Details

analyze810.0ms

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

21.0ms	46×	body	1280	valid
16.0ms	34×	body	1280	invalid
14.0ms	43×	body	640	invalid
13.0ms	162×	body	80	valid
8.0ms	25×	body	640	valid
7.0ms	16×	body	320	valid
3.0ms	14×	body	320	invalid
1.0ms	7×	body	160	valid
1.0ms	13×	body	80	invalid
1.0ms	6×	body	160	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: 0.3b

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))
40.0ms	(* (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

prune181.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

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

Merged error: 0.0b

Counts

105 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2)))))
0.4b	(/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2))))
8.3b	(sqrt (+ (* a1 a1) (* a2 a2)))
8.3b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

540×	`times-frac`
429×	`sqrt-prod`
297×	`add-sqr-sqrt`
295×	`add-cube-cbrt` `*-un-lft-identity`
48×	`associate-/r*`
22×	`sqrt-div`
17×	`associate-/r/`
12×	`associate-/l*`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`sqrt-undiv`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 411

Calls

4 calls:

19.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2)))))
7.0ms	(/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2))))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2)))))
10.0ms	(/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2))))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
12.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify150.0ms

Algorithm

egg-herbie

Counts

423 → 423

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5081	11244

prune538.0ms

Filtered

162 candidates to 423 candidates (-161.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	421	2	423
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	423	8	431

Merged error: 0b

Counts

431 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.1b	(* (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)))

rewrite158.0ms

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))
68.0ms	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
18.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
8.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
40.0ms	(* (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)))

simplify152.0ms

Algorithm

egg-herbie

Counts

725 → 725

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5384	16199

prune838.0ms

Filtered

250 candidates to 725 candidates (-190.0%)

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

localize17.0ms

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)))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
8.3b	(sqrt (+ (* a1 a1) (* a2 a2)))
8.3b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
102×	`sqrt-prod`
86×	`add-sqr-sqrt`
84×	`add-cube-cbrt` `*-un-lft-identity`
78×	`cbrt-prod`
58×	`associate-r`
38×	`add-exp-log`
29×	`add-cbrt-cube`
16×	`prod-exp` `cbrt-unprod`
11×	`pow1`
9×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sqrt-div` `associate-/l*`
4×	`add-log-exp`
3×	`flip3-+` `pow-prod-down` `associate-*l/` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 201

Calls

4 calls:

8.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
28.0ms	(* (* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
25.0ms	(* (* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify85.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4970	4143
1	4970	4143

prune355.0ms

Filtered

128 candidates to 213 candidates (-66.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	214	7	221

Merged error: 0b

Counts

221 → 7

regimes586.0ms

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	15	23
1	15	23

end0.0ms

sample3.0s

Algorithm

intervals

Results

649.0ms	1362×	body	1280	valid
536.0ms	1117×	body	1280	invalid
394.0ms	4723×	body	80	valid
361.0ms	1090×	body	640	valid
335.0ms	994×	body	640	invalid
129.0ms	541×	body	320	valid
114.0ms	476×	body	320	invalid
47.0ms	284×	body	160	valid
42.0ms	468×	body	80	invalid
41.0ms	232×	body	160	invalid

Details

analyze810.0ms

sample101.0ms

simplify4.0ms

prune12.0ms

localize11.0ms

rewrite25.0ms

series56.0ms

simplify61.0ms

prune181.0ms

localize16.0ms

rewrite58.0ms

series39.0ms

simplify150.0ms

prune538.0ms

localize15.0ms

rewrite158.0ms

series71.0ms

simplify152.0ms

prune838.0ms

localize17.0ms

rewrite53.0ms

series65.0ms

simplify85.0ms

prune355.0ms

regimes586.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.0s

Profiling