Details

sample81.0ms

Algorithm

intervals

Results

28.0ms	88×	body	1280	valid
15.0ms	67×	body	640	valid
12.0ms	246×	body	80	valid
9.0ms	35×	body	320	valid
2.0ms	15×	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: 0.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.5b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite50.0ms

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:

15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
16.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
4.0ms	(/ (cos th) (sqrt 2.0))
4.0ms	(/ (cos th) (sqrt 2.0))

series337.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
110.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
62.0ms	(/ (cos th) (sqrt 2.0))
58.0ms	(/ (cos th) (sqrt 2.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (40.0ms)

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

prune456.0ms

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))
0.4b	(* (/ (cos th) (sqrt 2.0)) a2)
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite46.0ms

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:

18.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
12.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
4.0ms	(/ (cos th) (sqrt 2.0))
4.0ms	(/ (cos th) (sqrt 2.0))

series331.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
101.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
62.0ms	(/ (cos th) (sqrt 2.0))
57.0ms	(/ (cos th) (sqrt 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (39.0ms)

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

prune461.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos th) (/ a2 (sqrt 2.0))) a2)
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.4b	(/ a2 (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

56×	`times-frac`
53×	`add-sqr-sqrt`
48×	`add-cube-cbrt` `*-un-lft-identity`
34×	`sqrt-prod`
29×	`add-exp-log` `add-cbrt-cube`
23×	`associate-l`
14×	`pow1`
12×	`associate-/r*`
11×	`prod-exp` `cbrt-unprod`
6×	`pow-prod-down` `associate-/l*`
5×	`cbrt-undiv` `div-exp`
4×	`associate-r` `add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`associate-*r/`

Counts

4 → 144

Calls

4 calls:

18.0ms	(* (* (cos th) (/ a2 (sqrt 2.0))) a2)
16.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
3.0ms	(/ a2 (sqrt 2.0))
4.0ms	(/ (cos th) (sqrt 2.0))

series342.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (* (cos th) (/ a2 (sqrt 2.0))) a2)
111.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
58.0ms	(/ a2 (sqrt 2.0))
62.0ms	(/ (cos th) (sqrt 2.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	513	1039
1	2269	924
2	5001	904

prune380.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.4b	(/ a2 (sqrt 2.0))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

1149×	`sqrt-prod`
1137×	`times-frac`
626×	`add-sqr-sqrt`
592×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
37×	`associate-/l*`
34×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r*`
23×	`div-inv`
13×	`unswap-sqr`
11×	`cbrt-undiv` `div-exp`
9×	`pow1` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 744

Calls

4 calls:

102.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
3.0ms	(/ a2 (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
23.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
58.0ms	(/ a2 (sqrt 2.0))
99.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
70.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify109.0ms

Algorithm

egg-herbie

Counts

756 → 756

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1569	9843
1	5002	8682

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes278.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	23
1	31	23

end0.0ms

sample2.3s

Algorithm

intervals

Results

821.0ms	2539×	body	1280	valid
492.0ms	2251×	body	640	valid
399.0ms	8054×	body	80	valid
173.0ms	1053×	body	320	valid
49.0ms	473×	body	160	valid