Details

Time bar (total: 32.8s)

sample190.0ms

Algorithm
intervals
Results
94.0ms559×body80nan
64.0ms362×body80valid

simplify1.3s

Counts
1 → 1

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 3 expressions with local error:

2.1b
(pow (* PI (* n 2)) (/ (- 1 k) 2))
0.3b
(* PI (* n 2))
0.2b
(/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))

rewrite69.0ms

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
30.0ms
(* PI (* n 2))
21.0ms
(/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))
16.0ms
(pow (* PI (* n 2)) (/ (- 1 k) 2))

series544.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
334.0ms
(/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))
163.0ms
(pow (* PI (* n 2)) (/ (- 1 k) 2))
46.0ms
(* PI (* n 2))

simplify716.0ms

Counts
160 → 127

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

1.9b
(pow (* n 2) (/ (- 1 k) 2))
0.5b
(pow PI (/ (- 1 k) 2))
0.2b
(* (pow PI (/ (- 1 k) 2)) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt k)))
0.2b
(/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt k))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
112×add-sqr-sqrt
108×times-frac
81×*-un-lft-identity
63×add-cube-cbrt
53×add-exp-log
44×pow-unpow
39×sqrt-prod
34×associate-*r*
27×sqr-pow
25×unpow-prod-down
20×prod-exp
16×div-exp pow-exp
15×unswap-sqr
12×difference-of-squares
11×pow-to-exp add-cbrt-cube
8×pow1
7×associate-*l*
6×associate-/r* distribute-lft-out--
5×div-sub associate-/l* pow-sub
4×insert-posit16 div-inv add-log-exp
3×pow-pow
2×cbrt-undiv cbrt-unprod
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 219
Calls
4 calls:
Slowest
32.0ms
(* (pow PI (/ (- 1 k) 2)) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt k)))
16.0ms
(/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt k))
8.0ms
(pow (* n 2) (/ (- 1 k) 2))
5.0ms
(pow PI (/ (- 1 k) 2))

series879.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
446.0ms
(* (pow PI (/ (- 1 k) 2)) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt k)))
233.0ms
(/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt k))
128.0ms
(pow (* n 2) (/ (- 1 k) 2))
72.0ms
(pow PI (/ (- 1 k) 2))

simplify1.0s

Counts
285 → 231

prune2.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

1.9b
(pow (* n 2) (/ (- 1 k) 2))
0.2b
(* (exp (* (/ (- 1 k) 2) (log PI))) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt k)))
0.2b
(/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt k))
0.0b
(* (/ (- 1 k) 2) (log PI))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
109×times-frac
84×*-un-lft-identity
66×add-cube-cbrt
39×sqrt-prod
38×associate-*r*
31×associate-*l*
29×add-exp-log
22×pow-unpow log-prod
20×sqr-pow
17×unswap-sqr
16×add-cbrt-cube exp-sum
14×unpow-prod-down
12×pow1 difference-of-squares
11×distribute-rgt-in distribute-lft-in
10×prod-exp
9×div-exp
6×associate-/r* pow-exp distribute-lft-out--
5×associate-/l*
4×cbrt-unprod insert-posit16 div-inv add-log-exp
3×pow-to-exp cbrt-undiv pow-prod-down
2×pow-pow div-sub *-commutative pow-sub
1×clear-num frac-2neg associate-*l/ associate-*r/ log-pow associate-/l/
Counts
4 → 221
Calls
4 calls:
Slowest
37.0ms
(* (exp (* (/ (- 1 k) 2) (log PI))) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt k)))
28.0ms
(* (/ (- 1 k) 2) (log PI))
8.0ms
(/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt k))
7.0ms
(pow (* n 2) (/ (- 1 k) 2))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
476.0ms
(* (exp (* (/ (- 1 k) 2) (log PI))) (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt k)))
459.0ms
(* (/ (- 1 k) 2) (log PI))
162.0ms
(/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt k))
122.0ms
(pow (* n 2) (/ (- 1 k) 2))

simplify1.5s

Counts
288 → 233

prune3.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

1.9b
(pow (* n 2) (/ (- 1 k) 2))
0.2b
(* (exp (* (/ (- 1 k) 2) (log PI))) (/ 1 (/ (sqrt k) (pow (* n 2) (/ (- 1 k) 2)))))
0.1b
(/ (sqrt k) (pow (* n 2) (/ (- 1 k) 2)))
0.1b
(/ 1 (/ (sqrt k) (pow (* n 2) (/ (- 1 k) 2))))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
522×times-frac
329×add-sqr-sqrt
251×*-un-lft-identity
227×add-cube-cbrt
135×sqrt-prod
110×associate-*r*
80×add-exp-log
62×sqr-pow
50×unpow-prod-down
48×div-exp
40×associate-/r*
33×unswap-sqr
28×log-prod exp-sum
24×prod-exp
22×pow-unpow
20×add-cbrt-cube
16×pow-exp
14×distribute-rgt-in distribute-lft-in
11×div-inv
10×pow1 rec-exp 1-exp associate-/r/
9×div-sub associate-*l* associate-/l* pow-sub
8×pow-to-exp
7×cbrt-undiv
6×difference-of-squares
4×insert-posit16 add-log-exp
3×cbrt-unprod distribute-lft-out--
2×clear-num pow-pow frac-2neg pow-prod-down
1×associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
4 → 453
Calls
4 calls:
Slowest
54.0ms
(* (exp (* (/ (- 1 k) 2) (log PI))) (/ 1 (/ (sqrt k) (pow (* n 2) (/ (- 1 k) 2)))))
23.0ms
(/ 1 (/ (sqrt k) (pow (* n 2) (/ (- 1 k) 2))))
14.0ms
(/ (sqrt k) (pow (* n 2) (/ (- 1 k) 2)))
11.0ms
(pow (* n 2) (/ (- 1 k) 2))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
543.0ms
(* (exp (* (/ (- 1 k) 2) (log PI))) (/ 1 (/ (sqrt k) (pow (* n 2) (/ (- 1 k) 2)))))
236.0ms
(/ (sqrt k) (pow (* n 2) (/ (- 1 k) 2)))
175.0ms
(/ 1 (/ (sqrt k) (pow (* n 2) (/ (- 1 k) 2))))
94.0ms
(pow (* n 2) (/ (- 1 k) 2))

simplify1.9s

Counts
635 → 465

prune6.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes100.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
4.0s20456×body80nan
2.7s11762×body80valid