Details

analyze765.0ms

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

sample99.0ms

Algorithm

intervals

Results

21.0ms	41×	body	1280	invalid
17.0ms	38×	body	1280	valid
12.0ms	41×	body	640	invalid
12.0ms	39×	body	640	valid
11.0ms	151×	body	80	valid
4.0ms	16×	body	320	valid
3.0ms	15×	body	320	invalid
2.0ms	12×	body	160	valid
2.0ms	21×	body	80	invalid
1.0ms	8×	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

prune11.0ms

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: 0.6b

Counts

2 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.4b	(* (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:

4.0ms	(+ (* a1 a1) (* a2 a2))
11.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
9.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series49.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
34.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
10.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4965	1529
1	4965	1529

prune175.0ms

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: 0.3b

Counts

105 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))
0.3b	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.4b	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))

rewrite149.0ms

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))
8.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))
17.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
66.0ms	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
14.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))
10.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
42.0ms	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))

simplify155.0ms

Algorithm

egg-herbie

Counts

725 → 725

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5384	16199

prune798.0ms

Filtered

249 candidates to 725 candidates (-191.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	723	2	725
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	727	6	733

Merged error: 0.3b

Counts

733 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cos th) (+ (* a1 a1) (* a2 a2))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.3b	(* (cos th) (+ (* a1 a1) (* a2 a2)))
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`
7×	`associate-*r/`
4×	`rec-exp` `1-exp` `associate-l` `pow-prod-down` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `-commutative` `inv-pow`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-/l/` `unswap-sqr`

Counts

4 → 742

Calls

4 calls:

58.0ms	(* (* (cos th) (+ (* a1 a1) (* a2 a2))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
6.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
15.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms	(/ 1 (sqrt (sqrt 2.0)))

series61.0ms

Counts

4 → 8

Calls

4 calls:

38.0ms	(* (* (cos th) (+ (* a1 a1) (* a2 a2))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
23.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify168.0ms

Algorithm

egg-herbie

Counts

750 → 750

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4972	11999
1	4972	11999

prune774.0ms

Filtered

225 candidates to 750 candidates (-233.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	750	0	750
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	750	6	756

Merged error: 0.3b

Counts

756 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos th) (fabs (cbrt (sqrt 2.0))))
0.3b	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (cbrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
0.3b	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (cbrt (sqrt 2.0))))
0.5b	(* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (cbrt (sqrt 2.0)))) (sqrt (sqrt 2.0))))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

1528×	`times-frac`
1515×	`sqrt-prod`
901×	`add-sqr-sqrt`
767×	`add-cube-cbrt` `*-un-lft-identity`
378×	`cbrt-prod`
364×	`associate-r`
46×	`associate-/l*`
34×	`add-exp-log` `add-cbrt-cube`
32×	`unswap-sqr`
24×	`associate-/r*` `div-inv`
14×	`cbrt-undiv` `div-exp`
13×	`associate-l`
6×	`pow1` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip-+`

Counts

4 → 949

Calls

4 calls:

3.0ms	(/ (cos th) (fabs (cbrt (sqrt 2.0))))
23.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (cbrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
9.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (cbrt (sqrt 2.0))))
117.0ms	(* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (cbrt (sqrt 2.0)))) (sqrt (sqrt 2.0))))

series165.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (cos th) (fabs (cbrt (sqrt 2.0))))
35.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (cbrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
24.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (cbrt (sqrt 2.0))))
97.0ms	(* (/ (cos th) (fabs (cbrt (sqrt 2.0)))) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (cbrt (sqrt 2.0)))) (sqrt (sqrt 2.0))))

simplify178.0ms

Algorithm

egg-herbie

Counts

961 → 961

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5046	27408

prune2.4s

Filtered

423 candidates to 961 candidates (-127.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	961	0	961
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	961	6	967

Merged error: 0.3b

Counts

967 → 6

regimes381.0ms

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	19	20
1	19	20

end0.0ms

sample2.8s

Algorithm

intervals

Results

601.0ms	1314×	body	1280	valid
520.0ms	1170×	body	1280	invalid
350.0ms	1116×	body	640	valid
349.0ms	4742×	body	80	valid
292.0ms	948×	body	640	invalid
123.0ms	547×	body	320	valid
108.0ms	488×	body	320	invalid
43.0ms	281×	body	160	valid
40.0ms	491×	body	80	invalid
37.0ms	245×	body	160	invalid

Details

analyze765.0ms

sample99.0ms

simplify4.0ms

prune11.0ms

localize11.0ms

rewrite28.0ms

series49.0ms

simplify62.0ms

prune175.0ms

localize13.0ms

rewrite149.0ms

series71.0ms

simplify155.0ms

prune798.0ms

localize17.0ms

rewrite142.0ms

series61.0ms

simplify168.0ms

prune774.0ms

localize17.0ms

rewrite234.0ms

series165.0ms

simplify178.0ms

prune2.4s

regimes381.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

Profiling