Details

analyze964.0ms

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

sample94.0ms

Algorithm

intervals

Results

19.0ms	43×	body	1280	invalid
18.0ms	39×	body	1280	valid
13.0ms	39×	body	640	valid
11.0ms	152×	body	80	valid
7.0ms	22×	body	640	invalid
4.0ms	17×	body	320	valid
4.0ms	17×	body	320	invalid
2.0ms	12×	body	160	invalid
1.0ms	9×	body	160	valid
1.0ms	17×	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

prune15.0ms

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))

rewrite23.0ms

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))
10.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
6.0ms	(/ (+ (* 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))

simplify63.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4965	1529
1	4965	1529

prune176.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	96	9	105

Merged error: 0.0b

Counts

105 → 9

localize13.0ms

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

rewrite159.0ms

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))
67.0ms	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
19.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
8.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
39.0ms	(* (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)))
15.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))

simplify157.0ms

Algorithm

egg-herbie

Counts

725 → 725

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5384	16199

prune827.0ms

Filtered

248 candidates to 725 candidates (-192.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	720	5	725
Fresh	5	2	7
Picked	1	0	1
Done	1	0	1
Total	727	7	734

Merged error: 0b

Counts

734 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

1467×	`sqrt-prod`
1455×	`times-frac`
762×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
378×	`cbrt-prod`
376×	`associate-r`
79×	`add-exp-log`
49×	`add-cbrt-cube`
37×	`associate-/l*`
32×	`div-exp`
29×	`div-inv`
25×	`prod-exp`
24×	`associate-/r*`
17×	`cbrt-undiv`
15×	`cbrt-unprod`
13×	`pow1`
7×	`pow-flip` `sqrt-pow1`
5×	`rec-exp` `1-exp`
4×	`add-log-exp`
3×	`frac-2neg` `pow1/2` `pow-prod-down` `associate-*l/` `clear-num` `associate-/l/`
2×	`pow1/3` `pow-div`
1×	`frac-times` `flip3-+` `associate-r/` `associate-l` `-commutative` `flip-+` `inv-pow`

Counts

4 → 936

Calls

4 calls:

6.0ms	(/ (+ (* a1 a1) (* a2 a2)) (fabs (cbrt (sqrt 2.0))))
69.0ms	(* (* (/ (+ (* a1 a1) (* a2 a2)) (fabs (cbrt (sqrt 2.0)))) (cos th)) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))))
20.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
5.0ms	(/ 1 (sqrt (sqrt 2.0)))

series89.0ms

Counts

4 → 8

Calls

4 calls:

14.0ms	(/ (+ (* a1 a1) (* a2 a2)) (fabs (cbrt (sqrt 2.0))))
75.0ms	(* (* (/ (+ (* a1 a1) (* a2 a2)) (fabs (cbrt (sqrt 2.0)))) (cos th)) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify204.0ms

Algorithm

egg-herbie

Counts

944 → 944

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5041	20955

prune2.0s

Filtered

340 candidates to 944 candidates (-177.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	944	0	944
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	944	7	951

Merged error: 0b

Counts

951 → 7

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)))

rewrite142.0ms

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))))
15.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms	(/ 1 (sqrt (sqrt 2.0)))

series42.0ms

Counts

4 → 8

Calls

4 calls:

16.0ms	(* (+ (* a1 a1) (* a2 a2)) (cos th))
26.0ms	(* (* (+ (* 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)))

simplify171.0ms

Algorithm

egg-herbie

Counts

748 → 748

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4977	11970
1	4977	11970

prune756.0ms

Filtered

224 candidates to 748 candidates (-233.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	748	0	748
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	748	7	755

Merged error: 0b

Counts

755 → 7

regimes400.0ms

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	23	26
1	23	26

end0.0ms

sample2.9s

Algorithm

intervals

Results

611.0ms	1327×	body	1280	valid
540.0ms	1194×	body	1280	invalid
360.0ms	1094×	body	640	valid
359.0ms	4717×	body	80	valid
303.0ms	947×	body	640	invalid
132.0ms	566×	body	320	valid
116.0ms	508×	body	320	invalid
49.0ms	296×	body	160	valid
43.0ms	530×	body	80	invalid
43.0ms	263×	body	160	invalid

Details

analyze964.0ms

sample94.0ms

simplify4.0ms

prune15.0ms

localize11.0ms

rewrite23.0ms

series56.0ms

simplify63.0ms

prune176.0ms

localize13.0ms

rewrite159.0ms

series70.0ms

simplify157.0ms

prune827.0ms

localize19.0ms

rewrite183.0ms

series89.0ms

simplify204.0ms

prune2.0s

localize14.0ms

rewrite142.0ms

series42.0ms

simplify171.0ms

prune756.0ms

regimes400.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.9s

Profiling