Details

sample81.0ms

Algorithm

intervals

Results

33.0ms	651×	body	80	nan
24.0ms	398×	body	80	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	8
1	59	8
2	119	8
3	325	8
4	1044	8
5	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite42.0ms

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×	`div-exp` `pow-prod-down` `associate-/r*` `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` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 157

Calls

4 calls:

17.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
3.0ms	(/ 1.0 (sqrt k))
6.0ms	(* (* 2.0 PI) n)
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series543.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
44.0ms	(/ 1.0 (sqrt k))
31.0ms	(* (* 2.0 PI) n)
145.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify107.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	981	1502
1	4021	1398
2	5003	1383

prune475.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite45.0ms

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×	`div-exp` `pow-prod-down` `associate-/r*` `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` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 157

Calls

4 calls:

20.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
3.0ms	(/ 1.0 (sqrt k))
6.0ms	(* (* 2.0 PI) n)
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series548.0ms

Counts

4 → 12

Calls

4 calls:

332.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
38.0ms	(/ 1.0 (sqrt k))
37.0ms	(* (* 2.0 PI) n)
140.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify100.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	981	1502
1	4021	1398
2	5003	1383

prune660.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (sqrt k)))
0.3b	(* (* 2.0 PI) n)
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.5b	(* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-sqr-sqrt`
141×	`times-frac`
135×	`sqrt-prod`
92×	`*-un-lft-identity`
74×	`add-cube-cbrt`
41×	`add-exp-log`
34×	`associate-r`
32×	`associate-l`
28×	`unswap-sqr`
23×	`add-cbrt-cube`
20×	`pow1`
19×	`pow-unpow`
14×	`prod-exp`
10×	`div-exp`
9×	`associate-/r*`
7×	`pow-prod-down` `cbrt-unprod`
5×	`cbrt-undiv` `pow-flip`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-pow` `1-exp` `pow-exp` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/2` `*-commutative`
1×	`frac-times` `pow-to-exp` `unpow-prod-down` `frac-2neg` `div-sub` `associate-r/` `associate-l/` `clear-num` `inv-pow` `pow-sub` `sqr-pow`

Counts

4 → 235

Calls

4 calls:

4.0ms	(/ 1 (sqrt (sqrt k)))
6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
41.0ms	(* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))))

series356.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ 1 (sqrt (sqrt k)))
31.0ms	(* (* 2.0 PI) n)
143.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
38.0ms	(* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))))

simplify104.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	1034	2184
1	4836	1918
2	5001	1916

prune581.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite36.0ms

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:

6.0ms	(* (* 2.0 PI) n)
6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series344.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) n)
36.0ms	(* (* 2.0 PI) n)
136.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
141.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	407	832
1	1658	770
2	5001	732

prune403.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes191.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	11
1	23	11

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	20676×	body	80	nan
719.0ms	11905×	body	80	valid