Details

analyze762.0ms

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

sample101.0ms

Algorithm

intervals

Results

22.0ms	48×	body	1280	valid
21.0ms	48×	body	1280	invalid
15.0ms	33×	body	640	valid
12.0ms	157×	body	80	valid
9.0ms	28×	body	640	invalid
3.0ms	14×	body	320	valid
2.0ms	9×	body	320	invalid
1.0ms	11×	body	80	invalid
1.0ms	6×	body	160	invalid
1.0ms	4×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	484	13
1	484	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: 0.4b

Counts

2 → 2

localize10.0ms

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))

series269.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* a1 a1) (* a2 a2))
251.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
11.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4991	1517
1	4991	1517

prune189.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	99	6	105

Merged error: 0b

Counts

105 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (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))
5.8b	(sqrt (+ (* a1 a1) (* a2 a2)))
5.8b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite39.0ms

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:

17.0ms	(* (* (sqrt (+ (* a1 a1) (* a2 a2))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)))
8.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (* (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)))

simplify75.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4949	2853
1	4949	2853

prune199.0ms

Filtered

99 candidates to 169 candidates (-70.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	169	6	175

Merged error: 0b

Counts

175 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (sqrt (+ (* a1 a1) (* a2 a2))) (/ (cos th) (sqrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0))))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
5.8b	(sqrt (+ (* a1 a1) (* a2 a2)))
5.8b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

123×	`sqrt-prod`
81×	`times-frac`
67×	`add-sqr-sqrt`
65×	`add-cube-cbrt` `*-un-lft-identity`
58×	`associate-r`
27×	`add-exp-log` `add-cbrt-cube`
12×	`sqrt-div`
11×	`pow1`
10×	`prod-exp` `cbrt-unprod`
9×	`frac-times` `associate-l/` `associate-/r`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`add-log-exp`
3×	`associate-r/` `pow-prod-down` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv`
1×	`frac-2neg` `associate-l` `clear-num` `*-commutative`

Counts

4 → 173

Calls

4 calls:

24.0ms	(* (* (sqrt (+ (* a1 a1) (* a2 a2))) (/ (cos th) (sqrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0))))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series49.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (* (sqrt (+ (* a1 a1) (* a2 a2))) (/ (cos th) (sqrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0))))
11.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify68.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4972	3151
1	4972	3151

prune274.0ms

Filtered

105 candidates to 185 candidates (-76.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	185	6	191

Merged error: 0b

Counts

191 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* (/ 1 (sqrt (sqrt 2.0))) (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))))
0.3b	(* (/ 1 (sqrt (sqrt 2.0))) (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))))
0.3b	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))
1.0b	(/ 1 (sqrt (sqrt 2.0)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-sqr-sqrt`
171×	`sqrt-prod`
153×	`times-frac`
99×	`*-un-lft-identity`
87×	`add-cube-cbrt`
64×	`add-exp-log`
38×	`add-cbrt-cube`
34×	`associate-l`
32×	`associate-r`
28×	`unswap-sqr`
25×	`prod-exp`
19×	`div-exp`
18×	`associate-/r*`
14×	`pow1`
13×	`cbrt-unprod`
10×	`cbrt-undiv`
6×	`associate-/l*`
5×	`rec-exp` `pow-flip` `1-exp` `associate-*r/`
4×	`sqrt-pow1` `pow-prod-down` `div-inv` `add-log-exp`
2×	`frac-times` `frac-2neg` `pow1/2` `associate-l/` `clear-num` `-commutative` `associate-/l/`
1×	`flip3-+` `flip-+` `inv-pow`

Counts

4 → 257

Calls

4 calls:

16.0ms	(* (cos th) (* (/ 1 (sqrt (sqrt 2.0))) (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))))
29.0ms	(* (/ 1 (sqrt (sqrt 2.0))) (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))))
8.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))
5.0ms	(/ 1 (sqrt (sqrt 2.0)))

series65.0ms

Counts

4 → 10

Calls

4 calls:

36.0ms	(* (cos th) (* (/ 1 (sqrt (sqrt 2.0))) (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))))
11.0ms	(* (/ 1 (sqrt (sqrt 2.0))) (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))))
18.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5652	4038

prune366.0ms

Filtered

129 candidates to 267 candidates (-107.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	266	1	267
Fresh	1	1	2
Picked	0	1	1
Done	1	2	3
Total	268	5	273

Merged error: 0b

Counts

273 → 5

regimes333.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	18
1	52	18

end0.0ms

sample2.8s

Algorithm

intervals

Results

616.0ms	1350×	body	1280	valid
526.0ms	1187×	body	1280	invalid
352.0ms	4688×	body	80	valid
349.0ms	1118×	body	640	valid
310.0ms	996×	body	640	invalid
123.0ms	545×	body	320	valid
112.0ms	495×	body	320	invalid
46.0ms	299×	body	160	valid
41.0ms	255×	body	160	invalid
39.0ms	476×	body	80	invalid

Details

analyze762.0ms

sample101.0ms

simplify12.0ms

prune12.0ms

localize10.0ms

rewrite25.0ms

series269.0ms

simplify72.0ms

prune189.0ms

localize13.0ms

rewrite39.0ms

series51.0ms

simplify75.0ms

prune199.0ms

localize15.0ms

rewrite44.0ms

series49.0ms

simplify68.0ms

prune274.0ms

localize13.0ms

rewrite71.0ms

series65.0ms

simplify57.0ms

prune366.0ms

regimes333.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

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