Details

analyze793.0ms

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

sample103.0ms

Algorithm

intervals

Results

23.0ms	50×	body	1280	valid
17.0ms	38×	body	1280	invalid
14.0ms	145×	body	80	valid
13.0ms	40×	body	640	invalid
12.0ms	38×	body	640	valid
4.0ms	16×	body	320	valid
3.0ms	11×	body	320	invalid
1.0ms	9×	body	160	invalid
1.0ms	7×	body	160	valid
1.0ms	11×	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

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:

4.0ms	(+ (* a1 a1) (* a2 a2))
14.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
7.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series54.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
36.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
12.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	6127	1529

prune181.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

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

Merged error: 0b

Counts

105 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

195×	`times-frac`
111×	`add-sqr-sqrt`
94×	`cbrt-prod`
91×	`add-cube-cbrt` `*-un-lft-identity`
67×	`associate-r`
47×	`sqrt-prod`
32×	`add-exp-log`
22×	`div-inv`
20×	`add-cbrt-cube`
12×	`cbrt-undiv` `div-exp`
10×	`associate-/r` `associate-/l`
7×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`pow1` `add-log-exp`
3×	`associate-l` `associate-/l/`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`+-commutative` `associate-r/` `pow-prod-down` `sum-log` `-commutative`

Counts

4 → 225

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
27.0ms	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
10.0ms	(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
14.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series92.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* a1 a1) (* a2 a2))
37.0ms	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
37.0ms	(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
11.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify65.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5057	4587

prune521.0ms

Filtered

169 candidates to 237 candidates (-40.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	238	8	246

Merged error: 0b

Counts

246 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
34×	`cbrt-prod`
29×	`times-frac`
25×	`*-un-lft-identity`
24×	`add-cube-cbrt`
20×	`add-exp-log`
19×	`associate-l`
16×	`associate-r`
13×	`add-cbrt-cube`
9×	`associate-/r*` `sqrt-prod`
8×	`pow1`
6×	`cbrt-div` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`flip3-+` `associate-*r/` `flip-+` `associate-/l/` `unswap-sqr`
4×	`cbrt-undiv` `frac-times` `div-exp`
3×	`div-inv`
2×	`pow-prod-down` `associate-l/` `-commutative`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `sum-log` `associate-/l*`

Counts

4 → 123

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
13.0ms	(* (cos th) (/ (* (cbrt (/ 1 2.0)) (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
11.0ms	(/ (* (cbrt (/ 1 2.0)) (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
9.0ms	(* (cbrt (/ 1 2.0)) (+ (* a1 a1) (* a2 a2)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* a1 a1) (* a2 a2))
72.0ms	(* (cos th) (/ (* (cbrt (/ 1 2.0)) (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
32.0ms	(/ (* (cbrt (/ 1 2.0)) (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
10.0ms	(* (cbrt (/ 1 2.0)) (+ (* a1 a1) (* a2 a2)))

simplify62.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5030	2115

prune269.0ms

Filtered

100 candidates to 135 candidates (-35.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	135	8	143

Merged error: 0b

Counts

143 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(* (cos th) (* (cbrt (/ 1 2.0)) (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))))
0.3b	(/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))
0.4b	(* (cbrt (/ 1 2.0)) (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
83×	`times-frac`
75×	`cbrt-prod`
58×	`*-un-lft-identity`
54×	`add-cube-cbrt`
32×	`associate-r`
25×	`sqrt-prod`
20×	`add-exp-log`
19×	`associate-l`
16×	`unswap-sqr`
13×	`add-cbrt-cube`
11×	`pow1`
9×	`associate-/r*`
7×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`associate-*r/`
4×	`cbrt-div` `pow-prod-down`
3×	`cbrt-undiv` `div-exp` `div-inv` `associate-/l*`
2×	`frac-times` `flip3-+` `associate-l/` `-commutative` `flip-+` `associate-/l/`
1×	`+-commutative` `frac-2neg` `clear-num` `sum-log`

Counts

4 → 166

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
15.0ms	(* (cos th) (* (cbrt (/ 1 2.0)) (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))))
7.0ms	(/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))
21.0ms	(* (cbrt (/ 1 2.0)) (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))))

series136.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
72.0ms	(* (cos th) (* (cbrt (/ 1 2.0)) (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))))
26.0ms	(/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))
32.0ms	(* (cbrt (/ 1 2.0)) (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))))

simplify68.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5284	3386

prune314.0ms

Filtered

126 candidates to 178 candidates (-41.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	178	8	186

Merged error: 0b

Counts

186 → 8

regimes570.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	20	19
1	20	19

end0.0ms

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

sample2.9s

Algorithm

intervals

Results

639.0ms	1395×	body	1280	valid
521.0ms	1138×	body	1280	invalid
366.0ms	1135×	body	640	valid
358.0ms	4623×	body	80	valid
324.0ms	1001×	body	640	invalid
129.0ms	558×	body	320	valid
127.0ms	520×	body	320	invalid
51.0ms	289×	body	160	valid
44.0ms	505×	body	80	invalid
42.0ms	265×	body	160	invalid

Details

analyze793.0ms

sample103.0ms

simplify5.0ms

prune12.0ms

localize11.0ms

rewrite28.0ms

series54.0ms

simplify38.0ms

prune181.0ms

localize14.0ms

rewrite69.0ms

series92.0ms

simplify65.0ms

prune521.0ms

localize18.0ms

rewrite42.0ms

series120.0ms

simplify62.0ms

prune269.0ms

localize16.0ms

rewrite54.0ms

series136.0ms

simplify68.0ms

prune314.0ms

regimes570.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze760.0ms

sample2.9s

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