Details

sample72.0ms

Algorithm

intervals

Results

21.0ms	67×	body	1280	valid
17.0ms	82×	body	640	valid
13.0ms	263×	body	80	valid
5.0ms	29×	body	320	valid
1.0ms	13×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	50	7
2	77	7
3	96	7
4	112	7
5	127	7
6	141	7
7	141	7

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.4b

Counts

2 → 1

localize10.0ms

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))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
49×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
38×	`times-frac`
31×	`sqrt-prod`
30×	`associate-l`
24×	`frac-times` `associate-/r*`
14×	`flip3-+` `flip-+`
12×	`associate-l/` `associate-/l`
10×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
8×	`associate-r`
5×	`pow1` `add-log-exp`
4×	`frac-2neg` `swap-sqr` `clear-num`
3×	`+-commutative` `unswap-sqr`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`pow-prod-down` `sum-log` `*-commutative`

Counts

3 → 143

Calls

3 calls:

15.0ms	(+ (* a1 a1) (* a2 a2))
26.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
4.0ms	(/ (cos th) (sqrt 2.0))

series307.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* a1 a1) (* a2 a2))
217.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
61.0ms	(/ (cos th) (sqrt 2.0))

simplify92.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	742	1415
1	4405	1320
2	5001	1317

prune276.0ms

Filtered

152 candidates to 97 candidates (36.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	145	7	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	146	7	153

Merged error: 0b

Counts

153 → 7

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.3b	(* (+ (* a1 a1) (* a2 a2)) (/ (cos th) (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
49×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
38×	`times-frac`
31×	`sqrt-prod`
24×	`frac-times` `associate-/r*`
22×	`associate-r`
16×	`associate-l`
14×	`flip3-+` `flip-+`
13×	`associate-/l*`
12×	`associate-*r/`
10×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`pow1` `clear-num` `add-log-exp`
4×	`frac-2neg` `swap-sqr`
3×	`unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `un-div-inv` `cbrt-unprod` `div-inv`
1×	`+-commutative` `pow-prod-down` `sum-log` `*-commutative`

Counts

3 → 141

Calls

3 calls:

16.0ms	(+ (* a1 a1) (* a2 a2))
27.0ms	(* (+ (* a1 a1) (* a2 a2)) (/ (cos th) (sqrt 2.0)))
4.0ms	(/ (cos th) (sqrt 2.0))

series260.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* a1 a1) (* a2 a2))
170.0ms	(* (+ (* a1 a1) (* a2 a2)) (/ (cos th) (sqrt 2.0)))
58.0ms	(/ (cos th) (sqrt 2.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	474	1412
1	2650	1333
2	5001	1296

prune255.0ms

Filtered

150 candidates to 92 candidates (38.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	150	7	157

Merged error: 0b

Counts

157 → 7

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

449×	`*-un-lft-identity`
356×	`times-frac`
161×	`add-sqr-sqrt` `add-cube-cbrt`
120×	`distribute-lft-out`
96×	`associate-l` `sqrt-prod`
48×	`swap-sqr`
28×	`associate-/r*`
20×	`associate-/l*`
12×	`associate-/r/`
11×	`div-inv`
10×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `frac-2neg` `clear-num`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log`

Counts

3 → 289

Calls

3 calls:

18.0ms	(+ (* a1 a1) (* a2 a2))
4.0ms	(/ (sqrt 2.0) (cos th))
27.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

series246.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* a1 a1) (* a2 a2))
47.0ms	(/ (sqrt 2.0) (cos th))
172.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

simplify89.0ms

Algorithm

egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	668	3627
1	2828	3430
2	5001	3430

prune331.0ms

Filtered

298 candidates to 121 candidates (59.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	295	3	298
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	298	7	305

Merged error: 0b

Counts

305 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (cos th))))
0.4b	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (cos th)))
6.4b	(sqrt (+ (* a1 a1) (* a2 a2)))
6.4b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

1062×	`*-un-lft-identity`
972×	`times-frac`
665×	`sqrt-prod`
499×	`add-sqr-sqrt`
449×	`add-cube-cbrt`
258×	`associate-r`
255×	`distribute-lft-out`
215×	`associate-l`
102×	`swap-sqr`
94×	`associate-/r*`
90×	`sqrt-div`
76×	`frac-times`
57×	`associate-/l*`
45×	`flip3-+` `flip-+`
38×	`associate-*r/`
28×	`div-inv`
24×	`associate-/r/`
18×	`add-exp-log` `add-cbrt-cube`
14×	`unswap-sqr`
8×	`pow1` `associate-/l/`
7×	`clear-num`
6×	`cbrt-undiv` `frac-2neg` `div-exp`
4×	`add-log-exp`
3×	`prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/` `un-div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 759

Calls

4 calls:

122.0ms	(* (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (cos th))))
31.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (cos th)))
16.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
16.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (cos th))))
166.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (cos th)))
43.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
37.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify140.0ms

Algorithm

egg-herbie

Counts

771 → 771

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1517	11402
1	5001	11039

prune1.1s

Filtered

771 candidates to 280 candidates (63.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	769	2	771
Fresh	2	2	4
Picked	1	0	1
Done	1	1	2
Total	773	5	778

Merged error: 0b

Counts

778 → 5

regimes174.0ms

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	18	20
1	18	20

end0.0ms

sample2.3s

Algorithm

intervals

Results

821.0ms	2509×	body	1280	valid
468.0ms	2099×	body	640	valid
411.0ms	8111×	body	80	valid
153.0ms	1003×	body	320	valid
62.0ms	528×	body	160	valid