Details

analyze764.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

sample95.0ms

Algorithm

intervals

Results

16.0ms	44×	body	640	valid
14.0ms	33×	body	1280	valid
10.0ms	152×	body	80	valid
4.0ms	19×	body	320	valid
1.0ms	8×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	105	13
1	105	13

prune12.0ms

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: 0.3b

Counts

2 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.1b	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
0.4b	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 94

Calls

3 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
11.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
7.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series56.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
36.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
15.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4965	1529
1	4965	1529

prune178.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Merged error: 0b

Counts

105 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.1b	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
0.2b	(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b	(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

195×	`times-frac`
111×	`add-sqr-sqrt`
94×	`cbrt-prod`
91×	`add-cube-cbrt` `*-un-lft-identity`
67×	`associate-r`
47×	`sqrt-prod`
32×	`add-exp-log`
22×	`div-inv`
20×	`add-cbrt-cube`
12×	`cbrt-undiv` `div-exp`
10×	`associate-/r` `associate-/l`
7×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`pow1` `add-log-exp`
3×	`associate-l` `associate-/l/`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`+-commutative` `associate-r/` `pow-prod-down` `sum-log` `-commutative`

Counts

4 → 225

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
26.0ms	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
10.0ms	(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
13.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
36.0ms	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
38.0ms	(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
15.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5231	4587

prune536.0ms

Filtered

172 candidates to 237 candidates (-37.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	237	8	245

Merged error: 0b

Counts

245 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt (+ (* a1 a1) (* a2 a2))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)))
0.4b	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
7.7b	(sqrt (+ (* a1 a1) (* a2 a2)))
7.7b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-prod`
72×	`times-frac`
61×	`add-sqr-sqrt`
59×	`add-cube-cbrt` `*-un-lft-identity`
40×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`sqrt-div`
6×	`associate-l/` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l*`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp` `pow-prod-down`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv` `associate-/l/`
1×	`sqrt-undiv` `frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 157

Calls

4 calls:

18.0ms	(* (* (sqrt (+ (* a1 a1) (* a2 a2))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)))
7.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
7.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series48.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (* (sqrt (+ (* a1 a1) (* a2 a2))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)))
11.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify57.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5477	2865

prune199.0ms

Filtered

100 candidates to 169 candidates (-69.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	169	8	177

Merged error: 0b

Counts

177 → 8

localize18.0ms

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))))
7.7b	(sqrt (+ (* a1 a1) (* a2 a2)))
7.7b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite62.0ms

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)))
34.0ms	(* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series46.0ms

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))))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify114.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4928	4726
1	4928	4726

prune401.0ms

Filtered

140 candidates to 238 candidates (-70.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	238	8	246

Merged error: 0b

Counts

246 → 8

regimes439.0ms

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	16	22
1	16	22

end0.0ms

sample3.0s

Algorithm

intervals

Results

576.0ms	1329×	body	1280	valid
339.0ms	1131×	body	640	valid
322.0ms	4701×	body	80	valid
120.0ms	555×	body	320	valid
42.0ms	284×	body	160	valid

Details

analyze764.0ms

sample95.0ms

simplify4.0ms

prune12.0ms

localize11.0ms

rewrite25.0ms

series56.0ms

simplify66.0ms

prune178.0ms

localize17.0ms

rewrite64.0ms

series94.0ms

simplify71.0ms

prune536.0ms

localize14.0ms

rewrite42.0ms

series48.0ms

simplify57.0ms

prune199.0ms

localize18.0ms

rewrite62.0ms

series46.0ms

simplify114.0ms

prune401.0ms

regimes439.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.0s

Profiling