Details

analyze65.0ms

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
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	50%	6.3%	6
43.7%	43.7%	12.6%	7
59.3%	26.5%	14.1%	8
59.3%	22.6%	18%	9
67.1%	13.7%	19.2%	10
67.1%	11.5%	21.4%	11
71%	6.9%	22%	12
71%	5.8%	23.2%	13
73%	3.5%	23.5%	14

sample13.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
0.0ms	4×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	6	6

prune3.0ms

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: 21.1b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
19.7b	(sqrt (+ (* x x) y))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

7.0ms	(+ (* x x) y)
4.0ms	(sqrt (+ (* x x) y))

series9.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify53.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4926	260
1	4926	260

prune41.0ms

Filtered

25 candidates to 32 candidates (-28.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	4	33

Merged error: 0b

Counts

33 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (+ (* x x) y)))
0.3b	(* (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))))
20.5b	(cbrt (+ (* x x) y))
20.5b	(cbrt (+ (* x x) y))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`cbrt-prod` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`cbrt-div`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `associate-*r/`
1×	`pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 74

Calls

4 calls:

4.0ms	(sqrt (cbrt (+ (* x x) y)))
8.0ms	(* (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))))
4.0ms	(cbrt (+ (* x x) y))
4.0ms	(cbrt (+ (* x x) y))

series75.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt (cbrt (+ (* x x) y)))
26.0ms	(* (fabs (cbrt (+ (* x x) y))) (sqrt (cbrt (+ (* x x) y))))
16.0ms	(cbrt (+ (* x x) y))
16.0ms	(cbrt (+ (* x x) y))

simplify52.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4898	1019
1	4898	1019

prune85.0ms

Filtered

65 candidates to 86 candidates (-32.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	86	4	90

Merged error: 0b

Counts

90 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* y (/ -1/2 x)) x)
0.2b	(* y (/ -1/2 x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip--` `div-inv`

Counts

2 → 43

Calls

2 calls:

5.0ms	(- (* y (/ -1/2 x)) x)
6.0ms	(* y (/ -1/2 x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(- (* y (/ -1/2 x)) x)
3.0ms	(* y (/ -1/2 x))

simplify39.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5315	373

prune50.0ms

Filtered

34 candidates to 49 candidates (-44.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	49	4	53

Merged error: 0b

Counts

53 → 4

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* y (/ 1/2 x)))
0.2b	(* y (/ 1/2 x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip-+` `div-inv`

Counts

2 → 43

Calls

2 calls:

5.0ms	(+ x (* y (/ 1/2 x)))
12.0ms	(* y (/ 1/2 x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(+ x (* y (/ 1/2 x)))
5.0ms	(* y (/ 1/2 x))

simplify72.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4953	372
1	4953	372

prune44.0ms

Filtered

34 candidates to 49 candidates (-44.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	49	4	53

Merged error: 0b

Counts

53 → 4

regimes276.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 21.8b

bsearch24.0ms

Steps

Iters	Range		Point
10	1.457766003862788e+122	6.791001045448548e+136	6.991599515320617e+135
9	-9.137348824835156e+162	-2.346935011879914e+153	-1.3297023429426835e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	28
1	33	28

end0.0ms

sample308.0ms

Algorithm

intervals

Results

190.0ms	8000×	body	80	valid
3.0ms	146×	body	80	nan

Details

analyze65.0ms

sample13.0ms

simplify3.0ms

prune3.0ms

localize4.0ms

rewrite11.0ms

series9.0ms

simplify53.0ms

prune41.0ms

localize10.0ms

rewrite21.0ms

series75.0ms

simplify52.0ms

prune85.0ms

localize5.0ms

rewrite13.0ms

series9.0ms

simplify39.0ms

prune50.0ms

localize8.0ms

rewrite18.0ms

series9.0ms

simplify72.0ms

prune44.0ms

regimes276.0ms

bsearch24.0ms

simplify1.0ms

end0.0ms

sample308.0ms

Profiling