Details

sample2.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 21.264648%

Guaranteed chance to sample good point: 60.031008%

Results

20.0ms	37×	body	1280	invalid
17.0ms	37×	body	1280	valid
13.0ms	42×	body	640	valid
11.0ms	149×	body	80	valid
9.0ms	28×	body	640	invalid
5.0ms	21×	body	320	invalid
4.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid
1.0ms	9×	body	80	invalid
1.0ms	5×	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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.5b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-l` `sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
4×	`pow1`
3×	`associate-r` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `flip3-+` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

2 → 87

Calls

2 calls:

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

series44.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	479	795
1	2384	738
2	5003	725

prune166.0ms

Filtered

64 candidates to 93 candidates (-45.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	86	7	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	7	94

Merged error: 0.0b

Counts

94 → 7

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-r` `sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
4×	`pow1`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
1×	`frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip-+`

Counts

2 → 83

Calls

2 calls:

10.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
7.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series46.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
11.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	314	880
1	1523	816
2	5001	800

prune127.0ms

Filtered

58 candidates to 89 candidates (-53.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	89	7	96

Merged error: 0b

Counts

96 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
0.3b	(* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
4.5b	(sqrt (+ (* a1 a1) (* a2 a2)))
4.5b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

149×	`add-sqr-sqrt`
146×	`times-frac`
127×	`sqrt-prod`
90×	`cbrt-prod`
87×	`add-cube-cbrt` `*-un-lft-identity`
58×	`associate-r`
27×	`add-exp-log`
21×	`unswap-sqr`
19×	`add-cbrt-cube`
10×	`associate-l`
9×	`associate-/r*`
8×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
6×	`sqrt-div` `associate-/l*`
4×	`add-log-exp`
3×	`flip3-+` `flip-+` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 226

Calls

4 calls:

8.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
30.0ms	(* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
11.0ms	(* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
10.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify102.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	667	4089
1	3611	3789
2	5001	3487

prune448.0ms

Filtered

139 candidates to 238 candidates (-71.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	238	7	245

Merged error: 0b

Counts

245 → 7

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod`
1119×	`times-frac`
624×	`add-sqr-sqrt`
577×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-r`
34×	`associate-/l*`
22×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
13×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
5×	`pow1`
3×	`associate-l` `prod-exp` `cbrt-unprod` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`flip3-+` `associate-r/` `pow-prod-down` `-commutative` `flip-+`

Counts

3 → 702

Calls

3 calls:

67.0ms	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
17.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
8.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))

series59.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
11.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
14.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))

simplify126.0ms

Algorithm

egg-herbie

Counts

711 → 711

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1532	12059
1	5002	10660

prune810.0ms

Filtered

241 candidates to 711 candidates (-195.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	711	0	711
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	711	7	718

Merged error: 0b

Counts

718 → 7

regimes429.0ms

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	19	20
1	19	20

end0.0ms

sample4.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 21.264648%

Guaranteed chance to sample good point: 60.031008%

Results

596.0ms	1326×	body	1280	valid
519.0ms	1161×	body	1280	invalid
357.0ms	4754×	body	80	valid
352.0ms	1126×	body	640	valid
301.0ms	947×	body	640	invalid
121.0ms	524×	body	320	valid
109.0ms	487×	body	320	invalid
42.0ms	270×	body	160	valid
37.0ms	227×	body	160	invalid
29.0ms	345×	body	80	invalid

Details

sample2.3s

simplify14.0ms

prune8.0ms

localize10.0ms

rewrite17.0ms

series44.0ms

simplify54.0ms

prune166.0ms

localize10.0ms

rewrite22.0ms

series46.0ms

simplify46.0ms

prune127.0ms

localize19.0ms

rewrite56.0ms

series50.0ms

simplify102.0ms

prune448.0ms

localize12.0ms

rewrite151.0ms

series59.0ms

simplify126.0ms

prune810.0ms

regimes429.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.9s

Profiling