Details

sample72.0ms

Algorithm

intervals

Results

27.0ms	84×	body	1280	valid
12.0ms	57×	body	640	valid
12.0ms	250×	body	80	valid
4.0ms	30×	body	320	valid
2.0ms	17×	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

prune12.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.5b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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:

9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
10.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms	(/ (cos th) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series342.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
115.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
56.0ms	(/ (cos th) (sqrt 2.0))
62.0ms	(/ (cos th) (sqrt 2.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	504	1284
1	2009	1156
2	5002	1136

prune491.0ms

Filtered

180 candidates to 116 candidates (64.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	168	12	180
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	170	12	182

Merged error: 0b

Counts

182 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

6.0ms	(* (cos th) (* a1 a1))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
8.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series327.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos th) (* a1 a1))
110.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
108.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
62.0ms	(/ (cos th) (sqrt 2.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	501	987
1	2139	864
2	5002	850

prune336.0ms

Filtered

144 candidates to 91 candidates (63.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	146	10	156

Merged error: 0b

Counts

156 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt 2.0) (* a1 a1))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.6b	(/ (cos th) (/ (sqrt 2.0) (* a1 a1)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

98×	`times-frac`
64×	`add-sqr-sqrt`
59×	`add-cube-cbrt` `*-un-lft-identity`
40×	`sqrt-prod`
32×	`add-exp-log` `add-cbrt-cube`
22×	`associate-l`
17×	`associate-/r*`
12×	`associate-/l*`
10×	`cbrt-undiv` `div-exp`
9×	`pow1`
8×	`prod-exp` `cbrt-unprod` `div-inv`
4×	`add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num` `unswap-sqr`
1×	`associate-r` `associate-l/` `associate-/r/` `-commutative`

Counts

4 → 171

Calls

4 calls:

5.0ms	(/ (sqrt 2.0) (* a1 a1))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
8.0ms	(/ (cos th) (/ (sqrt 2.0) (* a1 a1)))
5.0ms	(/ (cos th) (sqrt 2.0))

series333.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (sqrt 2.0) (* a1 a1))
110.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
110.0ms	(/ (cos th) (/ (sqrt 2.0) (* a1 a1)))
63.0ms	(/ (cos th) (sqrt 2.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	586	1372
1	2495	1242
2	5001	1224

prune444.0ms

Filtered

183 candidates to 121 candidates (66.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	183	10	193

Merged error: 0b

Counts

193 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite149.0ms

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:

50.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
16.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms	(/ (cos th) (sqrt 2.0))

series536.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
97.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
265.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
57.0ms	(/ (cos th) (sqrt 2.0))

simplify119.0ms

Algorithm

egg-herbie

Counts

756 → 756

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1544	9868
1	5001	8666

prune1.6s

Filtered

756 candidates to 353 candidates (46.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	756	0	756
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	756	10	766

Merged error: 0b

Counts

766 → 10

regimes337.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	11
1	15	11

end0.0ms

sample2.2s

Algorithm

intervals

Results

803.0ms	2491×	body	1280	valid
457.0ms	2075×	body	640	valid
397.0ms	8009×	body	80	valid
163.0ms	1063×	body	320	valid
52.0ms	505×	body	160	valid