Details

analyze534.0ms

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

simplify156.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (155.0ms)

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: 27.5b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (* x.im y.re) (* x.re y.im))
27.0b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

4.0ms	(- (* 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)))

series40.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(- (* x.im y.re) (* x.re y.im))
29.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify43.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5676	845

prune86.0ms

Filtered

39 candidates to 49 candidates (-25.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	7	50

Merged error: 23.2b

Counts

50 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* x.im y.re) (* x.re y.im))
16.3b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 85

Calls

4 calls:

3.0ms	(- (* x.im y.re) (* x.re y.im))
11.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* 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)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (* x.im y.re) (* x.re y.im))
38.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* 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)))

simplify50.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5760	1553

prune109.0ms

Filtered

77 candidates to 97 candidates (-26.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	98	6	104

Merged error: 23.2b

Counts

104 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

10.5b	(* y.re (/ x.im (sqrt (+ (* y.re y.re) (* y.im y.im)))))
30.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
19×	`sqrt-prod`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`sqrt-div`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `unswap-sqr`
2×	`prod-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

12.0ms	(* y.re (/ x.im (sqrt (+ (* 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)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify37.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5040	1084

prune123.0ms

Filtered

75 candidates to 101 candidates (-34.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	101	6	107

Merged error: 23.2b

Counts

107 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

8.0b	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
10.0b	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
10.2b	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
12.2b	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))

rewrite35.0ms

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)))
7.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
9.0ms	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))

series69.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
20.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
21.0ms	(* 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))))

simplify55.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5147	1682

prune109.0ms

Filtered

104 candidates to 138 candidates (-32.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	138	6	144

Merged error: 23.2b

Counts

144 → 6

regimes243.0ms

Accuracy

0% (0.9b remaining)

Error of 22.8b against oracle of 21.8b and baseline of 22.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	34
1	50	34

end0.0ms

sample575.0ms

Algorithm

intervals

Results

349.0ms	8000×	body	80	valid
19.0ms	458×	body	80	invalid

Details

analyze534.0ms

sample24.0ms

simplify156.0ms

prune3.0ms

localize9.0ms

rewrite13.0ms

series40.0ms

simplify43.0ms

prune86.0ms

localize12.0ms

rewrite24.0ms

series61.0ms

simplify50.0ms

prune109.0ms

localize13.0ms

rewrite28.0ms

series33.0ms

simplify37.0ms

prune123.0ms

localize11.0ms

rewrite35.0ms

series69.0ms

simplify55.0ms

prune109.0ms

regimes243.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample575.0ms

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