Details

Time bar (total: 38.6s)

sample174.0ms

Algorithm
intervals
Results
93.0ms626×body80nan
56.0ms393×body80valid

simplify1.4s

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize48.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
0.3b
(* (* n 2) PI)
0.9b
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

rewrite50.0ms

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:
14.0ms
(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
18.0ms
(* (* n 2) PI)
16.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series603.0ms

Counts
3 → 9
Calls
3 calls:
328.0ms
(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
48.0ms
(* (* n 2) PI)
227.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify1.3s

Counts
127 → 127
Iterations
IterNodes
done2001
22001
1662
0271

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.2b
(/ 1 (sqrt k))
0.3b
(* (* 2 PI) n)
0.9b
(pow (* (* 2 PI) n) (/ (- 1 k) 2))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt add-exp-log
62×times-frac
57×*-un-lft-identity
44×add-cube-cbrt
38×prod-exp
25×sqrt-prod
23×associate-*l*
22×pow-unpow
17×pow1
16×add-cbrt-cube
15×pow-exp
12×div-exp
10×unswap-sqr
8×associate-*r*
7×sqr-pow
6×rec-exp associate-/r* 1-exp pow-prod-down difference-of-squares
5×pow-to-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×pow-pow div-sub div-inv pow-flip associate-/l* distribute-lft-out-- pow-sub
2×cbrt-undiv unpow-prod-down *-commutative
1×frac-times clear-num frac-2neg sqrt-pow1 pow1/2 associate-*l/ associate-*r/ inv-pow
Counts
4 → 176
Calls
4 calls:
33.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
5.0ms
(/ 1 (sqrt k))
16.0ms
(* (* 2 PI) n)
31.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series660.0ms

Counts
4 → 12
Calls
4 calls:
382.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
32.0ms
(/ 1 (sqrt k))
72.0ms
(* (* 2 PI) n)
174.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify1.1s

Counts
188 → 188
Iterations
IterNodes
done2001
22001
1930
0345

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize23.0ms

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))))
0.3b
(* (* n 2) PI)
0.9b
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
352×times-frac
166×add-sqr-sqrt
163×*-un-lft-identity
161×add-cube-cbrt
108×sqrt-prod
72×add-exp-log
64×unpow-prod-up
54×associate-/r*
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/ div-inv pow-sub
5×pow-to-exp
4×cbrt-undiv insert-posit16 add-log-exp
3×pow-pow associate-*r* cbrt-unprod
2×clear-num frac-2neg difference-of-squares
1×associate-*l* *-commutative pow-flip distribute-lft-out-- inv-pow
Counts
4 → 343
Calls
4 calls:
34.0ms
(/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
20.0ms
(/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
28.0ms
(* (* n 2) PI)
33.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series1.3s

Counts
4 → 12
Calls
4 calls:
289.0ms
(/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
352.0ms
(/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
442.0ms
(* (* n 2) PI)
185.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify1.5s

Counts
355 → 355
Iterations
IterNodes
done2001
22001
11455
0536

prune4.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt k) (pow PI (- 1/2 (/ k 2))))
0.2b
(/ (pow (* n 2) (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))))
0.5b
(pow PI (- 1/2 (/ k 2)))
0.9b
(pow (* n 2) (- 1/2 (/ k 2)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
901×times-frac
359×add-sqr-sqrt
353×*-un-lft-identity
349×add-cube-cbrt
246×sqrt-prod
234×unpow-prod-up
229×unpow-prod-down
117×sub-neg sqr-pow
68×associate-/r*
53×add-exp-log
31×div-exp
16×pow-exp
13×associate-/l*
12×pow-unpow pow-sub
11×pow-to-exp add-cbrt-cube
10×associate-/r/ div-inv
8×pow1
5×prod-exp
4×cbrt-undiv insert-posit16 add-log-exp difference-of-squares
3×pow-pow
2×clear-num frac-2neg distribute-lft-out--
1×pow-prod-down associate-/l/
Counts
4 → 643
Calls
4 calls:
13.0ms
(/ (sqrt k) (pow PI (- 1/2 (/ k 2))))
24.0ms
(/ (pow (* n 2) (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))))
5.0ms
(pow PI (- 1/2 (/ k 2)))
8.0ms
(pow (* n 2) (- 1/2 (/ k 2)))

series927.0ms

Counts
4 → 12
Calls
4 calls:
270.0ms
(/ (sqrt k) (pow PI (- 1/2 (/ k 2))))
469.0ms
(/ (pow (* n 2) (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))))
61.0ms
(pow PI (- 1/2 (/ k 2)))
128.0ms
(pow (* n 2) (- 1/2 (/ k 2)))

simplify5.1s

Counts
655 → 655
Iterations
IterNodes
done2001
12001
0885

prune8.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes197.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done20
120
017

end0.0ms

sample7.4s

Algorithm
intervals
Results
4.0s21126×body80nan
2.4s11926×body80valid
0.0ms1×body160nan