Details

sample24.0ms

Algorithm

intervals

Results

11.0ms

432×

body

valid

simplify294.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (3.0ms)

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

prune8.0ms

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: 0.2b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.0b	(+ (* x x) (* y y))
0.2b	(+ (+ (+ (* 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))

simplify129.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (124.0ms)

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

prune77.0ms

Filtered

47 candidates to 35 candidates (25.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	39	8	47
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	40	9	49

Merged error: 0.1b

Counts

49 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y))
0.2b	(* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))))
6.9b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
6.9b	(sqrt (+ (+ (* x x) (* 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`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
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` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 98

Calls

4 calls:

13.0ms	(+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y))
13.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series29.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify51.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	244	1203
1	1165	1041
2	5001	979

prune122.0ms

Filtered

110 candidates to 67 candidates (39.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	108	11	119

Merged error: 0.0b

Counts

119 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

6.9b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
6.9b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
6.9b	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y)))
6.9b	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
14.0ms	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y)))
14.0ms	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
8.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
10.0ms	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y)))
8.0ms	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y)))

simplify73.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	149	996
1	437	956
2	1864	956
3	5001	938

prune126.0ms

Filtered

72 candidates to 64 candidates (11.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	72	11	83

Merged error: 0.0b

Counts

83 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

6.9b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
6.9b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
6.9b	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y)))
6.9b	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* y y)))))) (* y y)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
14.0ms	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y)))
31.0ms	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* y y)))))) (* y y)))

series31.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
7.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
8.0ms	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y)))
9.0ms	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* y y)))))) (* y y)))

simplify85.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	210	996
1	561	956
2	2436	956
3	5001	938

prune89.0ms

Filtered

72 candidates to 62 candidates (13.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	72	11	83

Merged error: 0.0b

Counts

83 → 11

regimes334.0ms

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

sample767.0ms

Algorithm

intervals

Results

406.0ms

14148×

body

valid

Details

sample24.0ms

simplify294.0ms

prune8.0ms

localize10.0ms

rewrite18.0ms

series19.0ms

simplify129.0ms

prune77.0ms

localize11.0ms

rewrite40.0ms

series29.0ms

simplify51.0ms

prune122.0ms

localize13.0ms

rewrite39.0ms

series33.0ms

simplify73.0ms

prune126.0ms

localize19.0ms

rewrite57.0ms

series31.0ms

simplify85.0ms

prune89.0ms

regimes334.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample767.0ms

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