Details

analyze514.0ms

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

sample24.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
1.0ms	16×	body	80	invalid

simplify153.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (152.0ms)

Iter	Nodes	Cost
0	4841	15
1	4841	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: 24.8b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(- (* x.im y.re) (* x.re y.im))
24.2b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

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:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series44.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ (* 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)))

simplify44.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5785	976

prune90.0ms

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: 19.4b

Counts

64 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

6.5b	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
7.1b	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
8.5b	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
9.7b	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))

rewrite34.0ms

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:

5.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
11.0ms	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
14.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
13.0ms	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))

simplify57.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5147	1682

prune165.0ms

Filtered

104 candidates to 138 candidates (-32.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	136	8	144

Merged error: 19.3b

Counts

144 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

7.1b	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
8.5b	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
28.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.0b	(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:

5.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(* y.im (/ x.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)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify76.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4954	1169
1	4954	1169

prune158.0ms

Filtered

82 candidates to 105 candidates (-28.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	105	8	113

Merged error: 19.3b

Counts

113 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

6.5b	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
9.7b	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))
28.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

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:

5.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(* y.re (/ x.im (+ (* 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)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(* y.re (/ x.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)))

simplify56.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5209	1169

prune93.0ms

Filtered

82 candidates to 105 candidates (-28.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	105	8	113

Merged error: 19.3b

Counts

113 → 8

regimes304.0ms

Accuracy

20.1% (2.6b remaining)

Error of 24.4b against oracle of 21.8b and baseline of 25.1b

bsearch40.0ms

Steps

Iters	Range		Point
11	2.872627748793113e-19	15435.245138455997	2.206658626264936e-10
7	-4.346316898740244e-112	-1.6826481347851376e-113	-3.4420726088017006e-112

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	93	75
1	93	75

end0.0ms

sample571.0ms

Algorithm

intervals

Results

347.0ms	8000×	body	80	valid
20.0ms	480×	body	80	invalid

Details

analyze514.0ms

sample24.0ms

simplify153.0ms

prune3.0ms

localize9.0ms

rewrite16.0ms

series44.0ms

simplify44.0ms

prune90.0ms

localize11.0ms

rewrite34.0ms

series54.0ms

simplify57.0ms

prune165.0ms

localize14.0ms

rewrite25.0ms

series74.0ms

simplify76.0ms

prune158.0ms

localize13.0ms

rewrite24.0ms

series40.0ms

simplify56.0ms

prune93.0ms

regimes304.0ms

bsearch40.0ms

simplify2.0ms

end0.0ms

sample571.0ms

Profiling