Details

Time bar (total: 25.8s)

sample185.0ms

Algorithm
intervals
Results
105.0ms621×body80nan
53.0ms359×body80valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
done2011
62011
5929
4327
3124
262
131
013

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
0.2b
(* (* n 2) PI)
1.6b
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
43×times-frac
33×add-sqr-sqrt
30×*-un-lft-identity
28×add-cube-cbrt
26×add-exp-log
24×sqrt-prod
16×unpow-prod-up
14×pow1
10×add-cbrt-cube
9×prod-exp
8×sub-neg unpow-prod-down sqr-pow
7×associate-/l*
6×pow-unpow associate-/r* pow-prod-down pow-exp
5×div-exp
3×pow-pow associate-*r* cbrt-unprod insert-posit16 add-log-exp
2×pow-to-exp pow-sub difference-of-squares
1×cbrt-undiv clear-num frac-2neg associate-*l* *-commutative div-inv distribute-lft-out-- associate-/l/
Counts
3 → 118
Calls
3 calls:
27.0ms
(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
15.0ms
(* (* n 2) PI)
21.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series604.0ms

Counts
3 → 9
Calls
3 calls:
352.0ms
(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
64.0ms
(* (* n 2) PI)
188.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify1.3s

Counts
127 → 127
Iterations
IterNodes
done2001
22001
1662
0271

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2))))
0.2b
(/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k))
0.4b
(pow PI (- 1/2 (/ k 2)))
1.3b
(pow (* n 2) (- 1/2 (/ k 2)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
31×add-sqr-sqrt prod-exp
23×pow-exp
18×*-un-lft-identity
16×pow-to-exp
14×add-cube-cbrt
13×div-exp
12×pow-unpow
11×add-cbrt-cube
10×unpow-prod-down pow-sub
9×associate-*r* sqr-pow
8×pow1 unpow-prod-up times-frac
7×associate-*l*
6×associate-/r* sqrt-prod unswap-sqr
4×sub-neg insert-posit16 add-log-exp difference-of-squares
3×pow-pow associate-/l/
2×frac-times cbrt-undiv pow-prod-down associate-*l/ associate-*r/ cbrt-unprod distribute-lft-out--
1×clear-num frac-2neg *-commutative div-inv associate-/l*
Counts
4 → 138
Calls
4 calls:
39.0ms
(* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2))))
41.0ms
(/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k))
11.0ms
(pow PI (- 1/2 (/ k 2)))
17.0ms
(pow (* n 2) (- 1/2 (/ k 2)))

series983.0ms

Counts
4 → 12
Calls
4 calls:
317.0ms
(* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2))))
508.0ms
(/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k))
47.0ms
(pow PI (- 1/2 (/ k 2)))
111.0ms
(pow (* n 2) (- 1/2 (/ k 2)))

simplify2.1s

Counts
150 → 150
Iterations
IterNodes
done2001
22001
1968
0331

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (pow (* n 2) (- 1/2 (/ k 2))) (* (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (pow PI (- 1/2 (/ k 2)))))) (sqrt k))
0.4b
(pow PI (- 1/2 (/ k 2)))
0.4b
(pow PI (- 1/2 (/ k 2)))
1.3b
(pow (* n 2) (- 1/2 (/ k 2)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×add-sqr-sqrt
19×*-un-lft-identity
18×pow-unpow
15×prod-exp pow-sub
13×add-cbrt-cube add-cube-cbrt
9×pow1 times-frac div-exp
8×sqrt-div pow-exp
7×unpow-prod-down associate-/l/
6×unpow-prod-up associate-/r* sqrt-prod difference-of-squares
5×frac-times pow-to-exp associate-*r/
4×pow-pow insert-posit16 add-log-exp
3×cbrt-undiv sub-neg associate-*l/ cbrt-unprod distribute-lft-out-- sqr-pow
1×clear-num frac-2neg pow-prod-down div-inv associate-/l*
Counts
4 → 115
Calls
4 calls:
71.0ms
(/ (* (pow (* n 2) (- 1/2 (/ k 2))) (* (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (pow PI (- 1/2 (/ k 2)))))) (sqrt k))
13.0ms
(pow PI (- 1/2 (/ k 2)))
6.0ms
(pow PI (- 1/2 (/ k 2)))
9.0ms
(pow (* n 2) (- 1/2 (/ k 2)))

series744.0ms

Counts
4 → 12
Calls
4 calls:
492.0ms
(/ (* (pow (* n 2) (- 1/2 (/ k 2))) (* (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (pow PI (- 1/2 (/ k 2)))))) (sqrt k))
64.0ms
(pow PI (- 1/2 (/ k 2)))
50.0ms
(pow PI (- 1/2 (/ k 2)))
137.0ms
(pow (* n 2) (- 1/2 (/ k 2)))

simplify2.0s

Counts
127 → 127
Iterations
IterNodes
done2001
22001
1887
0301

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.3b
(pow (* n 2) (- 1/2 (/ k 2)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×*-un-lft-identity
9×cbrt-prod
8×add-cube-cbrt
7×pow1 add-exp-log
6×pow-unpow
4×add-cbrt-cube insert-posit16 add-log-exp
3×pow1/3
2×unpow-prod-up pow-pow pow-exp difference-of-squares
1×pow-to-exp sub-neg unpow-prod-down times-frac pow-prod-down prod-exp distribute-lft-out-- pow-sub sqr-pow
Counts
4 → 60
Calls
4 calls:
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)
10.0ms
(pow (* n 2) (- 1/2 (/ k 2)))

series111.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
111.0ms
(pow (* n 2) (- 1/2 (/ k 2)))

simplify1.4s

Counts
66 → 66
Iterations
IterNodes
done2005
32005
2845
1274
0107

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes231.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done17
117
015

end0.0ms

sample8.1s

Algorithm
intervals
Results
3.9s20592×body80nan
3.0s11910×body80valid
0.0ms1×body160nan