Details

Time bar (total: 2.2m)

sample266.0ms

Algorithm
intervals
Results
150.0ms673×body80nan
76.0ms378×body80valid

simplify287.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
287.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 3 expressions with local error:

0.7b
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.2b
(* n (* 2 PI))
0.1b
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

rewrite53.0ms

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
27.0ms
(* n (* 2 PI))
13.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
10.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series519.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
316.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
159.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
44.0ms
(* n (* 2 PI))

simplify25.4s

Counts
124 → 127
Calls
124 calls:
Slowest
724.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
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)))))
575.0ms
(* (log (* n (* 2 PI))) (/ (- 1 k) 2))
564.0ms
(/ (* (* (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)))
535.0ms
(/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

3.2b
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
0.3b
(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
0.2b
(* n (* 2 PI))
0.1b
(/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
96×times-frac
86×add-sqr-sqrt *-un-lft-identity
62×add-cube-cbrt
50×pow-unpow
49×unpow-prod-down
42×sqrt-prod
37×add-exp-log
19×pow-exp
17×sqr-pow
15×pow1
12×prod-exp difference-of-squares
11×add-cbrt-cube
9×associate-/l*
7×div-exp
6×associate-/r* pow-prod-down distribute-lft-out distribute-lft-out--
5×pow-to-exp
4×pow-pow insert-posit16 add-log-exp
3×associate-*l* cbrt-unprod div-inv
2×div-sub pow-sub
1×cbrt-undiv clear-num frac-2neg associate-*r* *-commutative associate-/l/
Counts
4 → 197
Calls
4 calls:
Slowest
21.0ms
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
17.0ms
(* n (* 2 PI))
15.0ms
(/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k))
11.0ms
(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))

series2.0s

Counts
4 → 12
Calls
4 calls:
Slowest
1.0s
(/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k))
637.0ms
(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
308.0ms
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
35.0ms
(* n (* 2 PI))

simplify38.7s

Counts
220 → 209
Calls
220 calls:
Slowest
749.0ms
(/ (pow (cbrt (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))) (/ (- 1 (sqrt k)) 2)) (sqrt (cbrt k)))
592.0ms
(- (* (* (+ (log n) (log (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (log (sqrt k)))
537.0ms
(* (* (+ (log n) (log (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
496.0ms
(* (+ (log n) (+ (log 2) (log PI))) (/ (+ 1 (sqrt k)) 1))
491.0ms
(- (* (* (log (* n (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (log (sqrt k)))

prune2.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

3.2b
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
0.3b
(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
0.2b
(* n (* 2 PI))
0.2b
(/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
96×times-frac
86×add-sqr-sqrt *-un-lft-identity
62×add-cube-cbrt
50×pow-unpow
49×unpow-prod-down
42×sqrt-prod
37×add-exp-log
19×pow-exp
17×sqr-pow
15×pow1
12×prod-exp difference-of-squares
11×add-cbrt-cube
9×associate-/r*
7×div-exp
6×pow-prod-down distribute-lft-out associate-/l* distribute-lft-out--
5×pow-to-exp
4×pow-pow insert-posit16 add-log-exp
3×associate-*l* cbrt-unprod div-inv
2×div-sub pow-sub
1×cbrt-undiv clear-num frac-2neg associate-*r* associate-/r/ *-commutative
Counts
4 → 197
Calls
4 calls:
Slowest
19.0ms
(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
18.0ms
(/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)))
14.0ms
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
12.0ms
(* n (* 2 PI))

series2.4s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)))
633.0ms
(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
332.0ms
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
38.0ms
(* n (* 2 PI))

simplify38.9s

Counts
220 → 209
Calls
220 calls:
Slowest
728.0ms
(- (log (sqrt k)) (* (* (log (* n (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)))
668.0ms
(/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) 2)) (/ (- 1 (sqrt k)) 2)))
614.0ms
(/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))))
612.0ms
(* (+ (log n) (+ (log 2) (log PI))) (/ (+ 1 (sqrt k)) 1))
608.0ms
(- (log (sqrt k)) (* (* (log (* n (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)))

prune2.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

3.2b
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
0.3b
(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
0.2b
(* n (* 2 PI))
0.2b
(/ 1 (sqrt k))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt *-un-lft-identity
60×times-frac
50×pow-unpow
43×add-cube-cbrt
26×add-exp-log
24×sqrt-prod
17×pow1
12×difference-of-squares
11×add-cbrt-cube pow-exp
9×prod-exp
7×unpow-prod-down
6×associate-/r* pow-prod-down distribute-lft-out distribute-lft-out--
4×pow-pow insert-posit16 add-log-exp
3×pow-to-exp associate-*l* cbrt-unprod div-inv pow-flip associate-/l* sqr-pow
2×div-exp
1×cbrt-undiv rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 1-exp div-sub associate-*r* *-commutative inv-pow pow-sub
Counts
4 → 154
Calls
4 calls:
Slowest
24.0ms
(* n (* 2 PI))
19.0ms
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
12.0ms
(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
9.0ms
(/ 1 (sqrt k))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
626.0ms
(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
312.0ms
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
66.0ms
(* n (* 2 PI))
49.0ms
(/ 1 (sqrt k))

simplify7.3s

Counts
139 → 166
Calls
139 calls:
Slowest
460.0ms
(* (log (* n (* 2 PI))) (/ (+ 1 (sqrt k)) 1))
451.0ms
(* (* (log (* n (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
445.0ms
(* (* (+ (log n) (log (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
441.0ms
(* (+ (log n) (+ (log 2) (log PI))) (/ (+ 1 (sqrt k)) 1))
406.0ms
(* (log (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))) (/ (- 1 (sqrt k)) 2))

prune2.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes134.0ms

Accuracy

0% (0.9b remaining)

Error of 1.0b against oracle of 0.1b and baseline of 1.0b

bsearch3.0ms

end0.0ms

sample8.2s

Algorithm
intervals
Results
4.1s21207×body80nan
3.3s11907×body80valid
1.0ms2×body160nan