Details

analyze515.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

sample22.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	16×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	37	15
1	37	15

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: 33.1b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(- (* x.im y.re) (* x.re y.im))
32.5b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 54

Calls

3 calls:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series43.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
10.0ms	(- (* x.im y.re) (* x.re y.im))
28.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify42.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4998	977
1	4998	977

prune88.0ms

Filtered

49 candidates to 63 candidates (-28.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	6	64

Merged error: 28.6b

Counts

64 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

2.3b	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
4.3b	(* x.im (/ y.re (+ (* y.re y.re) (* y.im y.im))))
21.7b	(/ y.re (+ (* y.re y.re) (* y.im y.im)))
21.9b	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
30×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
6×	`associate-l` `associate-/r` `associate-/l`
4×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 126

Calls

4 calls:

8.0ms	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
8.0ms	(* x.im (/ y.re (+ (* y.re y.re) (* y.im y.im))))
5.0ms	(/ y.re (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
17.0ms	(* x.im (/ y.re (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(/ y.re (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4999	1682
1	4999	1682

prune163.0ms

Filtered

108 candidates to 138 candidates (-27.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	132	6	138
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	134	10	144

Merged error: 28.6b

Counts

144 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

2.3b	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
21.9b	(/ y.im (+ (* y.re y.re) (* y.im y.im)))
35.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`sqrt-prod`
4×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 93

Calls

4 calls:

8.0ms	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
5.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4989	1169
1	4989	1169

prune128.0ms

Filtered

84 candidates to 105 candidates (-25.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	105	10	115

Merged error: 28.6b

Counts

115 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

21.7b	(/ y.re (+ (* y.re y.re) (* y.im y.im)))
21.9b	(/ y.im (+ (* y.re y.re) (* y.im y.im)))
21.9b	(/ y.im (+ (* y.re y.re) (* y.im y.im)))
21.9b	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
12×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `add-log-exp`

Counts

4 → 116

Calls

4 calls:

7.0ms	(/ y.re (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

series28.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ y.re (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

simplify90.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4894	1636
1	4894	1636

prune115.0ms

Filtered

100 candidates to 128 candidates (-28.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	128	10	138

Merged error: 28.6b

Counts

138 → 10

regimes321.0ms

Accuracy

0% (1.1b remaining)

Error of 23.5b against oracle of 22.4b and baseline of 23.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	33
1	17	33

end0.0ms

analyze517.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

sample572.0ms

Algorithm

intervals

Results

355.0ms	8000×	body	80	valid
20.0ms	479×	body	80	invalid

Details

analyze515.0ms

sample22.0ms

simplify3.0ms

prune3.0ms

localize12.0ms

rewrite15.0ms

series43.0ms

simplify42.0ms

prune88.0ms

localize11.0ms

rewrite30.0ms

series47.0ms

simplify47.0ms

prune163.0ms

localize13.0ms

rewrite22.0ms

series36.0ms

simplify55.0ms

prune128.0ms

localize15.0ms

rewrite25.0ms

series28.0ms

simplify90.0ms

prune115.0ms

regimes321.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze517.0ms

sample572.0ms

Profiling