Details

analyze456.0ms

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
6.2%	93.6%	0.1%	6
12.5%	87.4%	0.1%	7
15.6%	84.3%	0.1%	8
18.7%	71.8%	9.5%	9
23.4%	56%	20.6%	10
26.3%	52.2%	21.5%	11
31%	40.1%	28.9%	12
35.6%	28.9%	35.5%	13
36.8%	27.5%	35.7%	14

sample23.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
2.0ms	59×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	37	12
1	37	12

prune8.0ms

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: 19.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (+ x y))
0.8b	(+ (* x y) (* z (+ x y)))
18.8b	(sqrt (+ (* x y) (* z (+ x y))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`pow1` `add-cube-cbrt`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`associate-r`
3×	`flip3-+` `associate-l` `sqrt-prod` `flip-+`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `sqrt-div` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

6.0ms	(* z (+ x y))
4.0ms	(+ (* x y) (* z (+ x y)))
4.0ms	(sqrt (+ (* x y) (* z (+ x y))))

series47.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(* z (+ x y))
7.0ms	(+ (* x y) (* z (+ x y)))
35.0ms	(sqrt (+ (* x y) (* z (+ x y))))

simplify42.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4917	621
1	4917	621

prune104.0ms

Filtered

43 candidates to 60 candidates (-39.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	50	10	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	11	61

Merged error: 19.8b

Counts

61 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
0.8b	(+ (* x y) (* (* z (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y))))
18.8b	(sqrt (+ (* x y) (* (* z (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`cbrt-prod` `add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 54

Calls

4 calls:

3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
4.0ms	(+ (* x y) (* (* z (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y))))
4.0ms	(sqrt (+ (* x y) (* (* z (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y)))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (+ x y))
30.0ms	(cbrt (+ x y))
11.0ms	(+ (* x y) (* (* z (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y))))
38.0ms	(sqrt (+ (* x y) (* (* z (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y)))))

simplify36.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5122	728

prune110.0ms

Filtered

49 candidates to 66 candidates (-34.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	64	13	77

Merged error: 19.6b

Counts

77 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(cbrt z)
0.8b	(+ (* x y) (* (* (cbrt z) (cbrt z)) (* (+ x y) (cbrt z))))
18.8b	(sqrt (+ (* x y) (* (* (cbrt z) (cbrt z)) (* (+ x y) (cbrt z)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`sqrt-prod`
2×	`flip3-+` `pow1/3` `sqrt-div` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 48

Calls

4 calls:

2.0ms	(cbrt z)
2.0ms	(cbrt z)
8.0ms	(+ (* x y) (* (* (cbrt z) (cbrt z)) (* (+ x y) (cbrt z))))
7.0ms	(sqrt (+ (* x y) (* (* (cbrt z) (cbrt z)) (* (+ x y) (cbrt z)))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt z)
21.0ms	(cbrt z)
11.0ms	(+ (* x y) (* (* (cbrt z) (cbrt z)) (* (+ x y) (cbrt z))))
40.0ms	(sqrt (+ (* x y) (* (* (cbrt z) (cbrt z)) (* (+ x y) (cbrt z)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4935	556
1	4935	556

prune97.0ms

Filtered

40 candidates to 60 candidates (-50.0%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	59	14	73

Merged error: 19.6b

Counts

73 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(cbrt z)
0.8b	(+ (* x y) (* (* (cbrt z) (cbrt z)) (* (+ x y) (* (* (cbrt (cbrt z)) (cbrt (cbrt z))) (cbrt (cbrt z))))))
18.8b	(sqrt (+ (* x y) (* (* (cbrt z) (cbrt z)) (* (+ x y) (* (* (cbrt (cbrt z)) (cbrt (cbrt z))) (cbrt (cbrt z)))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`sqrt-prod`
2×	`flip3-+` `pow1/3` `sqrt-div` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt z)
1.0ms	(cbrt z)
5.0ms	(+ (* x y) (* (* (cbrt z) (cbrt z)) (* (+ x y) (* (* (cbrt (cbrt z)) (cbrt (cbrt z))) (cbrt (cbrt z))))))
5.0ms	(sqrt (+ (* x y) (* (* (cbrt z) (cbrt z)) (* (+ x y) (* (* (cbrt (cbrt z)) (cbrt (cbrt z))) (cbrt (cbrt z)))))))

series95.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt z)
24.0ms	(cbrt z)
12.0ms	(+ (* x y) (* (* (cbrt z) (cbrt z)) (* (+ x y) (* (* (cbrt (cbrt z)) (cbrt (cbrt z))) (cbrt (cbrt z))))))
39.0ms	(sqrt (+ (* x y) (* (* (cbrt z) (cbrt z)) (* (+ x y) (* (* (cbrt (cbrt z)) (cbrt (cbrt z))) (cbrt (cbrt z)))))))

simplify41.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4890	548
1	4890	548

prune61.0ms

Filtered

41 candidates to 60 candidates (-46.3%)

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	10	10
Picked	0	1	1
Done	0	3	3
Total	60	14	74

Merged error: 19.6b

Counts

74 → 14

regimes258.0ms

Accuracy

0% (0.2b remaining)

Error of 19.5b against oracle of 19.4b and baseline of 19.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	12
1	15	12

end0.0ms

sample657.0ms

Algorithm

intervals

Results

349.0ms	8000×	body	80	valid
94.0ms	2235×	body	80	nan

Details

analyze456.0ms

sample23.0ms

simplify4.0ms

prune8.0ms

localize9.0ms

rewrite14.0ms

series47.0ms

simplify42.0ms

prune104.0ms

localize13.0ms

rewrite15.0ms

series108.0ms

simplify36.0ms

prune110.0ms

localize18.0ms

rewrite21.0ms

series94.0ms

simplify57.0ms

prune97.0ms

localize20.0ms

rewrite13.0ms

series95.0ms

simplify41.0ms

prune61.0ms

regimes258.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample657.0ms

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