Details

sample209.0ms

Algorithm

intervals

Results

121.0ms	643×	body	80	nan
61.0ms	365×	body	80	valid

simplify41.0ms

Calls

1 calls:

Slowest

40.0ms

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

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 3 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

18×	`times-frac`
15×	`add-cube-cbrt`
15×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
10×	`unpow-prod-up`
9×	`add-exp-log`
6×	`associate-/l*`
5×	`add-cbrt-cube`
5×	`unpow-prod-down`
5×	`sub-neg`
4×	`pow1`
3×	`add-log-exp`
3×	`div-exp`
3×	`associate-/r*`
3×	`pow-unpow`
2×	`pow-sub`
2×	`pow-exp`
2×	`pow-to-exp`
1×	`associate-/l/`
1×	`div-inv`
1×	`*-commutative`
1×	`associate-r`
1×	`frac-2neg`
1×	`pow-pow`
1×	`clear-num`
1×	`cbrt-undiv`

Calls

3 calls:

Slowest

9.0ms	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
3.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))
2.0ms	(* PI (* n 2))

series453.0ms

Calls

3 calls:

Slowest

214.0ms	(/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
174.0ms	(pow (* PI (* n 2)) (- 1/2 (/ k 2)))
65.0ms	(* PI (* n 2))

simplify3.2s

Calls

67 calls:

Slowest

678.0ms	(- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k)))
572.0ms	(- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k)))
309.0ms	(* (log (* PI (* n 2))) (- 1/2 (/ k 2)))
251.0ms	(- (+ (* 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)))))
223.0ms	(- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k)))

prune902.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log`
8×	`add-cube-cbrt`
8×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
6×	`prod-exp`
6×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-l`
4×	`add-log-exp`
4×	`associate-r`
4×	`pow-unpow`
4×	`rec-exp`
3×	`pow-sub`
3×	`div-inv`
3×	`pow-exp`
3×	`div-sub`
3×	`associate-/r*`
3×	`pow-to-exp`
2×	`pow-flip`
2×	`*-commutative`
2×	`unpow-prod-down`
1×	`inv-pow`
1×	`cbrt-unprod`
1×	`associate-*r/`
1×	`associate-*l/`
1×	`pow1/2`
1×	`frac-2neg`
1×	`pow-pow`
1×	`clear-num`
1×	`frac-times`

Calls

4 calls:

Slowest

18.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
3.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
2.0ms	(* (* 2 PI) n)
2.0ms	(/ 1 (sqrt k))

series374.0ms

Calls

4 calls:

Slowest

176.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
129.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
54.0ms	(* (* 2 PI) n)
15.0ms	(/ 1 (sqrt k))

simplify2.7s

Calls

42 calls:

Slowest

484.0ms	(* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
445.0ms	(* (* (* (/ 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))))
257.0ms	(+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
245.0ms	(- (+ (* 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)))))
221.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))

prune902.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

18×	`times-frac`
15×	`add-cube-cbrt`
15×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
10×	`unpow-prod-up`
9×	`add-exp-log`
6×	`associate-/l*`
5×	`add-cbrt-cube`
5×	`unpow-prod-down`
5×	`sub-neg`
4×	`pow1`
3×	`add-log-exp`
3×	`div-exp`
3×	`associate-/r*`
3×	`pow-unpow`
2×	`pow-sub`
2×	`pow-exp`
2×	`pow-to-exp`
1×	`associate-/l/`
1×	`div-inv`
1×	`*-commutative`
1×	`frac-2neg`
1×	`pow-pow`
1×	`clear-num`
1×	`cbrt-undiv`

Calls

3 calls:

Slowest

5.0ms	(/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k))
3.0ms	(pow (* (* n PI) 2) (- 1/2 (/ k 2)))
0.0ms	(* n PI)

series390.0ms

Calls

3 calls:

Slowest

209.0ms	(/ (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (sqrt k))
146.0ms	(pow (* (* n PI) 2) (- 1/2 (/ k 2)))
35.0ms	(* n PI)

simplify3.0s

Calls

67 calls:

Slowest

527.0ms	(- (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))) (log (sqrt k)))
518.0ms	(- (* (log (* (* n PI) 2)) (- 1/2 (/ k 2))) (log (sqrt k)))
286.0ms	(* (log (* (* n PI) 2)) (- 1/2 (/ k 2)))
272.0ms	(/ (* (* (pow (* (* n PI) 2) (- 1/2 (/ k 2))) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
206.0ms	(- (log (pow (* (* n PI) 2) (- 1/2 (/ k 2)))) (log (sqrt k)))

prune703.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log`
6×	`add-cube-cbrt`
6×	`prod-exp`
6×	`*-un-lft-identity`
6×	`pow-to-exp`
6×	`add-sqr-sqrt`
5×	`add-cbrt-cube`
4×	`associate-l`
4×	`associate-r`
4×	`pow-unpow`
4×	`pow1`
3×	`add-log-exp`
3×	`pow-exp`
2×	`pow-sub`
2×	`*-commutative`
2×	`div-sub`
2×	`unpow-prod-down`
1×	`div-inv`
1×	`cbrt-unprod`
1×	`associate-*r/`
1×	`pow-pow`

Calls

3 calls:

Slowest

16.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
3.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
2.0ms	(* (* 2 PI) n)

series375.0ms

Calls

3 calls:

Slowest

155.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
152.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
68.0ms	(* (* 2 PI) n)

simplify2.0s

Calls

31 calls:

Slowest

490.0ms	(* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
214.0ms	(+ (* (log k) -1/2) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
204.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
198.0ms	(- (+ (* 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)))))
187.0ms	(+ (log (pow k -1/2)) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))

prune562.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes208.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample7.5s

Algorithm

intervals

Results

4.2s	20330×	body	80	nan
2.6s	11923×	body	80	valid
1.0ms	2×	body	160	nan