Details

Time bar (total: 4.9m)

sample183.0ms

Algorithm
intervals
Results
77.0ms616×body80nan
76.0ms359×body80valid
0.0ms1×body160nan

simplify277.0ms

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize45.0ms

Local error

Found 3 expressions with local error:

0.5b
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b
(* n (* 2 PI))
0.2b
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

rewrite83.0ms

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
30.0ms
(* n (* 2 PI))
28.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
21.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series594.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
331.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
215.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
48.0ms
(* n (* 2 PI))

simplify27.5s

Counts
124 → 127
Calls
124 calls:
Slowest
707.0ms
(/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
706.0ms
(/ (* (* (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)))
705.0ms
(- (+ (* 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)))))
544.0ms
(/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))
535.0ms
(/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b
(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
31.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
31.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
26.0ms
(* (* 2 PI) n)
10.0ms
(/ 1 (sqrt k))

series609.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
330.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
189.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
57.0ms
(* (* 2 PI) n)
33.0ms
(/ 1 (sqrt k))

simplify20.6s

Counts
171 → 188
Calls
171 calls:
Slowest
855.0ms
(* (* (* (/ 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))))
706.0ms
(- (+ (* 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)))))
664.0ms
(* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
579.0ms
(* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
517.0ms
(* (log (* (* 2 PI) n)) (/ (- 1 k) 2))

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.4b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.3b
(* n (* 2 PI))
0.3b
(* n (* 2 PI))

rewrite65.0ms

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
19.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
15.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
13.0ms
(* n (* 2 PI))
13.0ms
(* n (* 2 PI))

series443.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
172.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
56.0ms
(* n (* 2 PI))
34.0ms
(* n (* 2 PI))

simplify14.4s

Counts
184 → 226
Calls
184 calls:
Slowest
450.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
424.0ms
(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
415.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
400.0ms
(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
393.0ms
(* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2))

prune3.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow (* 2 PI) (/ (- 1 k) 2))
0.4b
(pow n (/ (- 1 k) 2))
0.3b
(/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))
0.2b
(/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
551×times-frac
270×add-sqr-sqrt *-un-lft-identity
252×add-cube-cbrt
167×unpow-prod-down
138×sqrt-prod
93×sqr-pow
53×add-exp-log
44×pow-unpow
40×associate-/r*
31×div-exp
16×pow-exp
13×associate-/l*
12×div-sub div-inv pow-sub difference-of-squares
11×pow-to-exp add-cbrt-cube
10×associate-/r/
8×pow1
6×distribute-lft-out--
5×prod-exp
4×cbrt-undiv insert-posit16 add-log-exp
3×pow-pow
2×clear-num frac-2neg
1×pow-prod-down associate-/l/
Counts
4 → 451
Calls
4 calls:
Slowest
27.0ms
(/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))
14.0ms
(/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))
8.0ms
(pow n (/ (- 1 k) 2))
8.0ms
(pow (* 2 PI) (/ (- 1 k) 2))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
671.0ms
(/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))
490.0ms
(/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))
87.0ms
(pow (* 2 PI) (/ (- 1 k) 2))
64.0ms
(pow n (/ (- 1 k) 2))

simplify3.4m

Counts
693 → 463
Calls
693 calls:
Slowest
1.2s
(/ (pow n (/ (- 1 k) 2)) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))
914.0ms
(/ (pow (cbrt n) (/ (- 1 k) 2)) (/ 1 (pow (* 2 PI) (/ (- 1 k) 2))))
877.0ms
(/ (pow (* (cbrt n) (cbrt n)) (/ (- 1 k) 2)) (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2))))))
875.0ms
(/ (pow n (/ (/ (- 1 k) 2) 2)) (/ (sqrt (sqrt k)) (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2))))))
832.0ms
(/ (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ k 2)))

prune6.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes99.0ms

Accuracy

0% (0.4b remaining)

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

bsearch4.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
3.7s20430×body80nan
2.7s11919×body80valid
1.0ms3×body160nan