Details

Time bar (total: 2.0m)

sample323.0ms

Algorithm
intervals
Results
174.0ms627×body80nan
90.0ms368×body80valid

simplify108.0ms

Calls
1 calls:
Slowest
108.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize91.0ms

Local error

Found 3 expressions with local error:

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

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
18×times-frac
15×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×unpow-prod-up
9×add-exp-log
6×associate-/l*
5×sub-neg unpow-prod-down add-cbrt-cube
4×pow1
3×expm1-log1p-u pow-unpow associate-/r* div-exp insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp pow-exp pow-sub
1×cbrt-undiv clear-num pow-pow frac-2neg associate-*l* *-commutative div-inv associate-/l/
Calls
3 calls:
Slowest
76.0ms
(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
21.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
10.0ms
(* (* n 2) PI)

series631.0ms

Calls
3 calls:
Slowest
376.0ms
(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
177.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
79.0ms
(* (* n 2) PI)

simplify7.2s

Calls
67 calls:
Slowest
1.2s
(- (+ (* 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)))))
538.0ms
(- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (log (sqrt k)))
454.0ms
(exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
406.0ms
(- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
355.0ms
(- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 3 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
63×times-frac
45×unpow-prod-down
34×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×add-exp-log
14×div-inv associate-/l*
7×associate-/r* add-cbrt-cube div-exp
6×associate-/r/
5×unpow-prod-up fma-udef
4×pow1 pow-exp
3×expm1-log1p-u pow-unpow insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp cbrt-undiv clear-num frac-2neg
1×pow-pow
Calls
3 calls:
Slowest
16.0ms
(/ (pow (/ (* -2 PI) (/ -1 n)) (fma -1/2 k 1/2)) (sqrt k))
7.0ms
(/ (* -2 PI) (/ -1 n))
7.0ms
(pow (/ (* -2 PI) (/ -1 n)) (fma -1/2 k 1/2))

series829.0ms

Calls
3 calls:
Slowest
323.0ms
(pow (/ (* -2 PI) (/ -1 n)) (fma -1/2 k 1/2))
278.0ms
(/ (pow (/ (* -2 PI) (/ -1 n)) (fma -1/2 k 1/2)) (sqrt k))
228.0ms
(/ (* -2 PI) (/ -1 n))

simplify20.2s

Calls
137 calls:
Slowest
994.0ms
(- (+ (* 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)))))
789.0ms
(- (* (- (log (* -2 PI)) (log (/ -1 n))) (fma -1/2 k 1/2)) (log (sqrt k)))
729.0ms
(- (log (pow (/ (* -2 PI) (/ -1 n)) (fma -1/2 k 1/2))) (log (sqrt k)))
618.0ms
(/ (* (cbrt (pow (/ (* -2 PI) (/ -1 n)) (fma -1/2 k 1/2))) (cbrt (pow (/ (* -2 PI) (/ -1 n)) (fma -1/2 k 1/2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
602.0ms
(- (* (log (/ (* -2 PI) (/ -1 n))) (fma -1/2 k 1/2)) (log (sqrt k)))

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
26×add-exp-log
25×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
19×associate-*r*
11×add-cbrt-cube
9×unpow-prod-up div-exp fma-udef
8×pow-to-exp unpow-prod-down prod-exp
5×pow1 associate-/l*
4×expm1-log1p-u associate-*l* pow-exp insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow associate-/r*
2×cbrt-undiv *-commutative cbrt-unprod div-inv
1×clear-num pow-pow frac-2neg associate-*r/
Calls
4 calls:
Slowest
16.0ms
(* (pow 2 (fma -1/2 k 1/2)) (/ (pow (* PI n) (fma -1/2 k 1/2)) (sqrt k)))
11.0ms
(/ (pow (* PI n) (fma -1/2 k 1/2)) (sqrt k))
3.0ms
(pow (* PI n) (fma -1/2 k 1/2))
0.0ms
(* PI n)

series760.0ms

Calls
4 calls:
Slowest
336.0ms
(* (pow 2 (fma -1/2 k 1/2)) (/ (pow (* PI n) (fma -1/2 k 1/2)) (sqrt k)))
221.0ms
(/ (pow (* PI n) (fma -1/2 k 1/2)) (sqrt k))
144.0ms
(pow (* PI n) (fma -1/2 k 1/2))
59.0ms
(* PI n)

