Details

sample100.0ms

Algorithm

intervals

Results

36.0ms	90×	body	1280	valid
20.0ms	253×	body	80	valid
18.0ms	74×	body	640	valid
7.0ms	36×	body	320	valid
2.0ms	18×	body	160	valid

simplify16.0ms

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: 0.5b

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 a2))
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite45.0ms

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:

14.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
14.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
4.0ms	(/ (cos th) (sqrt 2.0))
4.0ms	(/ (cos th) (sqrt 2.0))

series339.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
111.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
61.0ms	(/ (cos th) (sqrt 2.0))
56.0ms	(/ (cos th) (sqrt 2.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (38.0ms)

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

prune465.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b	(/ (pow a2 2) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

142×	`times-frac`
121×	`add-sqr-sqrt`
94×	`add-cube-cbrt` `*-un-lft-identity`
77×	`sqrt-prod`
53×	`associate-r`
41×	`unpow-prod-down`
33×	`add-exp-log`
25×	`associate-l` `add-cbrt-cube`
15×	`unpow2` `sqr-pow`
12×	`associate-/r*` `unswap-sqr`
11×	`pow1` `associate-/l*`
10×	`prod-exp`
9×	`div-exp`
8×	`cbrt-unprod`
5×	`cbrt-undiv`
4×	`pow-prod-down` `div-inv` `add-log-exp`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `*-commutative`
1×	`associate-r/` `associate-l/`

Counts

4 → 240

Calls

4 calls:

24.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms	(/ (pow a2 2) (sqrt 2.0))
4.0ms	(/ (cos th) (sqrt 2.0))

series342.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
113.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
57.0ms	(/ (pow a2 2) (sqrt 2.0))
62.0ms	(/ (cos th) (sqrt 2.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	693	1786
1	3017	1552
2	5001	1540

prune579.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
0.1b	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
0.3b	(/ (pow a2 2) (sqrt 2.0))
0.3b	(/ (pow a1 2) (sqrt 2.0))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

208×	`times-frac`
172×	`add-sqr-sqrt`
128×	`add-cube-cbrt` `*-un-lft-identity`
110×	`sqrt-prod`
104×	`associate-r`
82×	`unpow-prod-down`
34×	`add-exp-log`
30×	`unpow2` `sqr-pow`
18×	`add-cbrt-cube` `unswap-sqr`
16×	`associate-/l*`
12×	`div-exp` `associate-/r*`
8×	`pow1` `prod-exp`
6×	`associate-l`
4×	`cbrt-undiv` `pow-to-exp` `pow-exp` `cbrt-unprod` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 312

Calls

4 calls:

20.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
20.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
5.0ms	(/ (pow a2 2) (sqrt 2.0))
9.0ms	(/ (pow a1 2) (sqrt 2.0))

series343.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
108.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
62.0ms	(/ (pow a2 2) (sqrt 2.0))
58.0ms	(/ (pow a1 2) (sqrt 2.0))

simplify86.0ms

Algorithm

egg-herbie

Counts

324 → 324

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	746	2292
1	3355	1966
2	5001	1946

prune889.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (fabs a1) (cos th)) (/ (sqrt (pow a1 2)) (sqrt 2.0)))
0.3b	(/ (pow a2 2) (sqrt 2.0))
0.4b	(/ (sqrt (pow a1 2)) (sqrt 2.0))
19.6b	(sqrt (pow a1 2))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

208×	`sqrt-prod`
180×	`times-frac`
126×	`add-sqr-sqrt`
124×	`add-cube-cbrt` `*-un-lft-identity`
70×	`associate-r`
64×	`unpow-prod-down`
23×	`add-exp-log`
22×	`unpow2` `sqr-pow`
20×	`add-cbrt-cube`
19×	`associate-/l*`
12×	`associate-/r*`
9×	`pow1`
6×	`div-exp` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `rem-sqrt-square` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`frac-2neg` `clear-num`
1×	`pow-to-exp` `sqrt-undiv` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l` `pow-exp` `-commutative`

Counts

4 → 283

Calls

4 calls:

24.0ms	(* (* (fabs a1) (cos th)) (/ (sqrt (pow a1 2)) (sqrt 2.0)))
5.0ms	(/ (pow a2 2) (sqrt 2.0))
6.0ms	(/ (sqrt (pow a1 2)) (sqrt 2.0))
2.0ms	(sqrt (pow a1 2))

series230.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (* (fabs a1) (cos th)) (/ (sqrt (pow a1 2)) (sqrt 2.0)))
59.0ms	(/ (pow a2 2) (sqrt 2.0))
56.0ms	(/ (sqrt (pow a1 2)) (sqrt 2.0))
8.0ms	(sqrt (pow a1 2))

simplify91.0ms

Algorithm

egg-herbie

Counts

295 → 295

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	782	2387
1	3859	2041
2	5002	1985

prune691.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes208.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	16
1	23	16

end0.0ms

sample2.7s

Algorithm

intervals

Results

937.0ms	2584×	body	1280	valid
637.0ms	8012×	body	80	valid
513.0ms	2066×	body	640	valid
199.0ms	1017×	body	320	valid
72.0ms	540×	body	160	valid