Details

analyze66.0ms

Algorithm: search

sample19.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify277.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	13	7
1	23	6
2	35	4
3	45	4
4	54	4
5	87	4
6	156	4
7	206	4
8	219	4
9	314	4
10	644	4
11	3183	4
12	5001	4

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.1b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.0b	(+ (* x x) (* y y))
0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
10×	`sum-log`
3×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`associate-+l+`

Counts

3 → 38

Calls

3 calls:

5.0ms	(+ (+ (* x x) (* y y)) (* y y))
3.0ms	(+ (* x x) (* y y))
8.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series19.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ (+ (* x x) (* y y)) (* y y))
5.0ms	(+ (* x x) (* y y))
7.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify126.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (120.0ms)

Iter	Nodes	Cost
0	218	352
1	1048	312
2	4094	291
3	5002	280

prune61.0ms

Filtered

35 candidates to 47 candidates (-34.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	4	48

Merged error: 0.1b

Counts

48 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
0.2b	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
4.9b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
4.9b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-log-exp`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `sum-log` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `associate-+l+` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 101

Calls

4 calls:

8.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
17.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
6.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
6.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series30.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
8.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
8.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
8.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify47.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	221	1378
1	1003	1237
2	5001	1160

prune111.0ms

Filtered

68 candidates to 113 candidates (-66.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	109	8	117

Merged error: 0.0b

Counts

117 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))))
4.9b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
4.9b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
4.9b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

75×	`sqrt-prod`
52×	`add-sqr-sqrt`
35×	`sqrt-pow1`
30×	`pow1` `sqrt-div`
19×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `add-log-exp`
3×	`rem-sqrt-square`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 128

Calls

4 calls:

21.0ms	(* (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))))
6.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
6.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
7.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))))
8.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
8.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
8.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify56.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	213	1782
1	870	1660
2	5001	1613

prune120.0ms

Filtered

78 candidates to 140 candidates (-79.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	139	9	148

Merged error: 0.0b

Counts

148 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) 3) (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))))
0.6b	(pow (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) 3)
4.9b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
4.9b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

93×	`sqrt-prod`
70×	`add-sqr-sqrt`
32×	`sqrt-div`
27×	`unpow-prod-down` `cube-prod`
24×	`associate-l` `unswap-sqr`
23×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log`
9×	`flip3-+` `associate-r` `flip-+`
8×	`cube-div`
7×	`add-cbrt-cube`
6×	`sqrt-pow1`
5×	`pow-pow` `sqr-pow`
4×	`frac-times` `pow1/2` `add-log-exp`
3×	`pow-unpow` `prod-exp`
2×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `unpow3` `associate-r/` `associate-l/` `pow-exp`
1×	`pow-plus` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 151

Calls

4 calls:

24.0ms	(* (pow (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) 3) (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))))
9.0ms	(pow (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) 3)
7.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
6.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (pow (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) 3) (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))))
35.0ms	(pow (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) 3)
8.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
11.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify91.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	452	2795
1	2177	2411
2	5002	2189

prune142.0ms

Filtered

84 candidates to 163 candidates (-94.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	160	3	163
Fresh	2	3	5
Picked	1	0	1
Done	0	3	3
Total	163	9	172

Merged error: 0.0b

Counts

172 → 9

regimes297.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

end0.0ms

analyze67.0ms

Algorithm: search

sample363.0ms

Algorithm

intervals

Results

249.0ms	8000×	body	80	valid
0.0ms	4×	body	80	invalid

Details

analyze66.0ms

sample19.0ms

simplify277.0ms

prune6.0ms

localize7.0ms

rewrite18.0ms

series19.0ms

simplify126.0ms

prune61.0ms

localize12.0ms

rewrite40.0ms

series30.0ms

simplify47.0ms

prune111.0ms

localize16.0ms

rewrite46.0ms

series32.0ms

simplify56.0ms

prune120.0ms

localize14.0ms

rewrite53.0ms

series61.0ms

simplify91.0ms

prune142.0ms

regimes297.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze67.0ms

sample363.0ms

Profiling