Details

analyze70.0ms

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	7×	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: 18.3b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
17.0b	(sqrt (+ (* x x) y))

rewrite10.0ms

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:

5.0ms	(+ (* 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))

simplify22.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5020	261

prune47.0ms

Filtered

25 candidates to 32 candidates (-28.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	5	33

Merged error: 0b

Counts

33 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

17.0b	(sqrt (* (* (cbrt (+ (* x x) y)) (cbrt (+ (* x x) y))) (cbrt (+ (* x x) y))))
17.9b	(cbrt (+ (* x x) y))
17.9b	(cbrt (+ (* x x) y))
17.9b	(cbrt (+ (* x x) y))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

16.0ms	(sqrt (* (* (cbrt (+ (* x x) y)) (cbrt (+ (* x x) y))) (cbrt (+ (* x x) y))))
4.0ms	(cbrt (+ (* x x) y))
3.0ms	(cbrt (+ (* x x) y))
4.0ms	(cbrt (+ (* x x) y))

series57.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(sqrt (* (* (cbrt (+ (* x x) y)) (cbrt (+ (* x x) y))) (cbrt (+ (* x x) y))))
16.0ms	(cbrt (+ (* x x) y))
16.0ms	(cbrt (+ (* x x) y))
16.0ms	(cbrt (+ (* x x) y))

simplify66.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5119	1635

prune105.0ms

Filtered

64 candidates to 101 candidates (-57.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	101	5	106

Merged error: 0b

Counts

106 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x x) y)
5.8b	(- (pow x 4) (* y y))
17.0b	(sqrt (/ (- (pow x 4) (* y y)) (- (* x x) y)))
32.9b	(/ (- (pow x 4) (* y y)) (- (* x x) y))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
49×	`times-frac`
44×	`difference-of-squares`
30×	`sqrt-prod`
27×	`add-cube-cbrt` `*-un-lft-identity`
10×	`unpow-prod-down` `sqr-pow`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `flip3--` `flip--`
4×	`associate-/r*` `associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 119

Calls

4 calls:

4.0ms	(- (* x x) y)
4.0ms	(- (pow x 4) (* y y))
8.0ms	(sqrt (/ (- (pow x 4) (* y y)) (- (* x x) y)))
9.0ms	(/ (- (pow x 4) (* y y)) (- (* x x) y))

series29.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(- (* x x) y)
6.0ms	(- (pow x 4) (* y y))
11.0ms	(sqrt (/ (- (pow x 4) (* y y)) (- (* x x) y)))
9.0ms	(/ (- (pow x 4) (* y y)) (- (* x x) y))

simplify43.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4960	1958
1	4960	1958

prune181.0ms

Filtered

104 candidates to 131 candidates (-26.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	131	5	136

Merged error: 0b

Counts

136 → 5

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

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:

2.0ms	(+ x (* y (/ 1/2 x)))
6.0ms	(* y (/ 1/2 x))

series7.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(+ x (* y (/ 1/2 x)))
3.0ms	(* y (/ 1/2 x))

simplify47.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4983	372
1	4983	372

prune49.0ms

Filtered

34 candidates to 49 candidates (-44.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	49	5	54

Merged error: 0b

Counts

54 → 5

regimes321.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 21.9b

bsearch64.0ms

Steps

Iters	Range		Point
6	3.900448473869837e+135	1.9509790560975906e+136	9.945221091740827e+135
8	-5.128092268654204e+155	-3.264674126780922e+151	-1.3352553940598147e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	29
1	25	29

end0.0ms

analyze84.0ms

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

sample333.0ms

Algorithm

intervals

Results

206.0ms	8000×	body	80	valid
4.0ms	172×	body	80	nan

Details

analyze70.0ms

sample13.0ms

simplify3.0ms

prune3.0ms

localize4.0ms

rewrite10.0ms

series9.0ms

simplify22.0ms

prune47.0ms

localize10.0ms

rewrite31.0ms

series57.0ms

simplify66.0ms

prune105.0ms

localize11.0ms

rewrite30.0ms

series29.0ms

simplify43.0ms

prune181.0ms

localize6.0ms

rewrite10.0ms

series7.0ms

simplify47.0ms

prune49.0ms

regimes321.0ms

bsearch64.0ms

simplify2.0ms

end0.0ms

analyze84.0ms

sample333.0ms

Profiling