Details

Time bar (total: 25.4s)

sample175.0ms

Algorithm
intervals
Results
72.0ms49×body1280valid
32.0ms37×body640valid
29.0ms137×body80valid
15.0ms25×body320valid
3.0ms8×body160valid

simplify2.6s

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize43.0ms

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)))

rewrite272.0ms

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:
15.0ms
(* (* -2 J) (cos (/ K 2)))
25.0ms
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
145.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
86.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (* -2 J) (cos (/ K 2)))
131.0ms
(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
192.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
141.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify1.8s

Counts
102 → 102
Iterations
IterNodes
done5000
21535
1482
0179

prune614.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.6b

localize84.0ms

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)))

rewrite263.0ms

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:
58.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
56.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
67.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
80.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series795.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
248.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
164.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
134.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify2.5s

Counts
92 → 92
Iterations
IterNodes
done5001
31632
2443
1177
092

prune694.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.6b

localize132.0ms

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)))

rewrite177.0ms

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:
58.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
34.0ms
(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
29.0ms
(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
55.0ms
(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series893.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
259.0ms
(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
233.0ms
(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
262.0ms
(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify2.2s

Counts
74 → 74
Iterations
IterNodes
done5000
31330
2399
1166
086

prune782.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.6b

localize53.0ms

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)))

rewrite355.0ms

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:
97.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
89.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
108.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
58.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series765.0ms

Counts
4 → 12
Calls
4 calls:
270.0ms
(sqrt (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
166.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
143.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
186.0ms
(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify1.9s

Counts
86 → 86
Iterations
IterNodes
done5001
31632
2443
1177
092

prune762.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 12.6b

regimes761.0ms

Accuracy

89.3% (0.5b remaining)

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

bsearch2.0ms

simplify12.0ms

Iterations
IterNodes
done39
139
027

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.7s1477×body1280valid
1.4s1252×body640valid
1.1s4333×body80valid
482.0ms629×body320valid
170.0ms310×body160valid