Details

Time bar (total: 39.9s)

sample160.0ms

Algorithm
intervals
Results
73.0ms607×body80nan
64.0ms382×body80valid

simplify94.0ms

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 3 expressions with local error:

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

series527.0ms

Calls
3 calls:
Slowest
289.0ms
(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
196.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
41.0ms
(* (* n 2) PI)

simplify4.3s

Calls
67 calls:
Slowest
719.0ms
(- (+ (* 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)))))
415.0ms
(- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (log (sqrt k)))
324.0ms
(exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
220.0ms
(exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
202.0ms
(- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))

prune913.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.9b
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
0.3b
(* (* n 2) PI)
0.2b
(/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
0.1b
(/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))

rewrite17.0ms

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
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
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
3.0ms
(* (* n 2) PI)

series890.0ms

Calls
4 calls:
Slowest
350.0ms
(/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
344.0ms
(/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
152.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
43.0ms
(* (* n 2) PI)

simplify5.2s

Calls
95 calls:
Slowest
746.0ms
(- (+ (* 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)))))
420.0ms
(- (log (sqrt k)) (log (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
257.0ms
(exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
237.0ms
(- (log (sqrt k)) (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))))
236.0ms
(exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
20×times-frac add-exp-log
17×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×div-inv
11×rec-exp
8×associate-/r* div-exp
6×pow1 add-cbrt-cube associate-/r/ pow-sub
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×pow-to-exp pow-unpow pow-exp
2×unpow-prod-up clear-num frac-2neg pow-flip
1×cbrt-undiv sub-neg unpow-prod-down pow-pow pow1/2 associate-*l* *-commutative inv-pow associate-/l/
Calls
4 calls:
Slowest
7.0ms
(/ (/ 1 (sqrt k)) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
3.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
3.0ms
(* (* n 2) PI)
1.0ms
(/ 1 (sqrt k))

series551.0ms

Calls
4 calls:
Slowest
308.0ms
(/ (/ 1 (sqrt k)) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
175.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
35.0ms
(/ 1 (sqrt k))
33.0ms
(* (* n 2) PI)

simplify6.8s

Calls
83 calls:
Slowest
759.0ms
(/ (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (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))))))
701.0ms
(- (+ (* 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)))))
323.0ms
(exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
322.0ms
(- (log (/ 1 (sqrt k))) (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))))
300.0ms
(- (- (log (sqrt k))) (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

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

series841.0ms

Calls
4 calls:
Slowest
347.0ms
(/ (pow k -1/2) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
257.0ms
(/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
175.0ms
(pow (* (* n 2) PI) (- 1/2 (/ k 2)))
62.0ms
(* (* n 2) PI)

simplify8.0s

Calls
76 calls:
Slowest
815.0ms
(- (+ (* 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)))))
617.0ms
(+ (* 1/8 (/ (* (pow (log (* 2 PI)) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* k (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* (log n) k) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/4 (/ (* (log (* 2 PI)) (* (log n) (pow k 2))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (* 1/8 (/ (* (pow (log n) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))))
480.0ms
(- (* (log k) -1/2) (- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))
460.0ms
(- (log (pow k -1/2)) (- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))
424.0ms
(/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes134.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample6.9s

Algorithm
intervals
Results
4.2s20279×body80nan
2.2s11735×body80valid
1.0ms2×body160nan