Details

Time bar (total: 42.0s)

sample218.0ms

Algorithm
intervals
Results
99.0ms623×body80nan
87.0ms364×body80valid

simplify97.0ms

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 3 expressions with local error:

1.6b
(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))

rewrite26.0ms

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
13.0ms
(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
6.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
5.0ms
(* (* n 2) PI)

series569.0ms

Calls
3 calls:
Slowest
332.0ms
(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
204.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
33.0ms
(* (* n 2) PI)

simplify4.3s

Calls
67 calls:
Slowest
749.0ms
(- (+ (* 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)))))
391.0ms
(- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (log (sqrt k)))
310.0ms
(exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
207.0ms
(exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
204.0ms
(/ (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))

prune951.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
0.2b
(* (* n 2) PI)
0.2b
(/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
0.2b
(/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
29×associate-/r*
26×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×unpow-prod-up add-exp-log
8×sub-neg unpow-prod-down
6×pow1 add-cbrt-cube div-exp
4×expm1-log1p-u rec-exp insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp pow-unpow pow-exp associate-/r/ div-inv associate-/l* pow-sub
2×clear-num frac-2neg
1×cbrt-undiv pow-pow associate-*l* *-commutative pow-flip inv-pow
Calls
4 calls:
Slowest
7.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
6.0ms
(/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
3.0ms
(/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
3.0ms
(* (* n 2) PI)

series993.0ms

Calls
4 calls:
Slowest
380.0ms
(/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
350.0ms
(/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
216.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
46.0ms
(* (* n 2) PI)

simplify5.6s

Calls
95 calls:
Slowest
677.0ms
(- (+ (* 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)))))
388.0ms
(- (log (sqrt k)) (log (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
345.0ms
(exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
233.0ms
(exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
232.0ms
(/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

1.6b
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
0.2b
(* (* n 2) PI)
0.2b
(* (sqrt k) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
0.2b
(/ 1 (* (sqrt k) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
11×rec-exp
10×pow1
8×prod-exp
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube
5×associate-*r*
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp pow-unpow pow-exp associate-/r/
2×unpow-prod-up pow-prod-down associate-*r/ un-div-inv *-commutative div-inv pow-flip pow-sub
1×clear-num associate-/r* sub-neg unpow-prod-down pow-pow frac-2neg cbrt-unprod inv-pow
Calls
4 calls:
Slowest
14.0ms
(* (sqrt k) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
11.0ms
(/ 1 (* (sqrt k) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))
6.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
5.0ms
(* (* n 2) PI)

series951.0ms

Calls
4 calls:
Slowest
361.0ms
(* (sqrt k) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
341.0ms
(/ 1 (* (sqrt k) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))
197.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
53.0ms
(* (* n 2) PI)

simplify4.2s

Calls
41 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)))))
447.0ms
(* (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))
378.0ms
(+ (log (sqrt k)) (- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))
372.0ms
(exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
252.0ms
(+ (log (sqrt k)) (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))))

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 3 expressions with local error:

1.6b
(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))

rewrite32.0ms

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))
6.0ms
(pow (/ (* -2 PI) (/ -1 n)) (fma -1/2 k 1/2))

series610.0ms

Calls
3 calls:
Slowest
348.0ms
(/ (pow (/ (* -2 PI) (/ -1 n)) (fma -1/2 k 1/2)) (sqrt k))
221.0ms
(pow (/ (* -2 PI) (/ -1 n)) (fma -1/2 k 1/2))
40.0ms
(/ (* -2 PI) (/ -1 n))

simplify11.5s

Calls
137 calls:
Slowest
779.0ms
(- (+ (* 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)))))
485.0ms
(- (log (pow (/ (* -2 PI) (/ -1 n)) (fma -1/2 k 1/2))) (log (sqrt k)))
325.0ms
(/ (* (* (pow (/ (* -2 PI) (/ -1 n)) (fma -1/2 k 1/2)) (pow (/ (* -2 PI) (/ -1 n)) (fma -1/2 k 1/2))) (pow (/ (* -2 PI) (/ -1 n)) (fma -1/2 k 1/2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
305.0ms
(exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
305.0ms
(exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes125.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
4.1s20624×body80nan
2.8s11917×body80valid
0.0ms1×body160nan