Details

Time bar (total: 1.3m)

sample230.0ms

Algorithm
intervals
Results
122.0ms609×body80nan
73.0ms365×body80valid

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done2000
5970
4328
3124
262
131
013

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

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))
0.7b
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
493×times-frac
383×add-sqr-sqrt
380×*-un-lft-identity
378×add-cube-cbrt
328×unpow-prod-up
312×prod-diff
141×sqrt-prod
46×associate-/l*
26×add-exp-log
25×div-inv
14×pow1
10×add-cbrt-cube
9×prod-exp
8×sub-neg unpow-prod-down sqr-pow
6×pow-unpow associate-/r* pow-prod-down pow-exp
5×div-exp
3×expm1-log1p-u pow-pow associate-*l* cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp pow-sub difference-of-squares
1×cbrt-undiv clear-num frac-2neg associate-*r* *-commutative distribute-lft-out-- associate-/l/
Counts
3 → 436
Calls
3 calls:
26.0ms
(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
15.0ms
(* n (* 2 PI))
22.0ms
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series601.0ms

Counts
3 → 9
Calls
3 calls:
345.0ms
(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
36.0ms
(* n (* 2 PI))
219.0ms
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify2.0s

Counts
445 → 445
Iterations
IterNodes
done2001
11526
0695

prune3.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
0.2b
(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
0.2b
(* n (* 2 PI))
0.7b
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite234.0ms

Algorithm
rewrite-expression-head
Rules
3088×times-frac
1878×add-sqr-sqrt
1875×*-un-lft-identity
1873×add-cube-cbrt
1312×unpow-prod-up
1248×prod-diff
693×sqrt-prod
327×associate-/r*
102×div-inv
72×add-exp-log
32×sub-neg unpow-prod-down div-exp sqr-pow
18×prod-exp
16×pow1 add-cbrt-cube
15×pow-exp
9×associate-/l*
6×rec-exp pow-unpow 1-exp pow-prod-down associate-/r/ pow-sub
5×pow-to-exp
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp
3×pow-pow associate-*l* cbrt-unprod
2×clear-num frac-2neg difference-of-squares
1×associate-*r* *-commutative pow-flip distribute-lft-out-- inv-pow
Counts
4 → 1599
Calls
4 calls:
42.0ms
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
25.0ms
(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
25.0ms
(* n (* 2 PI))
33.0ms
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series884.0ms

Counts
4 → 12
Calls
4 calls:
304.0ms
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
333.0ms
(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
54.0ms
(* n (* 2 PI))
193.0ms
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify3.4s

Counts
1611 → 1611
Iterations
IterNodes
done2002
01728

prune11.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
0.2b
(/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))
0.2b
(* n (* 2 PI))
0.7b
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite452.0ms

Algorithm
rewrite-expression-head
Rules
11044×times-frac
8334×sqrt-prod
6333×add-sqr-sqrt
6330×*-un-lft-identity
6328×add-cube-cbrt
4141×unpow-prod-up
3939×prod-diff
464×associate-/l*
315×div-inv
101×sub-neg unpow-prod-down sqr-pow
46×add-exp-log
18×associate-/r*
16×add-cbrt-cube div-exp
15×pow1
12×prod-exp
9×pow-exp
6×pow-unpow pow-prod-down
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow associate-*l* cbrt-unprod
2×clear-num frac-2neg pow-sub difference-of-squares associate-/l/
1×associate-*r* *-commutative distribute-lft-out--
Counts
4 → 4788
Calls
4 calls:
23.0ms
(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
35.0ms
(/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))
19.0ms
(* n (* 2 PI))
24.0ms
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series911.0ms

Counts
4 → 12
Calls
4 calls:
337.0ms
(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
344.0ms
(/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))
44.0ms
(* n (* 2 PI))
184.0ms
(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify10.0s

Counts
4800 → 4800
Iterations
IterNodes
done3687
03687

prune32.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b
(* n (* 2 PI))
0.2b
(* n (* 2 PI))
0.6b
(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
0.6b
(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
44×pow-unpow
42×times-frac
38×*-un-lft-identity
26×pow1 add-exp-log add-cube-cbrt
14×add-cbrt-cube
12×pow-prod-down prod-exp difference-of-squares
6×pow-pow associate-*l* pow-exp cbrt-unprod distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp unpow-prod-down div-sub associate-*r* *-commutative div-inv pow-sub sqr-pow
Counts
4 → 126
Calls
4 calls:
20.0ms
(* n (* 2 PI))
27.0ms
(* n (* 2 PI))
31.0ms
(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
31.0ms
(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))

series541.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* n (* 2 PI))
51.0ms
(* n (* 2 PI))
201.0ms
(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
226.0ms
(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))

simplify1.0s

Counts
138 → 138
Iterations
IterNodes
done2011
21480
1455
0165

prune905.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes567.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done18
118
014

end0.0ms

sample7.5s

Algorithm
intervals
Results
4.3s20622×body80nan
2.3s11847×body80valid
1.0ms2×body160nan