Details

analyze760.0ms

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

sample97.0ms

Algorithm

intervals

Results

22.0ms	50×	body	1280	valid
16.0ms	51×	body	640	valid
15.0ms	35×	body	1280	invalid
10.0ms	132×	body	80	valid
9.0ms	30×	body	640	invalid
4.0ms	16×	body	320	valid
2.0ms	8×	body	320	invalid
1.0ms	7×	body	160	valid
1.0ms	6×	body	160	invalid
1.0ms	9×	body	80	invalid

simplify5.0ms

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: 0.4b

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))

rewrite26.0ms

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))

series58.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
41.0ms	(* (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

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	95	10	105

Merged error: 0.0b

Counts

105 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))
0.4b	(* (/ (cos th) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))))
0.6b	(/ (cos th) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
70×	`times-frac`
49×	`add-cube-cbrt` `*-un-lft-identity`
46×	`cbrt-prod`
32×	`add-exp-log`
31×	`associate-r`
23×	`sqrt-prod`
22×	`add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
9×	`prod-exp` `cbrt-unprod`
8×	`unswap-sqr`
7×	`associate-l`
6×	`pow1` `associate-/l*` `add-log-exp`
4×	`div-inv`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative`

Counts

4 → 155

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
8.0ms	(/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))
23.0ms	(* (/ (cos th) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))))
8.0ms	(/ (cos th) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

series105.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
26.0ms	(/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))
41.0ms	(* (/ (cos th) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))))
33.0ms	(/ (cos th) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify57.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5023	2754

prune352.0ms

Filtered

120 candidates to 167 candidates (-39.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	2	6	8
Picked	0	1	1
Done	1	0	1
Total	167	10	177

Merged error: 0b

Counts

177 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(* (cos th) (cbrt (/ 1 2.0)))
0.2b	(/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))
0.4b	(* (* (cos th) (cbrt (/ 1 2.0))) (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

65×	`times-frac`
63×	`add-sqr-sqrt`
58×	`cbrt-prod`
55×	`*-un-lft-identity`
54×	`add-cube-cbrt`
47×	`associate-r`
21×	`sqrt-prod`
20×	`add-exp-log`
14×	`add-cbrt-cube`
11×	`pow1`
9×	`associate-/r*`
7×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
4×	`associate-r/` `associate-l*` `pow-prod-down` `unswap-sqr`
3×	`cbrt-undiv` `cbrt-div` `div-exp` `div-inv` `associate-/l*`
2×	`flip3-+` `*-commutative` `flip-+` `associate-/l/`
1×	`+-commutative` `frac-times` `frac-2neg` `associate-*l/` `clear-num` `sum-log`

Counts

4 → 152

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
7.0ms	(* (cos th) (cbrt (/ 1 2.0)))
8.0ms	(/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))
17.0ms	(* (* (cos th) (cbrt (/ 1 2.0))) (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))))

series111.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
5.0ms	(* (cos th) (cbrt (/ 1 2.0)))
26.0ms	(/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))
75.0ms	(* (* (cos th) (cbrt (/ 1 2.0))) (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))))

simplify74.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4960	2673
1	4960	2673

prune317.0ms

Filtered

123 candidates to 164 candidates (-33.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	166	8	174

Merged error: 0b

Counts

174 → 8

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (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-l` `sqrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1` `add-log-exp`
3×	`flip3-+` `associate-r` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative`

Counts

3 → 98

Calls

3 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
11.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt 2.0))

series50.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* a1 a1) (* a2 a2))
39.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4969	1316
1	4969	1316

prune144.0ms

Filtered

76 candidates to 107 candidates (-40.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	107	8	115

Merged error: 0b

Counts

115 → 8

regimes478.0ms

Accuracy

0% (0.4b 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	20	19
1	20	19

end0.0ms

sample2.9s

Algorithm

intervals

Results

626.0ms	1374×	body	1280	valid
536.0ms	1187×	body	1280	invalid
369.0ms	1159×	body	640	valid
348.0ms	4596×	body	80	valid
312.0ms	972×	body	640	invalid
134.0ms	586×	body	320	valid
120.0ms	515×	body	320	invalid
44.0ms	285×	body	160	valid
42.0ms	526×	body	80	invalid
39.0ms	257×	body	160	invalid

Details

analyze760.0ms

sample97.0ms

simplify5.0ms

prune11.0ms

localize11.0ms

rewrite26.0ms

series58.0ms

simplify63.0ms

prune176.0ms

localize14.0ms

rewrite48.0ms

series105.0ms

simplify57.0ms

prune352.0ms

localize15.0ms

rewrite43.0ms

series111.0ms

simplify74.0ms

prune317.0ms

localize12.0ms

rewrite23.0ms

series50.0ms

simplify52.0ms

prune144.0ms

regimes478.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.9s

Profiling