Details

Time bar (total: 11.5s)

sample122.0ms

Algorithm
intervals
Results
62.0ms606×body80nan
28.0ms372×body80valid

simplify31.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b
(* (* 2.0 PI) n)
0.3b
(/ 1.0 (sqrt k))
1.5b
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
55×times-frac
49×*-un-lft-identity
46×add-exp-log
43×add-cube-cbrt
23×associate-*l* sqrt-prod
22×prod-exp
19×pow-unpow
16×add-cbrt-cube
15×pow1
9×pow-exp
8×associate-*r*
6×div-exp pow-prod-down associate-/r* unswap-sqr
5×cbrt-unprod sqr-pow
4×add-log-exp
3×pow-to-exp pow-pow div-sub div-inv associate-/l* distribute-lft-out-- pow-sub difference-of-squares
2×cbrt-undiv unpow-prod-down *-commutative
1×frac-times frac-2neg associate-*r/ associate-*l/ clear-num
Counts
4 → 149
Calls
4 calls:
39.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
24.0ms
(* (* 2.0 PI) n)
6.0ms
(/ 1.0 (sqrt k))
21.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series588.0ms

Counts
4 → 12
Calls
4 calls:
347.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
41.0ms
(* (* 2.0 PI) n)
41.0ms
(/ 1.0 (sqrt k))
158.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify98.0ms

Counts
161 → 161

prune452.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
0.3b
(/ 1.0 (sqrt k))
0.5b
(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
1.0b
(pow n (/ (- 1.0 k) 2.0))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
77×add-sqr-sqrt
70×times-frac
64×*-un-lft-identity
52×add-cube-cbrt
38×pow-unpow
30×add-exp-log
23×sqrt-prod
22×associate-*l*
11×prod-exp add-cbrt-cube
8×pow1
7×pow-exp
6×associate-/r* distribute-lft-out-- difference-of-squares unswap-sqr sqr-pow
5×unpow-prod-down div-exp associate-*r*
4×pow-to-exp div-sub div-inv pow-sub add-log-exp
3×pow-pow associate-/l*
2×cbrt-undiv cbrt-unprod
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 161
Calls
4 calls:
30.0ms
(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
6.0ms
(/ 1.0 (sqrt k))
16.0ms
(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
8.0ms
(pow n (/ (- 1.0 k) 2.0))

series513.0ms

Counts
4 → 12
Calls
4 calls:
317.0ms
(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
40.0ms
(/ 1.0 (sqrt k))
84.0ms
(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
72.0ms
(pow n (/ (- 1.0 k) 2.0))

simplify74.0ms

Counts
173 → 173

prune574.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
0.3b
(/ 1.0 (sqrt k))
0.5b
(pow PI (/ (- 1.0 k) 2.0))
1.0b
(pow n (/ (- 1.0 k) 2.0))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
64×add-exp-log add-sqr-sqrt *-un-lft-identity
52×add-cube-cbrt
38×pow-unpow prod-exp
22×associate-*l*
21×sqrt-prod
18×add-cbrt-cube
14×pow-to-exp pow-exp
11×div-exp
10×div-sub pow-sub
8×pow1
6×unpow-prod-down associate-/r* cbrt-unprod distribute-lft-out-- difference-of-squares
5×frac-times associate-*r/
4×div-inv add-log-exp
3×cbrt-undiv associate-*l/ associate-/l*
2×pow-pow sqr-pow
1×frac-2neg associate-*r* pow-prod-down clear-num *-commutative
Counts
4 → 170
Calls
4 calls:
62.0ms
(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
6.0ms
(/ 1.0 (sqrt k))
8.0ms
(pow PI (/ (- 1.0 k) 2.0))
8.0ms
(pow n (/ (- 1.0 k) 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
919.0ms
(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
43.0ms
(/ 1.0 (sqrt k))
56.0ms
(pow PI (/ (- 1.0 k) 2.0))
74.0ms
(pow n (/ (- 1.0 k) 2.0))

simplify102.0ms

Counts
182 → 182

prune607.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)))) (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
0.2b
(/ (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)))) (sqrt k))
0.5b
(pow PI (/ (- 1.0 k) 2.0))
1.0b
(pow n (/ (- 1.0 k) 2.0))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
173×add-exp-log
112×prod-exp
50×add-sqr-sqrt
45×*-un-lft-identity
44×div-exp
42×times-frac
38×pow-to-exp pow-unpow pow-exp
33×add-cube-cbrt
27×add-cbrt-cube
10×unpow-prod-down associate-*l* cbrt-unprod
9×sqrt-prod
8×div-sub pow-sub
7×associate-*r*
6×pow1 cbrt-undiv associate-/r* distribute-lft-out-- difference-of-squares
5×associate-*r/
4×div-inv add-log-exp sqr-pow
3×associate-/l/ unswap-sqr
2×frac-times pow-pow associate-*l/
1×frac-2neg clear-num *-commutative associate-/l*
Counts
4 → 179
Calls
4 calls:
68.0ms
(* (/ (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)))) (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
41.0ms
(/ (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)))) (sqrt k))
7.0ms
(pow PI (/ (- 1.0 k) 2.0))
8.0ms
(pow n (/ (- 1.0 k) 2.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
966.0ms
(* (/ (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)))) (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
640.0ms
(/ (* 1.0 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)))) (sqrt k))
54.0ms
(pow PI (/ (- 1.0 k) 2.0))
73.0ms
(pow n (/ (- 1.0 k) 2.0))

simplify50.0ms

Counts
191 → 191

prune563.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes122.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.0s21106×body80nan
1.3s11995×body80valid
0.0ms1×body160nan