Details

Time bar (total: 2.8m)

sample256.0ms

Algorithm
intervals
Results
142.0ms625×body80nan
79.0ms383×body80valid

simplify1.3s

Counts
1 → 1
Iterations
IterNodes
62053
5821
4322
3123
260
129
013

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
0.3b
(* PI (* n 2))
0.4b
(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

rewrite78.0ms

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 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 → 433
Calls
3 calls:
16.0ms
(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
15.0ms
(* PI (* n 2))
23.0ms
(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

series570.0ms

Counts
3 → 9
Calls
3 calls:
332.0ms
(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
37.0ms
(* PI (* n 2))
201.0ms
(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

simplify2.8s

Counts
442 → 442
Iterations
IterNodes
24092
11514
0695

prune6.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.3b
(* (* 2 PI) n)
0.3b
(/ 1 (sqrt k))
0.4b
(pow (* (* 2 PI) n) (/ (- 1 k) 2))

rewrite130.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 180
Calls
4 calls:
56.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
25.0ms
(* (* 2 PI) n)
9.0ms
(/ 1 (sqrt k))
35.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series700.0ms

Counts
4 → 12
Calls
4 calls:
358.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
64.0ms
(* (* 2 PI) n)
54.0ms
(/ 1 (sqrt k))
223.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify1.7s

Counts
192 → 192
Iterations
IterNodes
22832
1938
0349

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
0.2b
(/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
0.3b
(* PI (* n 2))
0.4b
(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

rewrite182.0ms

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 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 → 1595
Calls
4 calls:
23.0ms
(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
23.0ms
(/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
24.0ms
(* PI (* n 2))
17.0ms
(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

series1.2s

Counts
4 → 12
Calls
4 calls:
297.0ms
(/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
340.0ms
(/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
36.0ms
(* PI (* n 2))
549.0ms
(pow (* PI (* n 2)) (- 1/2 (/ k 2)))

simplify1.8m

Counts
1607 → 1607
Iterations
IterNodes
14761
01727

prune28.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 (sqrt k)) (pow (* 2 n) (- 1/2 (/ k 2))))
0.3b
(/ 1 (sqrt k))
0.4b
(pow (* 2 n) (- 1/2 (/ k 2)))
0.5b
(pow PI (- 1/2 (/ k 2)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
167×add-sqr-sqrt
146×*-un-lft-identity
138×add-cube-cbrt
127×times-frac
123×unpow-prod-up
117×prod-diff
48×add-exp-log
46×associate-*r*
25×sqrt-prod
22×associate-*l*
21×prod-exp
12×pow-unpow
11×add-cbrt-cube pow-exp div-inv
10×pow1 div-exp unswap-sqr
8×sqr-pow
6×pow-to-exp associate-/r*
5×rec-exp unpow-prod-down 1-exp
4×expm1-log1p-u log1p-expm1-u pow-sub add-log-exp difference-of-squares
3×sub-neg pow-pow pow-flip associate-/l*
2×cbrt-undiv cbrt-unprod distribute-lft-out--
1×frac-times clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative inv-pow
Counts
4 → 284
Calls
4 calls:
48.0ms
(* (/ 1 (sqrt k)) (pow (* 2 n) (- 1/2 (/ k 2))))
9.0ms
(/ 1 (sqrt k))
9.0ms
(pow (* 2 n) (- 1/2 (/ k 2)))
6.0ms
(pow PI (- 1/2 (/ k 2)))

series439.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(* (/ 1 (sqrt k)) (pow (* 2 n) (- 1/2 (/ k 2))))
34.0ms
(/ 1 (sqrt k))
150.0ms
(pow (* 2 n) (- 1/2 (/ k 2)))
47.0ms
(pow PI (- 1/2 (/ k 2)))

simplify2.8s

Counts
296 → 296
Iterations
IterNodes
24356
11699
0564

prune4.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes176.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
216
116
014

end0.0ms

sample8.2s

Algorithm
intervals
Results
4.1s21239×body80nan
2.9s11990×body80valid
1.0ms3×body160nan