Details

Time bar (total: 33.6s)

sample158.0ms

Algorithm
intervals
Results
80.0ms544×body80nan
56.0ms357×body80valid

simplify95.0ms

Calls
1 calls:
Slowest
94.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize48.0ms

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)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube prod-exp
5×associate-*l*
4×rec-exp pow-unpow associate-*r* insert-posit16 add-log-exp
3×pow-to-exp associate-/r* div-sub pow-exp div-inv pow-sub
2×unpow-prod-down *-commutative pow-flip
1×frac-times clear-num pow-pow frac-2neg pow1/2 associate-*l/ associate-*r/ cbrt-unprod inv-pow
Calls
4 calls:
Slowest
11.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
7.0ms
(* (* 2 PI) n)
6.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
1.0ms
(/ 1 (sqrt k))

series424.0ms

Calls
4 calls:
Slowest
177.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
148.0ms
(pow (* (* 2 PI) n) (/ (- 1 k) 2))
80.0ms
(* (* 2 PI) n)
18.0ms
(/ 1 (sqrt k))

simplify4.1s

Calls
42 calls:
Slowest
672.0ms
(- (+ (* 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)))))
561.0ms
(* (* (* (/ 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))))
485.0ms
(* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
438.0ms
(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
248.0ms
(exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))

prune961.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow (* 2 PI) (/ (- 1 k) 2))
0.4b
(pow n (/ (- 1 k) 2))
0.3b
(/ 1 (sqrt k))
0.2b
(* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×pow-unpow
6×pow1 add-cbrt-cube prod-exp
4×pow-to-exp rec-exp div-sub associate-*r* associate-*l* insert-posit16 div-inv pow-sub add-log-exp
3×associate-/r* pow-exp
2×unpow-prod-down pow-flip
1×frac-times clear-num pow-pow frac-2neg pow1/2 associate-*l/ associate-*r/ *-commutative cbrt-unprod inv-pow
Calls
4 calls:
Slowest
8.0ms
(* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))
2.0ms
(pow (* 2 PI) (/ (- 1 k) 2))
1.0ms
(pow n (/ (- 1 k) 2))
1.0ms
(/ 1 (sqrt k))

series259.0ms

Calls
4 calls:
Slowest
125.0ms
(* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))
77.0ms
(pow n (/ (- 1 k) 2))
40.0ms
(pow (* 2 PI) (/ (- 1 k) 2))
18.0ms
(/ 1 (sqrt k))

simplify4.2s

Calls
47 calls:
Slowest
502.0ms
(* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow (* 2 PI) (/ (- 1 k) 2))))
431.0ms
(* (log (* 2 PI)) (/ (- 1 k) 2))
365.0ms
(* 2 PI)
309.0ms
(exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))
277.0ms
(+ (log (/ 1 (sqrt k))) (* (log (* 2 PI)) (/ (- 1 k) 2)))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow PI (/ (- 1 k) 2))
0.4b
(pow n (/ (- 1 k) 2))
0.3b
(/ 1 (sqrt k))
0.2b
(* (/ 1 (sqrt k)) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
18×prod-exp
10×pow-to-exp div-sub pow-sub
9×add-cbrt-cube
8×add-sqr-sqrt pow-unpow *-un-lft-identity add-cube-cbrt
7×pow1
6×rec-exp
5×frac-times associate-*r/
4×associate-*l* insert-posit16 div-inv add-log-exp
3×associate-/r* associate-*l/ cbrt-unprod
2×pow-flip
1×clear-num frac-2neg pow1/2 associate-*r* pow-prod-down *-commutative inv-pow
Calls
4 calls:
Slowest
43.0ms
(* (/ 1 (sqrt k)) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))
4.0ms
(/ 1 (sqrt k))
1.0ms
(pow PI (/ (- 1 k) 2))
1.0ms
(pow n (/ (- 1 k) 2))

series369.0ms

Calls
4 calls:
Slowest
210.0ms
(* (/ 1 (sqrt k)) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))
97.0ms
(pow n (/ (- 1 k) 2))
42.0ms
(pow PI (/ (- 1 k) 2))
19.0ms
(/ 1 (sqrt k))

simplify6.1s

Calls
53 calls:
Slowest
629.0ms
(* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))))
474.0ms
(+ (log (/ 1 (sqrt k))) (+ (* (log 2) (/ (- 1 k) 2)) (log (pow PI (/ (- 1 k) 2)))))
444.0ms
(+ (- (log (sqrt k))) (+ (* (log 2) (/ (- 1 k) 2)) (* (log PI) (/ (- 1 k) 2))))
423.0ms
(+ (log (/ 1 (sqrt k))) (+ (log (pow 2 (/ (- 1 k) 2))) (* (log PI) (/ (- 1 k) 2))))
386.0ms
(+ (log (/ 1 (sqrt k))) (+ (log (pow 2 (/ (- 1 k) 2))) (log (pow PI (/ (- 1 k) 2)))))

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(pow PI (/ (- 1 k) 2))
0.4b
(pow n (/ (- 1 k) 2))
0.3b
(* (sqrt (/ 1 (sqrt k))) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))
0.3b
(/ 1 (sqrt k))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
15×add-exp-log
10×div-sub pow-sub
9×add-sqr-sqrt *-un-lft-identity add-cbrt-cube prod-exp add-cube-cbrt
8×pow-unpow
7×pow1 associate-*l*
6×pow-to-exp
5×frac-times associate-*r/
4×sqrt-div sqrt-prod insert-posit16 div-inv add-log-exp
3×associate-/r* associate-*l/ cbrt-unprod
2×pow-flip
1×rec-exp clear-num frac-2neg pow1/2 associate-*r* pow-prod-down *-commutative inv-pow
Calls
4 calls:
Slowest
26.0ms
(* (sqrt (/ 1 (sqrt k))) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))
2.0ms
(pow n (/ (- 1 k) 2))
1.0ms
(pow PI (/ (- 1 k) 2))
1.0ms
(/ 1 (sqrt k))

series298.0ms

Calls
4 calls:
Slowest
197.0ms
(* (sqrt (/ 1 (sqrt k))) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))
54.0ms
(pow n (/ (- 1 k) 2))
35.0ms
(pow PI (/ (- 1 k) 2))
12.0ms
(/ 1 (sqrt k))

simplify5.0s

Calls
52 calls:
Slowest
576.0ms
(* (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))) (* (* (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))) (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))))
575.0ms
(* (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))) (* (* (* (pow 2 (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))) (* (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (pow PI (/ (- 1 k) 2)))))
384.0ms
(- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI))))
369.0ms
(+ (log (sqrt (/ 1 (sqrt k)))) (+ (* (log 2) (/ (- 1 k) 2)) (* (log PI) (/ (- 1 k) 2))))
289.0ms
(+ (log (sqrt (/ 1 (sqrt k)))) (+ (log (pow 2 (/ (- 1 k) 2))) (* (log PI) (/ (- 1 k) 2))))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes236.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
3.6s20514×body80nan
3.2s11755×body80valid
1.0ms2×body160nan