Details

Time bar (total: 4.8m)

sample200.0ms

Algorithm
intervals
Results
105.0ms603×body80nan
63.0ms358×body80valid

simplify313.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
313.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize35.0ms

Local error

Found 4 expressions with local error:

2.9b
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
0.3b
(/ 1 (sqrt k))
0.2b
(* (* 2 PI) n)
0.1b
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

rewrite99.0ms

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
43.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
27.0ms
(* (* 2 PI) n)
17.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
9.0ms
(/ 1 (sqrt k))

series633.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
349.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
199.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
55.0ms
(* (* 2 PI) n)
30.0ms
(/ 1 (sqrt k))

simplify20.4s

Counts
171 → 188
Calls
171 calls:
Slowest
793.0ms
(* (* (* (/ 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))))
656.0ms
(- (+ (* 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)))))
574.0ms
(* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
491.0ms
(* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2))
467.0ms
(* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

2.6b
(pow n (/ (- 1 k) 2))
0.5b
(pow (* 2 PI) (/ (- 1 k) 2))
0.3b
(/ 1 (sqrt k))
0.2b
(* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
91×add-sqr-sqrt
80×times-frac
76×*-un-lft-identity
54×add-cube-cbrt
48×add-exp-log
44×pow-unpow
25×sqrt-prod
22×associate-*l*
21×prod-exp
12×difference-of-squares
11×add-cbrt-cube pow-exp
10×pow1 div-exp unswap-sqr
8×sqr-pow
6×pow-to-exp associate-/r* distribute-lft-out--
5×rec-exp unpow-prod-down 1-exp associate-*r*
4×div-sub insert-posit16 div-inv pow-sub add-log-exp
3×pow-pow pow-flip associate-/l*
2×cbrt-undiv cbrt-unprod
1×frac-times clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative inv-pow
Counts
4 → 189
Calls
4 calls:
Slowest
23.0ms
(* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))
16.0ms
(/ 1 (sqrt k))
15.0ms
(pow (* 2 PI) (/ (- 1 k) 2))
9.0ms
(pow n (/ (- 1 k) 2))

series503.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
280.0ms
(* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))
104.0ms
(pow (* 2 PI) (/ (- 1 k) 2))
80.0ms
(pow n (/ (- 1 k) 2))
38.0ms
(/ 1 (sqrt k))

simplify18.7s

Counts
184 → 201
Calls
184 calls:
Slowest
726.0ms
(* (log (* 2 PI)) (/ (- 1 k) 2))
638.0ms
(* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow (* 2 PI) (/ (- 1 k) 2))))
443.0ms
(+ (- (log 1) (log (sqrt k))) (* (log (* 2 PI)) (/ (- 1 k) 2)))
429.0ms
(+ (- 0 (log (sqrt k))) (* (log (* 2 PI)) (/ (- 1 k) 2)))
394.0ms
(* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* 2 PI) (/ (- 1 k) 2))))

prune2.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

2.6b
(pow n (/ (- 1 k) 2))
0.3b
(/ 1 (sqrt k))
0.2b
(* (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow n (/ (- 1 k) 2)))
0.1b
(* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))

rewrite332.0ms

Algorithm
rewrite-expression-head
Rules
834×add-exp-log
722×prod-exp
276×pow-exp
173×pow-to-exp
106×div-exp
74×add-sqr-sqrt
62×times-frac
59×*-un-lft-identity
53×rec-exp 1-exp
46×add-cube-cbrt
45×div-sub
27×pow-sub
25×add-cbrt-cube sqrt-prod
23×associate-*l*
22×pow-unpow
18×frac-times associate-*l/
12×associate-*r*
11×cbrt-unprod
10×unswap-sqr
8×associate-*r/ sqr-pow
7×pow1 unpow-prod-down
6×associate-/r* difference-of-squares
4×insert-posit16 add-log-exp
3×cbrt-undiv div-inv pow-flip associate-/l* distribute-lft-out--
2×*-commutative
1×clear-num pow-pow frac-2neg sqrt-pow1 pow1/2 inv-pow
Counts
4 → 394
Calls
4 calls:
Slowest
284.0ms
(* (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow n (/ (- 1 k) 2)))
21.0ms
(* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))
9.0ms
(/ 1 (sqrt k))
5.0ms
(pow n (/ (- 1 k) 2))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
671.0ms
(* (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow n (/ (- 1 k) 2)))
210.0ms
(* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))
113.0ms
(pow n (/ (- 1 k) 2))
47.0ms
(/ 1 (sqrt k))

simplify1.8m

Counts
397 → 406
Calls
397 calls:
Slowest
888.0ms
(* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))))
819.0ms
(+ (+ (+ (- (log (sqrt k))) (* (log (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (* (log (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (log (pow n (/ (- 1 k) 2))))
785.0ms
(+ (+ (+ (log (/ 1 (sqrt k))) (* (log (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (* (log (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (log (pow n (/ (- 1 k) 2))))
749.0ms
(* (* (* 1 (pow (* 2 PI) (/ (/ 1 2) 2))) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow n (/ (- 1 k) 2)))
721.0ms
(* (* (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))) (* (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))) (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))))

prune6.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

2.6b
(pow n (/ (- 1 k) 2))
0.3b
(/ 1 (sqrt k))
0.2b
(* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow n (/ (- 1 k) 2))))
0.1b
(* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
883×add-exp-log
756×prod-exp
283×pow-exp
176×pow-to-exp
114×div-exp
72×add-sqr-sqrt
62×times-frac
57×rec-exp *-un-lft-identity 1-exp
45×div-sub
44×add-cube-cbrt
32×add-cbrt-cube
27×pow-sub
25×sqrt-prod
23×associate-*l*
22×pow-unpow
18×frac-times
15×cbrt-unprod
12×associate-*l/ associate-*r/
10×unswap-sqr
9×pow1
7×sqr-pow
6×associate-/r* associate-*r* difference-of-squares
4×cbrt-undiv unpow-prod-down insert-posit16 add-log-exp
3×div-inv pow-flip associate-/l* distribute-lft-out--
2×*-commutative
1×clear-num pow-pow frac-2neg sqrt-pow1 pow1/2 pow-prod-down inv-pow
Counts
4 → 405
Calls
4 calls:
Slowest
125.0ms
(* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow n (/ (- 1 k) 2))))
22.0ms
(* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))
5.0ms
(/ 1 (sqrt k))
5.0ms
(pow n (/ (- 1 k) 2))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
724.0ms
(* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow n (/ (- 1 k) 2))))
240.0ms
(* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))
96.0ms
(pow n (/ (- 1 k) 2))
36.0ms
(/ 1 (sqrt k))

simplify1.9m

Counts
410 → 417
Calls
410 calls:
Slowest
1.1s
(* (* (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))) (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))) (* (* (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow n (/ (- 1 k) 2))) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow n (/ (- 1 k) 2)))))
1.1s
(* (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))) (* (* (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow n (/ (- 1 k) 2))) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow n (/ (- 1 k) 2)))))
975.0ms
(* (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))) (* (* (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow n (/ (- 1 k) 2))) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow n (/ (- 1 k) 2)))) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow n (/ (- 1 k) 2)))))
948.0ms
(+ (+ (- (log 1) (log (sqrt k))) (log (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))) (+ (log (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (* (log n) (/ (- 1 k) 2))))
857.0ms
(* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))))

prune6.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes213.0ms

Accuracy

0% (0.4b remaining)

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

bsearch3.0ms

end0.0ms

sample7.8s

Algorithm
intervals
Results
3.7s20289×body80nan
3.4s11844×body80valid
1.0ms4×body160nan