Details

Time bar (total: 1.6m)

sample197.0ms

Algorithm
intervals
Results
118.0ms690×body80nan
55.0ms390×body80valid

simplify321.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
321.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

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))

rewrite62.0ms

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
28.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
22.0ms
(* n (* 2 PI))
10.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series557.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
317.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
201.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
38.0ms
(* n (* 2 PI))

simplify26.9s

Counts
124 → 127
Calls
124 calls:
Slowest
748.0ms
(/ (* (* (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)))
741.0ms
(/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
709.0ms
(- (+ (* 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)))))
566.0ms
(* (log (* n (* 2 PI))) (/ (- 1 k) 2))
522.0ms
(/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

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
35.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
14.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
13.0ms
(* (* 2 PI) n)
8.0ms
(/ 1 (sqrt k))

series647.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
349.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
197.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
51.0ms
(* (* 2 PI) n)
50.0ms
(/ 1 (sqrt k))

simplify20.8s

Counts
171 → 188
Calls
171 calls:
Slowest
915.0ms
(* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
742.0ms
(* (* (* (/ 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))))
729.0ms
(- (+ (* 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)))))
560.0ms
(* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
519.0ms
(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize44.0ms

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)))

rewrite61.0ms

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
24.0ms
(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
22.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
13.0ms
(* (* 2 PI) n)

series603.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
351.0ms
(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
192.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
60.0ms
(* (* 2 PI) n)

simplify12.7s

Counts
87 → 112
Calls
87 calls:
Slowest
756.0ms
(- (+ (* 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)))))
533.0ms
(* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
503.0ms
(* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2))
493.0ms
(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
474.0ms
(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

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
17.0ms
(* n (* 2 PI))
16.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
14.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
12.0ms
(* n (* 2 PI))

series469.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
192.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
182.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
54.0ms
(* n (* 2 PI))
41.0ms
(* n (* 2 PI))

simplify14.6s

Counts
184 → 226
Calls
184 calls:
Slowest
488.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
482.0ms
(/ (/ (- 1 (sqrt k)) 2) (cbrt 2))
468.0ms
(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
419.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
402.0ms
(* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2))

prune3.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes224.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
4.2s20679×body80nan
2.7s11951×body80valid
0.0ms2×body160nan