simplify12.7s

Calls
93 calls:
Slowest
1.4s
(+ (log (pow 2 (fma -1/2 k 1/2))) (- (log (pow (* PI n) (fma -1/2 k 1/2))) (log (sqrt k))))
1.4s
(- (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (exp (* 1/2 (+ (log PI) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k)))))
834.0ms
(exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k))))
680.0ms
(/ (* (* (pow (* PI n) (fma -1/2 k 1/2)) (pow (* PI n) (fma -1/2 k 1/2))) (pow (* PI n) (fma -1/2 k 1/2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
533.0ms
(- (* (log (* PI n)) (fma -1/2 k 1/2)) (log (sqrt k)))

prune4.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow n (fma -1/2 k 1/2))
0.5b
(pow PI (fma -1/2 k 1/2))
0.3b
(* (pow 2 (fma -1/2 k 1/2)) (/ (pow PI (fma -1/2 k 1/2)) (/ (sqrt k) (pow n (fma -1/2 k 1/2)))))
0.2b
(/ (pow PI (fma -1/2 k 1/2)) (/ (sqrt k) (pow n (fma -1/2 k 1/2))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
236×times-frac
113×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
69×associate-*r*
63×unpow-prod-up fma-udef
46×add-exp-log
30×div-exp
24×pow-to-exp
18×add-cbrt-cube
16×associate-/r*
14×prod-exp
11×div-inv
6×cbrt-undiv pow-unpow
4×expm1-log1p-u pow1 associate-*l* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×cbrt-unprod
2×associate-/r/
1×clear-num frac-2neg associate-*r/ *-commutative
Calls
4 calls:
Slowest
54.0ms
(* (pow 2 (fma -1/2 k 1/2)) (/ (pow PI (fma -1/2 k 1/2)) (/ (sqrt k) (pow n (fma -1/2 k 1/2)))))
16.0ms
(/ (pow PI (fma -1/2 k 1/2)) (/ (sqrt k) (pow n (fma -1/2 k 1/2))))
2.0ms
(pow n (fma -1/2 k 1/2))
2.0ms
(pow PI (fma -1/2 k 1/2))

series956.0ms

Calls
4 calls:
Slowest
573.0ms
(* (pow 2 (fma -1/2 k 1/2)) (/ (pow PI (fma -1/2 k 1/2)) (/ (sqrt k) (pow n (fma -1/2 k 1/2)))))
245.0ms
(/ (pow PI (fma -1/2 k 1/2)) (/ (sqrt k) (pow n (fma -1/2 k 1/2))))
93.0ms
(pow n (fma -1/2 k 1/2))
44.0ms
(pow PI (fma -1/2 k 1/2))

simplify42.4s

Calls
266 calls:
Slowest
2.1s
(+ (log (pow 2 (fma -1/2 k 1/2))) (- (* (log PI) (fma -1/2 k 1/2)) (log (/ (sqrt k) (pow n (fma -1/2 k 1/2))))))
1.3s
(+ (* (log 2) (fma -1/2 k 1/2)) (- (* (log PI) (fma -1/2 k 1/2)) (- (log (sqrt k)) (* (log n) (fma -1/2 k 1/2)))))
1.1s
(+ (log (pow 2 (fma -1/2 k 1/2))) (- (* (log PI) (fma -1/2 k 1/2)) (- (log (sqrt k)) (log (pow n (fma -1/2 k 1/2))))))
1.0s
(- (* (log PI) (fma -1/2 k 1/2)) (log (/ (sqrt k) (pow n (fma -1/2 k 1/2)))))
1.0s
(+ (log (pow 2 (fma -1/2 k 1/2))) (- (* (log PI) (fma -1/2 k 1/2)) (- (log (sqrt k)) (* (log n) (fma -1/2 k 1/2)))))

prune7.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes169.0ms

Accuracy

0% (0.4b remaining)

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

bsearch4.0ms

end0.0ms

sample16.7s

Algorithm
intervals
Results
10.4s20312×body80nan
5.2s11888×body80valid