Details

sample7.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 21.264648%

Guaranteed chance to sample good point: 60.031008%

Results

23.0ms	52×	body	1280	valid
11.0ms	26×	body	1280	invalid
11.0ms	149×	body	80	valid
10.0ms	31×	body	640	invalid
9.0ms	28×	body	640	valid
4.0ms	19×	body	320	invalid
4.0ms	17×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	7×	body	160	invalid
1.0ms	11×	body	80	invalid

simplify15.0ms

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

prune14.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.4b

Counts

2 → 2

localize11.0ms

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))

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify52.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (39.0ms)

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

prune324.0ms

Filtered

116 candidates to 180 candidates (-55.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	170	10	180
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	172	10	182

Merged error: 0.0b

Counts

182 → 10

localize12.0ms

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

series43.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos th) (* a1 a1))
14.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
14.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (41.0ms)

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

prune215.0ms

Filtered

91 candidates to 144 candidates (-58.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	144	10	154

Merged error: 0.0b

Counts

154 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

616×	`sqrt-prod`
614×	`times-frac`
345×	`add-sqr-sqrt`
340×	`add-cube-cbrt` `*-un-lft-identity`
37×	`associate-/l*`
25×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r*`
22×	`associate-l`
14×	`div-inv`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 469

Calls

4 calls:

8.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
15.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms	(/ (cos th) (sqrt 2.0))

series39.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
8.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
11.0ms	(/ (cos th) (sqrt 2.0))

simplify120.0ms

Algorithm

egg-herbie

Counts

481 → 481

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	1115	6666
1	4568	5845
2	5002	5838

prune656.0ms

Filtered

189 candidates to 481 candidates (-154.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	481	0	481
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	481	10	491

Merged error: 0.0b

Counts

491 → 10

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

rewrite34.0ms

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:

9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
10.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
4.0ms	(/ (cos th) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series37.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
12.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
5.0ms	(/ (cos th) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (40.0ms)

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

prune243.0ms

Filtered

117 candidates to 177 candidates (-51.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	177	10	187

Merged error: 0.0b

Counts

187 → 10

regimes605.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	11
1	16	11

end0.0ms

sample10.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 21.264648%

Guaranteed chance to sample good point: 60.031008%

Results

591.0ms	1304×	body	1280	valid
515.0ms	1156×	body	1280	invalid
357.0ms	1137×	body	640	valid
354.0ms	4707×	body	80	valid
317.0ms	994×	body	640	invalid
124.0ms	543×	body	320	valid
121.0ms	536×	body	320	invalid
50.0ms	309×	body	160	valid
41.0ms	267×	body	160	invalid
26.0ms	313×	body	80	invalid

Details

sample7.2s

simplify15.0ms

prune14.0ms

localize11.0ms

rewrite32.0ms

series42.0ms

simplify52.0ms

prune324.0ms

localize12.0ms

rewrite33.0ms

series43.0ms

simplify52.0ms

prune215.0ms

localize14.0ms

rewrite64.0ms

series39.0ms

simplify120.0ms

prune656.0ms

localize12.0ms

rewrite34.0ms

series37.0ms

simplify54.0ms

prune243.0ms

regimes605.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample10.1s

Profiling