Details

sample119.0ms

Algorithm

intervals

Results

41.0ms	85×	body	1280	valid
24.0ms	78×	body	640	valid
18.0ms	239×	body	80	valid
9.0ms	38×	body	320	valid
2.0ms	11×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

localize10.0ms

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))

rewrite31.0ms

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))
15.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
8.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series57.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* a1 a1) (* a2 a2))
40.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
12.0ms	(/ (+ (* 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	5007	1529

prune182.0ms

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: 0b

Counts

105 → 8

localize219.0ms

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))))
5.5b	(sqrt (+ (* a1 a1) (* a2 a2)))
5.5b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite64.0ms

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:

20.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2)))))
8.0ms	(/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2))))
5.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ (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)))
11.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify136.0ms

Algorithm

egg-herbie

Counts

423 → 423

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4967	11244
1	4967	11244

prune340.0ms

Filtered

161 candidates to 423 candidates (-162.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	422	1	423
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	423	8	431

Merged error: 0b

Counts

431 → 8

localize16.0ms

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)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
5.5b	(sqrt (+ (* a1 a1) (* a2 a2)))
5.5b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

149×	`add-sqr-sqrt`
146×	`times-frac`
127×	`sqrt-prod`
90×	`cbrt-prod`
87×	`add-cube-cbrt` `*-un-lft-identity`
58×	`associate-r`
27×	`add-exp-log`
21×	`unswap-sqr`
19×	`add-cbrt-cube`
10×	`associate-l`
9×	`associate-/r*`
8×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
6×	`sqrt-div` `associate-/l*`
4×	`add-log-exp`
3×	`flip3-+` `flip-+` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 226

Calls

4 calls:

9.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
35.0ms	(* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
12.0ms	(* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify83.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4936	4726
1	4936	4726

prune438.0ms

Filtered

141 candidates to 238 candidates (-68.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	238	8	246

Merged error: 0b

Counts

246 → 8

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)))
0.3b	(* (/ (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)))
21.0ms	(* (/ (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))))

series110.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* a1 a1) (* a2 a2))
28.0ms	(/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))
39.0ms	(* (/ (cos th) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))))
38.0ms	(/ (cos th) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify70.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4958	2748
1	4958	2748

prune334.0ms

Filtered

120 candidates to 167 candidates (-39.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	3	2	5
Picked	0	1	1
Done	0	2	2
Total	168	7	175

Merged error: 0b

Counts

175 → 7

regimes455.0ms

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

sample3.5s

Algorithm

intervals

Results

1.2s	2688×	body	1280	valid
666.0ms	2072×	body	640	valid
611.0ms	7888×	body	80	valid
243.0ms	1030×	body	320	valid
89.0ms	543×	body	160	valid

Details

sample119.0ms

simplify3.0ms

prune12.0ms

localize10.0ms

rewrite31.0ms

series57.0ms

simplify62.0ms

prune182.0ms

localize219.0ms

rewrite64.0ms

series40.0ms

simplify136.0ms

prune340.0ms

localize16.0ms

rewrite64.0ms

series50.0ms

simplify83.0ms

prune438.0ms

localize14.0ms

rewrite48.0ms

series110.0ms

simplify70.0ms

prune334.0ms

regimes455.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.5s

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