Details

Time bar (total: 23.2s)

sample219.0ms

Algorithm
intervals
Results
104.0ms685×body80nan
49.0ms370×body80valid

simplify2.0s

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

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
(/ 1.0 (sqrt k))
0.2b
(* (* 2.0 PI) n)
0.7b
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite127.0ms

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:
53.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
18.0ms
(/ 1.0 (sqrt k))
26.0ms
(* (* 2.0 PI) n)
24.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series773.0ms

Counts
4 → 12
Calls
4 calls:
459.0ms
(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
57.0ms
(/ 1.0 (sqrt k))
58.0ms
(* (* 2.0 PI) n)
200.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.8s

Counts
161 → 161

prune767.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt k))
0.3b
(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.5b
(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
0.6b
(pow n (/ (- 1.0 k) 2.0))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
53×*-un-lft-identity
48×times-frac
41×add-cube-cbrt
38×pow-unpow
30×add-exp-log
16×prod-exp
13×pow-exp
12×sqrt-prod
10×unpow-prod-down
9×pow-to-exp sqr-pow
8×pow1 add-cbrt-cube
7×associate-*r*
6×div-sub associate-/r* distribute-lft-out-- pow-sub difference-of-squares unswap-sqr
5×associate-*l*
4×add-log-exp
3×pow-pow div-inv associate-/l*
2×pow-prod-down
1×cbrt-undiv frac-times frac-2neg associate-*r/ div-exp associate-*l/ clear-num *-commutative cbrt-unprod
Counts
4 → 150
Calls
4 calls:
12.0ms
(/ 1.0 (sqrt k))
46.0ms
(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
13.0ms
(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
15.0ms
(pow n (/ (- 1.0 k) 2.0))

series656.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ 1.0 (sqrt k))
416.0ms
(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
92.0ms
(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
92.0ms
(pow n (/ (- 1.0 k) 2.0))

simplify1.4s

Counts
162 → 162

prune797.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (- 1.0 k) 2.0))))
0.2b
(* (/ 1.0 (sqrt k)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (- 1.0 k) 2.0)))))
0.2b
(/ 1.0 (sqrt k))
0.6b
(pow n (/ (- 1.0 k) 2.0))

rewrite372.0ms

Algorithm
rewrite-expression-head
Rules
576×add-exp-log
481×prod-exp
199×pow-exp
124×pow-to-exp
61×div-sub
54×div-exp
51×times-frac
49×add-sqr-sqrt *-un-lft-identity
43×add-cube-cbrt
37×pow-sub
32×add-cbrt-cube
27×associate-*l*
22×frac-times associate-*r/
21×sqrt-prod
19×pow-unpow
15×cbrt-unprod
10×associate-*l/
7×pow1
6×associate-/r*
4×cbrt-undiv unpow-prod-down add-log-exp
3×div-inv associate-/l* distribute-lft-out-- difference-of-squares
2×associate-*r* *-commutative sqr-pow
1×pow-pow frac-2neg pow-prod-down clear-num
Counts
4 → 307
Calls
4 calls:
74.0ms
(* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (- 1.0 k) 2.0))))
253.0ms
(* (/ 1.0 (sqrt k)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (- 1.0 k) 2.0)))))
12.0ms
(/ 1.0 (sqrt k))
11.0ms
(pow n (/ (- 1.0 k) 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
533.0ms
(* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (- 1.0 k) 2.0))))
1.1s
(* (/ 1.0 (sqrt k)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (- 1.0 k) 2.0)))))
57.0ms
(/ 1.0 (sqrt k))
101.0ms
(pow n (/ (- 1.0 k) 2.0))

simplify729.0ms

Counts
319 → 319

prune923.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 PI) n)
0.3b
(/ 1.0 (sqrt (sqrt k)))
0.3b
(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
0.7b
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
594×sqrt-prod
591×times-frac
328×add-sqr-sqrt *-un-lft-identity
322×add-cube-cbrt
34×associate-/l*
22×add-exp-log
19×pow-unpow
18×associate-/r*
16×add-cbrt-cube
15×pow1
13×div-inv
6×pow-prod-down prod-exp
4×cbrt-undiv div-exp add-log-exp
3×pow-pow associate-*r* pow-exp cbrt-unprod distribute-lft-out-- difference-of-squares
2×frac-2neg clear-num
1×pow-to-exp unpow-prod-down div-sub associate-*l* *-commutative associate-/l/ pow-sub sqr-pow
Counts
4 → 439
Calls
4 calls:
39.0ms
(* (* 2.0 PI) n)
16.0ms
(/ 1.0 (sqrt (sqrt k)))
35.0ms
(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
43.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series653.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (* 2.0 PI) n)
276.0ms
(/ 1.0 (sqrt (sqrt k)))
50.0ms
(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
260.0ms
(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify761.0ms

Counts
451 → 451

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes173.0ms

Accuracy

28.8% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify865.0ms

end0.0ms

sample6.4s

Algorithm
intervals
Results
2.6s11948×body80valid
2.5s21032×body80nan
0.0ms2×body160nan