Details

Time bar (total: 45.1s)

sample238.0ms

Algorithm
intervals
Results
128.0ms654×body80nan
72.0ms362×body80valid

simplify3.8s

Counts
1 → 1
Iterations
IterNodes
done5000
62753
5970
4328
3124
262
131
013

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

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

rewrite108.0ms

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-*r* 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-*l* *-commutative distribute-lft-out-- associate-/l/
Counts
3 → 436
Calls
3 calls:
30.0ms
(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
29.0ms
(* (* n 2) PI)
36.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series612.0ms

Counts
3 → 9
Calls
3 calls:
347.0ms
(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
64.0ms
(* (* n 2) PI)
201.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify3.6s

Counts
445 → 445
Iterations
IterNodes
done5000
24377
11539
0699

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 3 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
45×add-sqr-sqrt
44×*-un-lft-identity
43×add-cube-cbrt
40×unpow-prod-up
33×sqrt-prod
24×prod-diff
23×add-exp-log
11×pow1
10×associate-/l*
8×sub-neg unpow-prod-down sqr-pow
7×add-cbrt-cube prod-exp
6×associate-/r* pow-exp
5×div-exp
4×pow-unpow pow-prod-down
3×expm1-log1p-u pow-pow associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp pow-sub
1×cbrt-undiv clear-num frac-2neg distribute-rgt-out-- *-commutative cbrt-unprod div-inv unswap-sqr associate-/l/
Counts
3 → 146
Calls
3 calls:
14.0ms
(/ (pow (* 2 (* PI n)) (- 1/2 (* k 1/2))) (sqrt k))
6.0ms
(* PI n)
22.0ms
(pow (* 2 (* PI n)) (- 1/2 (* k 1/2)))

series591.0ms

Counts
3 → 9
Calls
3 calls:
393.0ms
(/ (pow (* 2 (* PI n)) (- 1/2 (* k 1/2))) (sqrt k))
23.0ms
(* PI n)
175.0ms
(pow (* 2 (* PI n)) (- 1/2 (* k 1/2)))

simplify2.6s

Counts
155 → 155
Iterations
IterNodes
done5000
22186
1706
0300

prune775.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
63×add-exp-log
32×prod-exp
26×add-sqr-sqrt
22×pow-exp
18×*-un-lft-identity
17×add-cube-cbrt
15×pow-to-exp unpow-prod-up associate-*l*
13×add-cbrt-cube div-exp associate-*r*
9×pow1 prod-diff pow-sub
8×sqr-pow
7×unpow-prod-down unswap-sqr
6×associate-/r* times-frac sqrt-prod
4×expm1-log1p-u pow-unpow insert-posit16 log1p-expm1-u add-log-exp
3×sub-neg pow-prod-down cbrt-unprod associate-/l/
2×frac-times cbrt-undiv pow-pow associate-*l/ associate-*r/ *-commutative
1×clear-num frac-2neg distribute-rgt-out-- div-inv associate-/l*
Counts
4 → 148
Calls
4 calls:
43.0ms
(* (pow 2 (- 1/2 (* k 1/2))) (pow (* PI n) (- 1/2 (* k 1/2))))
44.0ms
(/ (* (pow 2 (- 1/2 (* k 1/2))) (pow (* PI n) (- 1/2 (* k 1/2)))) (sqrt k))
7.0ms
(* PI n)
7.0ms
(pow (* PI n) (- 1/2 (* k 1/2)))

series1.1s

Counts
4 → 12
Calls
4 calls:
337.0ms
(* (pow 2 (- 1/2 (* k 1/2))) (pow (* PI n) (- 1/2 (* k 1/2))))
600.0ms
(/ (* (pow 2 (- 1/2 (* k 1/2))) (pow (* PI n) (- 1/2 (* k 1/2)))) (sqrt k))
47.0ms
(* PI n)
166.0ms
(pow (* PI n) (- 1/2 (* k 1/2)))

simplify2.5s

Counts
160 → 160
Iterations
IterNodes
done5005
23101
1875
0309

prune791.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite261.0ms

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-*r* cbrt-unprod
2×clear-num frac-2neg difference-of-squares
1×associate-*l* *-commutative pow-flip distribute-lft-out-- inv-pow
Counts
4 → 1599
Calls
4 calls:
48.0ms
(/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
28.0ms
(* (* n 2) PI)
25.0ms
(/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
42.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series993.0ms

Counts
4 → 12
Calls
4 calls:
351.0ms
(/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
38.0ms
(* (* n 2) PI)
381.0ms
(/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
222.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify6.7s

Counts
1611 → 1611
Iterations
IterNodes
done5004
14745
01732

prune10.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes134.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done16
116
013

end0.0ms

sample6.7s

Algorithm
intervals
Results
3.7s21069×body80nan
2.0s11971×body80valid
1.0ms2×body160nan