Details

analyze464.0ms

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

sample25.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
3.0ms	61×	body	80	nan

simplify3.0ms

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: 17.3b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (+ x y))
0.4b	(+ (* x y) (* z (+ x y)))
16.4b	(sqrt (+ (* x y) (* z (+ x y))))

rewrite15.0ms

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))))

series52.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(* z (+ x y))
7.0ms	(+ (* x y) (* z (+ x y)))
39.0ms	(sqrt (+ (* x y) (* z (+ x y))))

simplify49.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5081	617

prune99.0ms

Filtered

43 candidates to 60 candidates (-39.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	54	6	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	7	61

Merged error: 17.2b

Counts

61 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* x y) (* z (+ x y)))
0.5b	(* (sqrt (sqrt (+ (* x y) (* z (+ x y))))) (sqrt (sqrt (+ (* x y) (* z (+ x y))))))
16.4b	(sqrt (+ (* x y) (* z (+ x y))))
16.4b	(sqrt (+ (* x y) (* z (+ x y))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`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` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-+r+` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 126

Calls

4 calls:

4.0ms	(+ (* x y) (* z (+ x y)))
16.0ms	(* (sqrt (sqrt (+ (* x y) (* z (+ x y))))) (sqrt (sqrt (+ (* x y) (* z (+ x y))))))
4.0ms	(sqrt (+ (* x y) (* z (+ x y))))
4.0ms	(sqrt (+ (* x y) (* z (+ x y))))

series115.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* x y) (* z (+ x y)))
35.0ms	(* (sqrt (sqrt (+ (* x y) (* z (+ x y))))) (sqrt (sqrt (+ (* x y) (* z (+ x y))))))
35.0ms	(sqrt (+ (* x y) (* z (+ x y))))
37.0ms	(sqrt (+ (* x y) (* z (+ x y))))

simplify51.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4934	2047
1	4934	2047

prune141.0ms

Filtered

74 candidates to 138 candidates (-86.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	139	6	145

Merged error: 17.2b

Counts

145 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* x y) (* z (+ x y))))) (sqrt (* (fabs (cbrt (+ (* x y) (* z (+ x y))))) (sqrt (cbrt (+ (* x y) (* z (+ x y))))))))
16.4b	(sqrt (+ (* x y) (* z (+ x y))))
17.0b	(cbrt (+ (* x y) (* z (+ x y))))
17.0b	(cbrt (+ (* x y) (* z (+ x y))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-div`
18×	`add-sqr-sqrt`
16×	`sqrt-prod`
12×	`pow1`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`cbrt-div`
9×	`flip3-+` `associate-l` `flip-+`
8×	`associate-*r/`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
5×	`sqrt-pow1` `pow-prod-down`
4×	`frac-times` `associate-r` `add-log-exp`
3×	`pow1/2` `unswap-sqr`
2×	`pow1/3` `associate-*l/`
1×	`rem-sqrt-square` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 80

Calls

4 calls:

16.0ms	(* (sqrt (sqrt (+ (* x y) (* z (+ x y))))) (sqrt (* (fabs (cbrt (+ (* x y) (* z (+ x y))))) (sqrt (cbrt (+ (* x y) (* z (+ x y))))))))
4.0ms	(sqrt (+ (* x y) (* z (+ x y))))
4.0ms	(cbrt (+ (* x y) (* z (+ x y))))
4.0ms	(cbrt (+ (* x y) (* z (+ x y))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (sqrt (sqrt (+ (* x y) (* z (+ x y))))) (sqrt (* (fabs (cbrt (+ (* x y) (* z (+ x y))))) (sqrt (cbrt (+ (* x y) (* z (+ x y))))))))
35.0ms	(sqrt (+ (* x y) (* z (+ x y))))
67.0ms	(cbrt (+ (* x y) (* z (+ x y))))
68.0ms	(cbrt (+ (* x y) (* z (+ x y))))

simplify47.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5299	2630

prune162.0ms

Filtered

78 candidates to 92 candidates (-17.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	92	6	98

Merged error: 17.2b

Counts

98 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* x y) (* z (+ x y)))
16.4b	(sqrt (+ (* x y) (* z (+ x y))))
17.0b	(cbrt (+ (* x y) (* z (+ x y))))
17.0b	(cbrt (+ (* x y) (* z (+ x y))))

rewrite17.0ms

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` `cbrt-div` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`sqrt-prod`
2×	`associate-+r+` `pow1/3` `sqrt-div`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 54

Calls

4 calls:

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

series177.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (* x y) (* z (+ x y)))
35.0ms	(sqrt (+ (* x y) (* z (+ x y))))
67.0ms	(cbrt (+ (* x y) (* z (+ x y))))
67.0ms	(cbrt (+ (* x y) (* z (+ x y))))

simplify28.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5974	942

prune104.0ms

Filtered

57 candidates to 66 candidates (-15.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	66	6	72

Merged error: 17.2b

Counts

72 → 6

regimes197.0ms

Accuracy

0% (0.1b remaining)

Error of 19.9b against oracle of 19.8b and baseline of 19.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	12
1	15	12

end0.0ms

analyze458.0ms

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

sample662.0ms

Algorithm

intervals

Results

354.0ms	8000×	body	80	valid
106.0ms	2300×	body	80	nan

Details

analyze464.0ms

sample25.0ms

simplify3.0ms

prune8.0ms

localize8.0ms

rewrite15.0ms

series52.0ms

simplify49.0ms

prune99.0ms

localize12.0ms

rewrite33.0ms

series115.0ms

simplify51.0ms

prune141.0ms

localize18.0ms

rewrite31.0ms

series297.0ms

simplify47.0ms

prune162.0ms

localize20.0ms

rewrite17.0ms

series177.0ms

simplify28.0ms

prune104.0ms

regimes197.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze458.0ms

sample662.0ms

Profiling