Details

analyze761.0ms

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

sample289.0ms

Algorithm

intervals

Results

213.0ms	35×	body	640	valid
19.0ms	42×	body	1280	valid
12.0ms	28×	body	1280	invalid
11.0ms	148×	body	80	valid
8.0ms	27×	body	640	invalid
3.0ms	16×	body	320	valid
3.0ms	12×	body	320	invalid
2.0ms	15×	body	160	valid
1.0ms	8×	body	160	invalid
1.0ms	14×	body	80	invalid

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: 0.4b

Counts

2 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
0.4b	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

rewrite28.0ms

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:

7.0ms	(+ (* a1 a1) (* a2 a2))
11.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
6.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series55.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* a1 a1) (* a2 a2))
38.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
11.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify61.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4965	1529
1	4965	1529

prune184.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	97	8	105

Merged error: 0b

Counts

105 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
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)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 713

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
69.0ms	(* (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)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
43.0ms	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
12.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
15.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))

simplify155.0ms

Algorithm

egg-herbie

Counts

725 → 725

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5384	16199

prune921.0ms

Filtered

249 candidates to 725 candidates (-191.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	724	1	725
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	725	8	733

Merged error: 0b

Counts

733 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* a1 a1) (* a2 a2)) (cos th))
0.4b	(* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
1.0b	(/ 1 (sqrt (sqrt 2.0)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

1116×	`sqrt-prod`
1098×	`times-frac`
581×	`add-sqr-sqrt`
579×	`add-cube-cbrt` `*-un-lft-identity`
286×	`associate-r`
54×	`add-exp-log`
34×	`add-cbrt-cube` `associate-/l*`
25×	`pow1`
22×	`div-inv`
20×	`sqrt-pow1` `div-exp`
18×	`associate-/r*`
16×	`prod-exp`
14×	`pow-flip`
10×	`cbrt-undiv` `pow1/2` `cbrt-unprod` `pow-div`
8×	`associate-*l/`
4×	`rec-exp` `1-exp` `associate-l` `pow-prod-down` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`frac-times` `frac-2neg` `clear-num` `*-commutative` `inv-pow`
1×	`associate-*r/` `associate-/l/` `unswap-sqr`

Counts

4 → 740

Calls

4 calls:

6.0ms	(* (+ (* a1 a1) (* a2 a2)) (cos th))
55.0ms	(* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
19.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms	(/ 1 (sqrt (sqrt 2.0)))

series46.0ms

Counts

4 → 8

Calls

4 calls:

19.0ms	(* (+ (* a1 a1) (* a2 a2)) (cos th))
27.0ms	(* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify166.0ms

Algorithm

egg-herbie

Counts

748 → 748

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4977	11970
1	4977	11970

prune884.0ms

Filtered

224 candidates to 748 candidates (-233.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	748	0	748
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	748	8	756

Merged error: 0b

Counts

756 → 8

localize13.0ms

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))
8.8b	(sqrt (+ (* a1 a1) (* a2 a2)))
8.8b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite43.0ms

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)))
7.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
8.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (* (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)))

simplify50.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5477	2865

prune180.0ms

Filtered

100 candidates to 169 candidates (-69.0%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	169	8	177

Merged error: 0b

Counts

177 → 8

regimes420.0ms

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	19	20
1	19	20

end0.0ms

sample2.7s

Algorithm

intervals

Results

594.0ms	1344×	body	1280	valid
498.0ms	1140×	body	1280	invalid
355.0ms	4680×	body	80	valid
353.0ms	1141×	body	640	valid
285.0ms	939×	body	640	invalid
120.0ms	537×	body	320	valid
109.0ms	487×	body	320	invalid
47.0ms	298×	body	160	valid
40.0ms	507×	body	80	invalid
36.0ms	240×	body	160	invalid

Details

analyze761.0ms

sample289.0ms

simplify4.0ms

prune12.0ms

localize11.0ms

rewrite28.0ms

series55.0ms

simplify61.0ms

prune184.0ms

localize15.0ms

rewrite162.0ms

series75.0ms

simplify155.0ms

prune921.0ms

localize14.0ms

rewrite154.0ms

series46.0ms

simplify166.0ms

prune884.0ms

localize13.0ms

rewrite43.0ms

series52.0ms

simplify50.0ms

prune180.0ms

regimes420.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

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