Details

Time bar (total: 2.3m)

sample241.0ms

Algorithm
intervals
Results
117.0ms673×body80nan
85.0ms378×body80valid

simplify287.0ms

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

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))

rewrite56.0ms

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
18.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
15.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
14.0ms
(* n (* 2 PI))

series439.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
248.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
156.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
35.0ms
(* n (* 2 PI))

simplify26.5s

Counts
124 → 127
Calls
124 calls:
Slowest
802.0ms
(* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))
711.0ms
(- (+ (* 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)))))
657.0ms
(/ (* (* (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)))
539.0ms
(/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))
538.0ms
(/ (pow n (/ (- 1 k) 2)) 1)

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

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))

rewrite65.0ms

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
18.0ms
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
16.0ms
(/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k))
13.0ms
(* n (* 2 PI))
12.0ms
(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))
588.0ms
(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
351.0ms
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
59.0ms
(* n (* 2 PI))

simplify38.8s

Counts
220 → 209
Calls
220 calls:
Slowest
618.0ms
(/ (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) 2)) (/ (- 1 (sqrt k)) 2)) (sqrt (sqrt k)))
543.0ms
(- (* (* (log (* n (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (log (sqrt k)))
538.0ms
(* (* (+ (log n) (log (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
534.0ms
(* (+ (log n) (+ (log 2) (log PI))) (/ (+ 1 (sqrt k)) 1))
473.0ms
(/ (pow (* (cbrt (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))) (cbrt (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)))) (/ (- 1 (sqrt k)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))

prune2.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize68.0ms

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)))

rewrite103.0ms

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
39.0ms
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
26.0ms
(/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)))
19.0ms
(* n (* 2 PI))
13.0ms
(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))

series2.0s

Counts
4 → 12
Calls
4 calls:
Slowest
1.0s
(/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)))
628.0ms
(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
308.0ms
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
65.0ms
(* n (* 2 PI))

simplify39.6s

Counts
220 → 209
Calls
220 calls:
Slowest
1.0s
(- (log (sqrt k)) (* (* (log (* n (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)))
662.0ms
(/ (* (* (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))))
643.0ms
(- (log (sqrt k)) (* (* (log (* n (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)))
609.0ms
(/ (sqrt k) (pow (sqrt (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))) (/ (- 1 (sqrt k)) 2)))
553.0ms
(- (log (sqrt k)) (* (log (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))) (/ (- 1 (sqrt k)) 2)))

prune2.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize67.0ms

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))

rewrite75.0ms

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
31.0ms
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
23.0ms
(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
13.0ms
(* n (* 2 PI))
5.0ms
(/ 1 (sqrt k))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
612.0ms
(pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
352.0ms
(pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
55.0ms
(* n (* 2 PI))
42.0ms
(/ 1 (sqrt k))

simplify7.3s

Counts
139 → 166
Calls
139 calls:
Slowest
566.0ms
(* (* (+ (log n) (log (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
488.0ms
(* (+ (log n) (+ (log 2) (log PI))) (/ (+ 1 (sqrt k)) 1))
471.0ms
(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
438.0ms
(* (* (log (* n (* 2 PI))) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))
430.0ms
(* (* (log (* 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

regimes160.0ms

Accuracy

0% (0.9b remaining)

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

bsearch3.0ms

end0.0ms

sample8.0s

Algorithm
intervals
Results
3.9s21207×body80nan
3.2s11907×body80valid
1.0ms2×body160nan