Details

Time bar (total: 28.9s)

sample271.0ms

Algorithm
intervals
Results
121.0ms618×body80nan
108.0ms354×body80valid

simplify3.3s

Counts
1 → 1
Iterations
IterNodes
done5000
62719
5929
4327
3124
262
131
013

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

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)
1.7b
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

rewrite65.0ms

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:
23.0ms
(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
19.0ms
(* (* n 2) PI)
17.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series575.0ms

Counts
3 → 9
Calls
3 calls:
351.0ms
(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
52.0ms
(* (* n 2) PI)
171.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify2.7s

Counts
127 → 127
Iterations
IterNodes
done5008
22241
1662
0271

prune668.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.2b
(* (* 2 PI) n)
0.2b
(/ 1 (sqrt k))
1.7b
(pow (* (* 2 PI) n) (/ (- 1 k) 2))

rewrite93.0ms

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:
36.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
23.0ms
(* (* 2 PI) n)
6.0ms
(/ 1 (sqrt k))
23.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series630.0ms

Counts
4 → 12
Calls
4 calls:
382.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
46.0ms
(* (* 2 PI) n)
29.0ms
(/ 1 (sqrt k))
174.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify2.6s

Counts
188 → 188
Iterations
IterNodes
done5001
22858
1931
0345

prune795.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* n 2) PI)
0.3b
(* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
1.7b
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
1.7b
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
444×sqrt-prod
278×times-frac
253×add-sqr-sqrt
111×*-un-lft-identity
107×add-cube-cbrt
92×unpow-prod-up
81×swap-sqr
54×sqr-pow
52×associate-*r*
50×associate-*l*
46×sub-neg
36×pow1 unswap-sqr
30×unpow-prod-down
23×add-exp-log
12×pow-unpow pow-prod-down
11×add-cbrt-cube
10×prod-exp
8×sqrt-pow1 pow1/2
6×pow-pow pow-exp
5×pow-prod-up
4×sqrt-div cbrt-unprod insert-posit16 div-inv add-log-exp difference-of-squares
3×pow-sqr
2×pow-to-exp *-commutative distribute-lft-out-- pow-sub
1×pow2 frac-times rem-square-sqrt pow-plus sqrt-unprod associate-*l/ associate-*r/
Counts
4 → 315
Calls
4 calls:
21.0ms
(* (* n 2) PI)
52.0ms
(* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
33.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
33.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series770.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (* n 2) PI)
341.0ms
(* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
173.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
193.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify2.7s

Counts
327 → 327
Iterations
IterNodes
done5001
23062
1946
0455

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* n 2) PI)
0.3b
(/ 1 (sqrt (sqrt k)))
1.7b
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
1.7b
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
36×sqrt-prod
33×*-un-lft-identity
29×times-frac add-cube-cbrt
25×add-exp-log
24×pow1
12×pow-unpow
11×add-cbrt-cube
9×associate-/r* pow-prod-down prod-exp
6×pow-pow pow-exp
5×pow-flip
4×unpow-prod-up sqrt-pow1 insert-posit16 add-log-exp difference-of-squares
3×associate-*r* cbrt-unprod associate-/l*
2×pow-to-exp sub-neg unpow-prod-down pow1/2 div-exp distribute-lft-out-- pow-sub sqr-pow
1×cbrt-undiv rec-exp clear-num frac-2neg 1-exp associate-*l* *-commutative div-inv inv-pow
Counts
4 → 131
Calls
4 calls:
21.0ms
(* (* n 2) PI)
13.0ms
(/ 1 (sqrt (sqrt k)))
26.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
24.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

series709.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (* n 2) PI)
224.0ms
(/ 1 (sqrt (sqrt k)))
213.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
207.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))

simplify1.8s

Counts
143 → 143
Iterations
IterNodes
done5004
21700
1540
0232

prune902.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes326.0ms

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
done18
118
013

end0.0ms

sample7.8s

Algorithm
intervals
Results
3.8s20134×body80nan
2.7s11804×body80valid
0.0ms1×body160nan