Details

analyze562.0ms

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
0.0ms	10×	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

prune4.0ms

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: 26.9b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
26.4b	(/ (- (* 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)))

series42.0ms

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))
27.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify43.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4998	977
1	4998	977

prune100.0ms

Filtered

49 candidates to 63 candidates (-28.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	56	7	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	8	64

Merged error: 21.9b

Counts

64 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

3.2b	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
3.3b	(* x.im (/ y.re (+ (* y.re y.re) (* y.im y.im))))
18.1b	(/ y.re (+ (* y.re y.re) (* y.im y.im)))
18.6b	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

rewrite32.0ms

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)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
14.0ms	(* 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

prune165.0ms

Filtered

108 candidates to 138 candidates (-27.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	3	3	6
Picked	1	0	1
Done	1	0	1
Total	139	7	146

Merged error: 21.9b

Counts

146 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

3.2b	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
18.6b	(/ y.im (+ (* y.re y.re) (* y.im y.im)))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

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:

10.0ms	(* 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)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series33.0ms

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)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4989	1169
1	4989	1169

prune137.0ms

Filtered

84 candidates to 105 candidates (-25.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	105	7	112

Merged error: 21.9b

Counts

112 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b	(* x.im (/ y.re (+ (* y.re y.re) (* y.im y.im))))
18.1b	(/ y.re (+ (* y.re y.re) (* y.im y.im)))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite26.0ms

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.im (/ y.re (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(/ y.re (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* x.im (/ y.re (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(/ y.re (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4985	1169
1	4985	1169

prune104.0ms

Filtered

84 candidates to 105 candidates (-25.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	105	7	112

Merged error: 21.9b

Counts

112 → 7

regimes277.0ms

Accuracy

0% (1.2b remaining)

Error of 23.4b against oracle of 22.2b and baseline of 23.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	33
1	17	33

end0.0ms

analyze523.0ms

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

sample648.0ms

Algorithm

intervals

Results

396.0ms	8000×	body	80	valid
26.0ms	476×	body	80	invalid

Details

analyze562.0ms

sample22.0ms

simplify3.0ms

prune4.0ms

localize12.0ms

rewrite15.0ms

series42.0ms

simplify43.0ms

prune100.0ms

localize12.0ms

rewrite32.0ms

series44.0ms

simplify47.0ms

prune165.0ms

localize16.0ms

rewrite25.0ms

series33.0ms

simplify58.0ms

prune137.0ms

localize14.0ms

rewrite26.0ms

series33.0ms

simplify57.0ms

prune104.0ms

regimes277.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze523.0ms

sample648.0ms

Profiling