series832.0ms

Counts
4 → 12
Calls
4 calls:
264.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
280.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
141.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
146.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify2.0s

Counts
92 → 92
Iterations
IterNodes
done5001
31632
2443
1177
092

prune677.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.6b

localize98.0ms

Local error

Found 4 expressions with local error:

11.3b
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
17.6b
(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
17.6b
(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
17.6b
(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
12×cbrt-prod
9×add-sqr-sqrt
8×add-cube-cbrt
6×cbrt-div
5×pow1
4×flip3-+ add-cbrt-cube add-exp-log sqrt-prod flip-+ insert-posit16 distribute-lft-out add-log-exp
3×pow1/3
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 62
Calls
4 calls:
62.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
52.0ms
(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
38.0ms
(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
49.0ms
(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series933.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
263.0ms
(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
279.0ms
(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
233.0ms
(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify2.1s

Counts
74 → 74
Iterations
IterNodes
done5000
31330
2399
1166
086

prune899.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.6b

localize69.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
11.3b
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
11.3b
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
11.3b
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite277.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-prod
17×*-un-lft-identity
14×add-sqr-sqrt
10×sqrt-div
9×pow1 add-cube-cbrt
7×sqrt-pow1
5×rem-sqrt-square pow1/2
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 distribute-lft-out add-log-exp
Counts
4 → 74
Calls
4 calls:
86.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
59.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
67.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
63.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series742.0ms

Counts
4 → 12
Calls
4 calls:
258.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
172.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
165.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
147.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify2.1s

Counts
86 → 86
Iterations
IterNodes
done5001
31632
2443
1177
092

prune708.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 12.6b

regimes661.0ms

Accuracy

89.3% (0.5b remaining)

Error of 13.1b against oracle of 12.6b and baseline of 17.6b

bsearch3.0ms

simplify7.0ms

Iterations
IterNodes
done39
139
027

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.3s1477×body1280valid
1.2s4333×body80valid
686.0ms1252×body640valid
243.0ms629×body320valid
125.0ms310×body160valid