Details

Time bar (total: 1.6m)

sample234.0ms

Algorithm
intervals
Results
132.0ms734×body80nan
70.0ms400×body80valid

simplify363.0ms

Calls
1 calls:
Slowest
362.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 3 expressions with local error:

1.1b
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.2b
(* n (* 2 PI))
0.2b
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

rewrite54.0ms

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
21.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
16.0ms
(* n (* 2 PI))
14.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))

series596.0ms

Calls
3 calls:
Slowest
328.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
212.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
57.0ms
(* n (* 2 PI))

simplify27.7s

Calls
124 calls:
Slowest
764.0ms
(- (+ (* 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)))))
736.0ms
(/ (* (* (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)))
727.0ms
(/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1))
546.0ms
(* (log (* n (* 2 PI))) (/ (- 1 k) 2))
520.0ms
(/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

1.1b
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b
(/ 1 (sqrt k))
0.2b
(* n (* 2 PI))
0.2b
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))

rewrite94.0ms

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-*r*
22×pow-unpow
17×pow1
16×add-cbrt-cube
15×pow-exp
12×div-exp
10×unswap-sqr
8×associate-*l*
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/ un-div-inv inv-pow
Calls
4 calls:
Slowest
45.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
26.0ms
(* n (* 2 PI))
15.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
5.0ms
(/ 1 (sqrt k))

series594.0ms

Calls
4 calls:
Slowest
346.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
165.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
42.0ms
(* n (* 2 PI))
41.0ms
(/ 1 (sqrt k))

simplify19.7s

Calls
173 calls:
Slowest
820.0ms
(* (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))))
734.0ms
(- (+ (* 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)))))
638.0ms
(* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ (sqrt 1) (sqrt (sqrt k))))
493.0ms
(* (pow (* n (* 2 PI)) (/ k 2)) (sqrt k))
488.0ms
(* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 3 expressions with local error:

1.1b
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.2b
(* n (* 2 PI))
0.2b
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
33×add-sqr-sqrt
30×prod-exp
26×*-un-lft-identity
22×pow-unpow
18×times-frac
17×pow-exp add-cube-cbrt
14×pow1
10×add-cbrt-cube
9×pow-to-exp
8×associate-*r* associate-*l* sqr-pow
7×unpow-prod-down
6×pow-prod-down difference-of-squares unswap-sqr
4×cbrt-unprod
3×pow-pow insert-posit16 distribute-lft-out-- add-log-exp
2×div-sub *-commutative pow-sub
1×associate-*l/ div-inv
Calls
3 calls:
Slowest
41.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))
27.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
26.0ms
(* n (* 2 PI))

series601.0ms

Calls
3 calls:
Slowest
367.0ms
(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))
191.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
43.0ms
(* n (* 2 PI))

simplify13.7s

Calls
87 calls:
Slowest
780.0ms
(- (+ (* 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)))))
586.0ms
(+ (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (log k) -1/2))
548.0ms
(+ (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (log k) -1/2))
531.0ms
(* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))
531.0ms
(* (log (* n (* 2 PI))) (/ (- 1 k) 2))

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize69.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
1.0b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.2b
(* n (* 2 PI))
0.2b
(* n (* 2 PI))

rewrite73.0ms

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
26.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
14.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
13.0ms
(* n (* 2 PI))
12.0ms
(* n (* 2 PI))

series486.0ms

Calls
4 calls:
Slowest
214.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
189.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
49.0ms
(* n (* 2 PI))
35.0ms
(* n (* 2 PI))

simplify14.7s

Calls
184 calls:
Slowest
455.0ms
(/ (/ (- 1 (sqrt k)) (sqrt 2)) 2)
450.0ms
(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
440.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
433.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
397.0ms
(pow n (/ (/ (- 1 k) 2) 2))

prune3.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes110.0ms

Accuracy

0% (0.5b remaining)

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

bsearch3.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
4.1s21033×body80nan
2.6s12009×body80valid
0.0ms2×body160nan