Details

Time bar (total: 1.2m)

sample209.0ms

Algorithm
intervals
Results
94.0ms573×body80nan
85.0ms346×body80valid

simplify316.0ms

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.9b
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
0.3b
(* (* 2 PI) n)
0.2b
(/ 1 (sqrt k))
0.2b
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

rewrite69.0ms

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
29.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
19.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
14.0ms
(* (* 2 PI) n)
5.0ms
(/ 1 (sqrt k))

series632.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
371.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
174.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
45.0ms
(* (* 2 PI) n)
41.0ms
(/ 1 (sqrt k))

simplify20.3s

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))))
778.0ms
(* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))
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)))))
601.0ms
(* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
536.0ms
(* (log (* (* 2 PI) n)) (/ (- 1 k) 2))

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 3 expressions with local error:

0.9b
(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)))

rewrite77.0ms

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
41.0ms
(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
18.0ms
(* (* 2 PI) n)
15.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series541.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
277.0ms
(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
229.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
35.0ms
(* (* 2 PI) n)

simplify12.0s

Counts
87 → 112
Calls
87 calls:
Slowest
702.0ms
(sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
639.0ms
(- (+ (* 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)))))
525.0ms
(* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
472.0ms
(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
413.0ms
(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.9b
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
0.9b
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
0.3b
(* (* 2 PI) n)
0.3b
(* (* 2 PI) n)

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt pow-unpow *-un-lft-identity
36×times-frac
26×pow1 add-exp-log add-cube-cbrt
14×add-cbrt-cube
12×pow-prod-down prod-exp difference-of-squares
6×pow-pow associate-*r* pow-exp cbrt-unprod distribute-lft-out--
4×insert-posit16 add-log-exp
2×pow-to-exp unpow-prod-down div-sub associate-*l* *-commutative div-inv pow-sub sqr-pow
Counts
4 → 118
Calls
4 calls:
Slowest
32.0ms
(* (* 2 PI) n)
30.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
30.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
21.0ms
(* (* 2 PI) n)

series465.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
182.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
167.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
61.0ms
(* (* 2 PI) n)
55.0ms
(* (* 2 PI) n)

simplify9.2s

Counts
88 → 130
Calls
88 calls:
Slowest
795.0ms
(- (+ (* 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)))))
726.0ms
(- (+ (* 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)))))
557.0ms
(* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2))
516.0ms
(* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
510.0ms
(* (log (* (* 2 PI) n)) (/ (- 1 k) 2))

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.9b
(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
0.9b
(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
0.3b
(* (* 2 PI) n)
0.3b
(* (* 2 PI) n)

rewrite91.0ms

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-*r* pow-exp cbrt-unprod
4×div-sub insert-posit16 add-log-exp
2×pow-to-exp unpow-prod-down associate-*l* *-commutative pow-sub sqr-pow
Counts
4 → 214
Calls
4 calls:
Slowest
27.0ms
(* (* 2 PI) n)
22.0ms
(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
16.0ms
(* (* 2 PI) n)
16.0ms
(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))

series488.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
214.0ms
(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
183.0ms
(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
50.0ms
(* (* 2 PI) n)
42.0ms
(* (* 2 PI) n)

simplify13.6s

Counts
184 → 226
Calls
184 calls:
Slowest
502.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
456.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
429.0ms
(* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))
401.0ms
(pow (* 2 PI) (/ (/ (- 1 k) 2) 2))
393.0ms
(* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))

prune3.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes165.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
4.1s20378×body80nan
2.5s11700×body80valid
0.0ms1×body160nan