Details

Time bar (total: 3.9m)

sample226.0ms

Algorithm
intervals
Results
126.0ms607×body80nan
68.0ms382×body80valid

simplify290.0ms

Calls
1 calls:
Slowest
290.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite84.0ms

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/
Calls
3 calls:
Slowest
34.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
26.0ms
(* n (* 2 PI))
21.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series546.0ms

Calls
3 calls:
Slowest
289.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
217.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
40.0ms
(* n (* 2 PI))

simplify27.4s

Calls
124 calls:
Slowest
741.0ms
(/ (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
730.0ms
(/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
716.0ms
(- (+ (* 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)))))
511.0ms
(* (log (* n (* 2 PI))) (/ (- 1 k) 2))
511.0ms
(/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.9b
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b
(* n (* 2 PI))
0.2b
(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
0.1b
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
273×times-frac
147×add-sqr-sqrt *-un-lft-identity
138×add-cube-cbrt
78×sqrt-prod
72×add-exp-log
40×associate-/r*
32×unpow-prod-down div-exp sqr-pow
22×pow-unpow
18×prod-exp
16×pow1 add-cbrt-cube
15×pow-exp
9×associate-/l*
7×div-inv
6×rec-exp 1-exp div-sub pow-prod-down associate-/r/ pow-sub difference-of-squares
5×pow-to-exp
4×cbrt-undiv insert-posit16 add-log-exp
3×pow-pow associate-*l* cbrt-unprod distribute-lft-out--
2×clear-num frac-2neg
1×associate-*r* *-commutative pow-flip inv-pow
Calls
4 calls:
Slowest
32.0ms
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
19.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
16.0ms
(* n (* 2 PI))
16.0ms
(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))

series949.0ms

Calls
4 calls:
Slowest
332.0ms
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
323.0ms
(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
241.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
54.0ms
(* n (* 2 PI))

simplify1.8m

Calls
390 calls:
Slowest
957.0ms
(/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
921.0ms
(/ (* (* 1 1) 1) (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
790.0ms
(/ 1 (/ 1 (pow n (/ (- 1 k) 2))))
771.0ms
(- (+ (* 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)))))
745.0ms
(/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))

prune3.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.8b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.3b
(* n (* 2 PI))
0.3b
(* n (* 2 PI))

rewrite111.0ms

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
Calls
4 calls:
Slowest
31.0ms
(* n (* 2 PI))
30.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
29.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
15.0ms
(* n (* 2 PI))

series452.0ms

Calls
4 calls:
Slowest
187.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
184.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
47.0ms
(* n (* 2 PI))
34.0ms
(* n (* 2 PI))

simplify14.0s

Calls
184 calls:
Slowest
453.0ms
(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
417.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
406.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
406.0ms
(* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2))
381.0ms
(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))

prune3.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.8b
(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
0.8b
(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
0.3b
(* n (* 2 PI))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
1260×times-frac
707×add-sqr-sqrt *-un-lft-identity
518×add-cube-cbrt
498×pow-unpow
126×difference-of-squares
63×distribute-lft-out--
30×div-inv
27×pow1 add-exp-log
12×pow-prod-down prod-exp
9×pow-pow add-cbrt-cube pow-exp
8×div-sub
4×insert-posit16 add-log-exp
3×pow-to-exp unpow-prod-down associate-*l* cbrt-unprod pow-sub sqr-pow
1×associate-*r* *-commutative
Calls
4 calls:
Slowest
22.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
17.0ms
(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
16.0ms
(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
13.0ms
(* n (* 2 PI))

series644.0ms

Calls
4 calls:
Slowest
232.0ms
(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
188.0ms
(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
173.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
51.0ms
(* n (* 2 PI))

simplify53.6s

Calls
542 calls:
Slowest
733.0ms
(- (+ (exp (* 1/8 (+ (log n) (log (* 2 PI))))) (+ (* 1/64 (* (log (* 2 PI)) (* (exp (* 1/8 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/128 (* (exp (* 1/8 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/128 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/8 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/8 (* (log (* 2 PI)) (* (exp (* 1/8 (+ (log n) (log (* 2 PI))))) k))) (* 1/8 (* (exp (* 1/8 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))
701.0ms
(- (+ (exp (* 1/8 (+ (log n) (log (* 2 PI))))) (+ (* 1/64 (* (log (* 2 PI)) (* (exp (* 1/8 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/128 (* (exp (* 1/8 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/128 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/8 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/8 (* (log (* 2 PI)) (* (exp (* 1/8 (+ (log n) (log (* 2 PI))))) k))) (* 1/8 (* (exp (* 1/8 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))
609.0ms
(* (+ (log n) (log (* 2 PI))) (/ (/ (/ (- 1 k) 2) 2) 2))
514.0ms
(pow n (/ (/ (/ (- 1 k) 2) 2) 2))
467.0ms
(pow n (/ (/ (/ (- 1 k) 2) 2) 2))

prune10.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes147.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch2.0ms

end0.0ms

sample6.7s

Algorithm
intervals
Results
3.7s20279×body80nan
2.3s11735×body80valid
1.0ms2×body160nan