Details

Time bar (total: 1.4m)

sample189.0ms

Algorithm
intervals
Results
97.0ms621×body80nan
64.0ms345×body80valid

simplify347.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
346.0ms
(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 3 expressions with local error:

1.4b
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b
(* n (* 2 PI))
0.2b
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
42×add-sqr-sqrt *-un-lft-identity
33×add-cube-cbrt
26×add-exp-log
22×pow-unpow
18×sqrt-prod
14×pow1
10×add-cbrt-cube
9×prod-exp
8×unpow-prod-down sqr-pow
6×associate-/r* pow-prod-down pow-exp difference-of-squares
5×div-exp associate-/l*
3×pow-pow associate-*l* cbrt-unprod insert-posit16 distribute-lft-out-- add-log-exp
2×pow-to-exp div-sub div-inv pow-sub
1×cbrt-undiv clear-num frac-2neg associate-*r* *-commutative associate-/l/
Counts
3 → 118
Calls
3 calls:
Slowest
21.0ms
(* n (* 2 PI))
21.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
13.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))

series492.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
266.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
174.0ms
(pow (* n (* 2 PI)) (/ (- 1 k) 2))
51.0ms
(* n (* 2 PI))

simplify26.0s

Counts
124 → 127
Calls
124 calls:
Slowest
705.0ms
(- (+ (* 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)))))
704.0ms
(* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
552.0ms
(/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
551.0ms
(/ (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
531.0ms
(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

1.4b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
1.4b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.3b
(* n (* 2 PI))
0.3b
(* n (* 2 PI))

rewrite87.0ms

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-*l* pow-exp cbrt-unprod
4×div-sub insert-posit16 add-log-exp
2×pow-to-exp unpow-prod-down associate-*r* *-commutative pow-sub sqr-pow
Counts
4 → 214
Calls
4 calls:
Slowest
35.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
16.0ms
(* n (* 2 PI))
15.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
12.0ms
(* n (* 2 PI))

series811.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
435.0ms
(* n (* 2 PI))
176.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
159.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
41.0ms
(* n (* 2 PI))

simplify13.3s

Counts
184 → 226
Calls
184 calls:
Slowest
434.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
433.0ms
(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
423.0ms
(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
402.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
387.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))

prune3.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize96.0ms

Local error

Found 4 expressions with local error:

1.4b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
1.4b
(pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))
0.5b
(cbrt (* n (* 2 PI)))
0.5b
(cbrt (* n (* 2 PI)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
164×add-sqr-sqrt *-un-lft-identity
140×pow-unpow
110×add-cube-cbrt
36×difference-of-squares
30×pow1
18×pow-pow distribute-lft-out--
16×add-exp-log
11×pow1/3
9×pow-prod-up
8×pow-prod-down div-inv
6×pow-plus pow-exp prod-exp
4×add-cbrt-cube div-sub insert-posit16 add-log-exp
3×pow-sqr
2×cbrt-prod pow2 pow-to-exp unpow-prod-down pow-sub sqr-pow
1×pow3
Counts
4 → 208
Calls
4 calls:
Slowest
78.0ms
(pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))
15.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
10.0ms
(cbrt (* n (* 2 PI)))
9.0ms
(cbrt (* n (* 2 PI)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
327.0ms
(cbrt (* n (* 2 PI)))
313.0ms
(cbrt (* n (* 2 PI)))
294.0ms
(pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))
192.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))

simplify14.1s

Counts
182 → 220
Calls
182 calls:
Slowest
483.0ms
(* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
450.0ms
(pow (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))
384.0ms
(* (exp (* 1/3 (- (log PI) (log (/ 1 n))))) (cbrt 2))
374.0ms
(pow n (/ (/ (- 1 k) 2) 2))
367.0ms
(* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2))

prune3.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize111.0ms

Local error

Found 4 expressions with local error:

1.8b
(pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1))
1.4b
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.3b
(cbrt (- 1 k))
0.3b
(cbrt (- 1 k))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
106×add-sqr-sqrt *-un-lft-identity
95×pow-unpow
73×add-cube-cbrt
22×difference-of-squares
16×pow1 add-exp-log
12×cbrt-prod
11×distribute-lft-out--
8×div-inv
6×pow-pow pow-prod-down pow-exp prod-exp
4×cbrt-div add-cbrt-cube insert-posit16 add-log-exp
2×pow-to-exp unpow-prod-down flip3-- pow1/3 div-sub flip-- sqr-pow
1×pow-sub
Counts
4 → 164
Calls
4 calls:
Slowest
29.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
24.0ms
(pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1))
6.0ms
(cbrt (- 1 k))
3.0ms
(cbrt (- 1 k))

series540.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
315.0ms
(pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1))
137.0ms
(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
52.0ms
(cbrt (- 1 k))
35.0ms
(cbrt (- 1 k))

simplify10.3s

Counts
138 → 176
Calls
138 calls:
Slowest
717.0ms
(* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))
404.0ms
(* (+ (log n) (log (* 2 PI))) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1))
368.0ms
(* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2))
350.0ms
(* (+ (log n) (+ (log 2) (log PI))) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1))
345.0ms
(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))

prune3.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes156.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch6.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
3.8s20678×body80nan
2.8s11986×body80valid