Details

analyze746.0ms

Algorithm: search

sample94.0ms

Algorithm

intervals

Results

23.0ms	53×	body	1280	valid
15.0ms	36×	body	1280	invalid
12.0ms	143×	body	80	valid
9.0ms	31×	body	640	valid
7.0ms	24×	body	640	invalid
5.0ms	21×	body	320	invalid
4.0ms	17×	body	320	valid
2.0ms	12×	body	160	valid
1.0ms	18×	body	80	invalid
1.0ms	8×	body	160	invalid

simplify14.0ms

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

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.4b

Counts

2 → 1

localize15.0ms

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))

rewrite32.0ms

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))
8.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
4.0ms	(/ (cos th) (sqrt 2.0))
4.0ms	(/ (cos th) (sqrt 2.0))

series40.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
14.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms	(/ (cos th) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (39.0ms)

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

prune332.0ms

Filtered

116 candidates to 180 candidates (-55.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	167	13	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	168	13	181

Merged error: 0b

Counts

181 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

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:

15.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
7.0ms	(/ (pow a1 2) (sqrt 2.0))
4.0ms	(/ (cos th) (sqrt 2.0))

series44.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
6.0ms	(/ (pow a1 2) (sqrt 2.0))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify77.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	694	1786
1	3024	1552
2	5001	1540

prune387.0ms

Filtered

142 candidates to 252 candidates (-77.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	248	4	252
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	254	11	265

Merged error: 0b

Counts

265 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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:

5.0ms	(* (cos th) (* a2 a2))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
7.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
4.0ms	(/ (cos th) (sqrt 2.0))

series46.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos th) (* a2 a2))
17.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
15.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	501	987
1	2125	864
2	5002	850

prune211.0ms

Filtered

91 candidates to 144 candidates (-58.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	146	9	155

Merged error: 0b

Counts

155 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

4.0ms	(* (cos th) a2)
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
7.0ms	(/ (* (* (cos th) a2) a2) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series44.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (cos th) a2)
17.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
15.0ms	(/ (* (* (cos th) a2) a2) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	517	953
1	2494	843
2	5003	830

prune175.0ms

Filtered

92 candidates to 143 candidates (-55.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	143	9	152

Merged error: 0b

Counts

152 → 9

regimes559.0ms

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	17	11
1	17	11

end0.0ms

analyze736.0ms

Algorithm: search

sample2.7s

Algorithm

intervals

Results

617.0ms	1412×	body	1280	valid
518.0ms	1152×	body	1280	invalid
337.0ms	4697×	body	80	valid
316.0ms	1044×	body	640	valid
292.0ms	960×	body	640	invalid
130.0ms	569×	body	320	valid
113.0ms	515×	body	320	invalid
41.0ms	278×	body	160	valid
38.0ms	497×	body	80	invalid
37.0ms	249×	body	160	invalid

Details

analyze746.0ms

sample94.0ms

simplify14.0ms

prune8.0ms

localize15.0ms

rewrite32.0ms

series40.0ms

simplify55.0ms

prune332.0ms

localize13.0ms

rewrite45.0ms

series44.0ms

simplify77.0ms

prune387.0ms

localize13.0ms

rewrite30.0ms

series46.0ms

simplify51.0ms

prune211.0ms

localize12.0ms

rewrite28.0ms

series44.0ms

simplify62.0ms

prune175.0ms

regimes559.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze736.0ms

sample2.7s

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