Details

sample82.0ms

Algorithm

intervals

Results

29.0ms	83×	body	1280	valid
13.0ms	62×	body	640	valid
13.0ms	267×	body	80	valid
5.0ms	36×	body	320	valid
2.0ms	23×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	50	7
2	77	7
3	96	7
4	112	7
5	127	7
6	141	7
7	141	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.6b	(/ (cos th) (sqrt 2.0))
0.6b	(/ (cos th) (sqrt 2.0))
0.6b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
70×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
32×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
12×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*` `unswap-sqr`
4×	`div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r` `associate-l/` `clear-num` `-commutative`

Counts

4 → 168

Calls

4 calls:

33.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
10.0ms	(/ (cos th) (sqrt 2.0))
10.0ms	(/ (cos th) (sqrt 2.0))
34.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))

series353.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
59.0ms	(/ (cos th) (sqrt 2.0))
68.0ms	(/ (cos th) (sqrt 2.0))
116.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))

simplify56.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	504	1284
1	2009	1156
2	5001	1136

prune467.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b	(* (/ (cos th) (sqrt 2.0)) a2)
0.6b	(/ (cos th) (sqrt 2.0))
0.6b	(/ (cos th) (sqrt 2.0))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
74×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
11×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*` `unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`associate-r` `pow-prod-down` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`

Counts

4 → 165

Calls

4 calls:

29.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
23.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
10.0ms	(/ (cos th) (sqrt 2.0))
10.0ms	(/ (cos th) (sqrt 2.0))

series339.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
109.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
56.0ms	(/ (cos th) (sqrt 2.0))
63.0ms	(/ (cos th) (sqrt 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	443	1207
1	1805	1104
2	5001	1084

prune458.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (/ (sqrt 2.0) (cos th))) (* a1 a1))
0.3b	(* (/ (cos th) (sqrt 2.0)) a2)
0.6b	(/ 1 (/ (sqrt 2.0) (cos th)))
0.6b	(/ (cos th) (sqrt 2.0))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac`
192×	`add-sqr-sqrt`
173×	`*-un-lft-identity`
170×	`add-cube-cbrt`
93×	`associate-l`
87×	`sqrt-prod`
67×	`add-exp-log`
37×	`add-cbrt-cube`
28×	`associate-/r*`
23×	`div-exp` `prod-exp`
12×	`pow1`
11×	`cbrt-undiv` `cbrt-unprod` `div-inv`
10×	`unswap-sqr`
6×	`rec-exp` `1-exp` `associate-/l*`
4×	`associate-r` `pow-prod-down` `add-log-exp`
2×	`frac-2neg` `associate-l/` `clear-num` `associate-/r/` `-commutative`
1×	`pow-flip` `inv-pow`

Counts

4 → 303

Calls

4 calls:

55.0ms	(* (/ 1 (/ (sqrt 2.0) (cos th))) (* a1 a1))
23.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
13.0ms	(/ 1 (/ (sqrt 2.0) (cos th)))
10.0ms	(/ (cos th) (sqrt 2.0))

series330.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (/ 1 (/ (sqrt 2.0) (cos th))) (* a1 a1))
103.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
55.0ms	(/ 1 (/ (sqrt 2.0) (cos th)))
64.0ms	(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1006	2602
1	5000	2225

prune975.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 2.0) (cos th))
0.2b	(/ (pow a1 2) (/ (sqrt 2.0) (cos th)))
0.3b	(* (/ (cos th) (sqrt 2.0)) a2)
0.6b	(/ (cos th) (sqrt 2.0))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

394×	`times-frac`
219×	`add-sqr-sqrt`
211×	`add-cube-cbrt` `*-un-lft-identity`
115×	`sqrt-prod`
69×	`unpow-prod-down`
31×	`associate-/r*`
26×	`add-exp-log`
23×	`unpow2` `sqr-pow`
22×	`associate-l`
18×	`add-cbrt-cube`
17×	`associate-/l*`
13×	`div-inv`
12×	`div-exp`
6×	`pow1` `cbrt-undiv`
4×	`add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `unswap-sqr`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod`
1×	`pow-prod-down` `associate-l/` `associate-/r/` `-commutative`

Counts

4 → 345

Calls

4 calls:

9.0ms	(/ (sqrt 2.0) (cos th))
17.0ms	(/ (pow a1 2) (/ (sqrt 2.0) (cos th)))
19.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
10.0ms	(/ (cos th) (sqrt 2.0))

series298.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (sqrt 2.0) (cos th))
97.0ms	(/ (pow a1 2) (/ (sqrt 2.0) (cos th)))
99.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
61.0ms	(/ (cos th) (sqrt 2.0))

simplify121.0ms

Algorithm

egg-herbie

Counts

357 → 357

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1032	3568
1	4914	3229
2	5002	3229

prune816.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes284.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	11
1	26	11
2	26	11

end0.0ms

sample2.3s

Algorithm

intervals

Results

793.0ms	2551×	body	1280	valid
435.0ms	2033×	body	640	valid
401.0ms	8028×	body	80	valid
166.0ms	1105×	body	320	valid
55.0ms	544×	body	160	valid