Details

sample196.0ms

Algorithm

intervals

Results

105.0ms	760×	body	80	nan
44.0ms	365×	body	80	valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
6	2792
5	816
4	285
3	114
2	58
1	29
0	13

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
55×	`times-frac`
49×	`*-un-lft-identity`
46×	`add-exp-log`
43×	`add-cube-cbrt`
23×	`associate-l` `sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
16×	`add-cbrt-cube`
15×	`pow1`
9×	`pow-exp`
8×	`associate-r`
6×	`associate-/r*` `div-exp` `pow-prod-down` `unswap-sqr`
5×	`cbrt-unprod` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-sub` `div-inv` `associate-/l*` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 157

Calls

4 calls:

38.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
9.0ms	(/ 1.0 (sqrt k))
17.0ms	(* (* 2.0 PI) n)
24.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series804.0ms

Counts

4 → 12

Calls

4 calls:

457.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
72.0ms	(/ 1.0 (sqrt k))
57.0ms	(* (* 2.0 PI) n)
218.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify3.5s

Counts

169 → 169

Iterations

Iter	Nodes
done	5004
2	3445
1	1004
0	361

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
55×	`times-frac`
49×	`*-un-lft-identity`
46×	`add-exp-log`
43×	`add-cube-cbrt`
25×	`associate-r`
23×	`sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
16×	`add-cbrt-cube`
15×	`pow1`
9×	`pow-exp`
6×	`associate-/r` `div-exp` `associate-l*` `pow-prod-down` `unswap-sqr`
5×	`cbrt-unprod` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-sub` `div-inv` `associate-/l*` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 157

Calls

4 calls:

53.0ms	(* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))
9.0ms	(/ 1.0 (sqrt k))
18.0ms	(* (* 2.0 PI) n)
22.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series679.0ms

Counts

4 → 12

Calls

4 calls:

400.0ms	(* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))
66.0ms	(/ 1.0 (sqrt k))
42.0ms	(* (* 2.0 PI) n)
171.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify3.5s

Counts

169 → 169

Iterations

Iter	Nodes
done	5006
2	3248
1	952
0	343

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
55×	`times-frac`
49×	`*-un-lft-identity`
46×	`add-exp-log`
43×	`add-cube-cbrt`
23×	`associate-l` `sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
16×	`add-cbrt-cube`
15×	`pow1`
9×	`pow-exp`
8×	`associate-r`
6×	`associate-/r*` `div-exp` `pow-prod-down` `unswap-sqr`
5×	`cbrt-unprod` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-sub` `div-inv` `associate-/l*` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 157

Calls

4 calls:

38.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
10.0ms	(/ 1.0 (sqrt k))
19.0ms	(* (* 2.0 PI) n)
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series834.0ms

Counts

4 → 12

Calls

4 calls:

479.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
53.0ms	(/ 1.0 (sqrt k))
64.0ms	(* (* 2.0 PI) n)
238.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify4.1s

Counts

169 → 169

Iterations

Iter	Nodes
done	5004
2	3445
1	1004
0	361

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

38×	`pow-unpow`
36×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
26×	`pow1` `add-exp-log`
24×	`add-cube-cbrt`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp`
6×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

14.0ms	(* (* 2.0 PI) n)
17.0ms	(* (* 2.0 PI) n)
17.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
17.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series497.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* 2.0 PI) n)
49.0ms	(* (* 2.0 PI) n)
171.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
229.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.8s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	1340
1	430
0	154

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes456.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.3s	20608×	body	80	nan
2.2s	11771×	body	80	valid