Details

Time bar (total: 9.6m)

sample177.0ms

Algorithm
intervals
Results
100.0ms700×body80nan
51.0ms373×body80valid

simplify679.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
679.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize44.0ms

Local error

Found 3 expressions with local error:

0.7b
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b
(* n (* 2 PI))
0.2b
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
42×add-sqr-sqrt *-un-lft-identity
33×add-cube-cbrt
26×add-exp-log
22×pow-unpow
18×sqrt-prod
14×pow1
10×add-cbrt-cube
9×prod-exp
8×unpow-prod-down sqr-pow
6×associate-/r* pow-prod-down pow-exp difference-of-squares
5×div-exp associate-/l*
3×pow-pow associate-*l* cbrt-unprod insert-posit16 distribute-lft-out-- add-log-exp
2×pow-to-exp div-sub div-inv pow-sub
1×cbrt-undiv clear-num frac-2neg associate-*r* *-commutative associate-/l/
Counts
3 → 118
Calls
3 calls:
Slowest
28.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
24.0ms
(* n (* 2 PI))
24.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series524.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
277.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
193.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
53.0ms
(* n (* 2 PI))

simplify48.3s

Counts
160 → 127
Calls
160 calls:
Slowest
748.0ms
(/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
748.0ms
(* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))
732.0ms
(pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
730.0ms
(pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
677.0ms
(- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
0.3b
(/ 1 (sqrt k))
0.3b
(* (* 2 PI) n)
0.2b
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

rewrite106.0ms

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:
Slowest
33.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
30.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
27.0ms
(* (* 2 PI) n)
10.0ms
(/ 1 (sqrt k))

series705.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
384.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
233.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
47.0ms
(/ 1 (sqrt k))
40.0ms
(* (* 2 PI) n)

simplify43.7s

Counts
218 → 188
Calls
218 calls:
Slowest
885.0ms
(* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
876.0ms
(pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
800.0ms
(* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
767.0ms
(- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
726.0ms
(* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b
(* n (* 2 PI))
0.2b
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
0.2b
(/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k)))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
954×times-frac sqrt-prod
452×add-sqr-sqrt *-un-lft-identity
443×add-cube-cbrt
101×unpow-prod-down sqr-pow
54×associate-/l*
46×add-exp-log
22×pow-unpow
18×associate-/r*
16×add-cbrt-cube div-exp
15×pow1
13×div-inv
12×prod-exp
9×pow-exp
6×pow-prod-down difference-of-squares
4×cbrt-undiv insert-posit16 add-log-exp
3×pow-to-exp pow-pow associate-*l* cbrt-unprod distribute-lft-out--
2×clear-num frac-2neg div-sub pow-sub associate-/l/
1×associate-*r* *-commutative
Counts
4 → 655
Calls
4 calls:
Slowest
27.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
25.0ms
(* n (* 2 PI))
18.0ms
(/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k)))
16.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))

series896.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
328.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
319.0ms
(/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k)))
194.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
56.0ms
(* n (* 2 PI))

simplify6.5m

Counts
1157 → 667
Calls
1157 calls:
Slowest
1.0s
(log (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
954.0ms
(/ (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (sqrt k)))
930.0ms
(/ (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt 1)))
892.0ms
(/ (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
885.0ms
(/ (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))

prune9.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.7b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.3b
(* n (* 2 PI))
0.3b
(* n (* 2 PI))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
166×add-sqr-sqrt *-un-lft-identity
140×pow-unpow
112×add-cube-cbrt
36×difference-of-squares
26×pow1 add-exp-log
18×distribute-lft-out--
14×add-cbrt-cube
12×pow-prod-down prod-exp
8×div-inv
6×pow-pow associate-*l* pow-exp cbrt-unprod
4×div-sub insert-posit16 add-log-exp
2×pow-to-exp unpow-prod-down associate-*r* *-commutative pow-sub sqr-pow
Counts
4 → 214
Calls
4 calls:
Slowest
21.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
15.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
13.0ms
(* n (* 2 PI))
12.0ms
(* n (* 2 PI))

series448.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
189.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
145.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
58.0ms
(* n (* 2 PI))
56.0ms
(* n (* 2 PI))

simplify1.1m

Counts
230 → 226
Calls
230 calls:
Slowest
798.0ms
(pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) 1))
789.0ms
(pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) (sqrt 2)))
779.0ms
(pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) 1))
765.0ms
(pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) 1))
760.0ms
(pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (sqrt 2)))

prune3.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes111.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch4.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
3.6s20746×body80nan
3.1s11932×body80valid
1.0ms2×body160nan