Details

Time bar (total: 3.2m)

sample217.0ms

Algorithm
intervals
Results
99.0ms652×body80nan
89.0ms406×body80valid

simplify308.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
308.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

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))

rewrite60.0ms

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
23.0ms
(* n (* 2 PI))
21.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
15.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))

series566.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
339.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
163.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
64.0ms
(* n (* 2 PI))

simplify27.8s

Counts
124 → 127
Calls
124 calls:
Slowest
739.0ms
(- (+ (* 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
(/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
639.0ms
(/ (* (* (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)))
541.0ms
(/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))
535.0ms
(* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

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)))

rewrite98.0ms

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
49.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
25.0ms
(* (* 2 PI) n)
16.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
5.0ms
(/ 1 (sqrt k))

series582.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
342.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
169.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
37.0ms
(/ 1 (sqrt k))
34.0ms
(* (* 2 PI) n)

simplify21.4s

Counts
171 → 188
Calls
171 calls:
Slowest
810.0ms
(* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
794.0ms
(- (+ (* 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)))))
784.0ms
(* (* (* (/ 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))))
551.0ms
(* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
515.0ms
(* (log (* (* 2 PI) n)) (/ (- 1 k) 2))

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 3 expressions with local error:

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

rewrite111.0ms

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-*r/ div-inv
Counts
3 → 103
Calls
3 calls:
Slowest
49.0ms
(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
31.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
28.0ms
(* (* 2 PI) n)

series583.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
319.0ms
(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
203.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
60.0ms
(* (* 2 PI) n)

simplify12.7s

Counts
87 → 112
Calls
87 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)))))
607.0ms
(* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
593.0ms
(* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2))
495.0ms
(* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))
438.0ms
(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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
Counts
4 → 295
Calls
4 calls:
Slowest
21.0ms
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
15.0ms
(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
14.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
13.0ms
(* n (* 2 PI))

series892.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
399.0ms
(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
284.0ms
(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
154.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
55.0ms
(* n (* 2 PI))

simplify1.8m

Counts
390 → 307
Calls
390 calls:
Slowest
1.0s
(/ (* (* 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)))))
943.0ms
(/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
805.0ms
(/ (cbrt 1) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
746.0ms
(/ 1 (/ 1 (pow n (/ (- 1 k) 2))))
731.0ms
(- (+ (* 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)))))

prune3.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes169.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch4.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
4.0s20730×body80nan
2.7s11909×body80valid