Details

analyze571.0ms

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

12.0ms	256×	body	80	valid
1.0ms	11×	body	80	invalid

simplify162.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (161.0ms)

Iter	Nodes	Cost
0	4841	15
1	4841	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: 25.2b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
24.7b	(/ (- (* 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:

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)))

series40.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (* 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)))

simplify42.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5676	845

prune98.0ms

Filtered

39 candidates to 49 candidates (-25.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	40	9	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	9	50

Merged error: 19.9b

Counts

50 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
16.1b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
27.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

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))
9.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
34.0ms	(/ (- (* 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)))

simplify48.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5760	1553

prune130.0ms

Filtered

77 candidates to 97 candidates (-26.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	98	8	106

Merged error: 19.9b

Counts

106 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

9.8b	(* y.re (/ x.im (sqrt (+ (* y.re y.re) (* y.im y.im)))))
27.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

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:

11.0ms	(* 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)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series32.0ms

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 (29.0ms)

Iter	Nodes	Cost
0	5040	1084

prune121.0ms

Filtered

75 candidates to 101 candidates (-34.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	101	8	109

Merged error: 19.9b

Counts

109 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

7.1b	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
8.9b	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
9.3b	(* 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))))

rewrite31.0ms

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

series55.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 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))))
12.0ms	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))

simplify58.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5147	1682

prune123.0ms

Filtered

104 candidates to 138 candidates (-32.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	137	9	146

Merged error: 19.9b

Counts

146 → 9

regimes485.0ms

Accuracy

41.1% (0.7b remaining)

Error of 22.6b against oracle of 21.9b and baseline of 23.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	96
1	79	96

end0.0ms

sample638.0ms

Algorithm

intervals

Results

397.0ms	8000×	body	80	valid
27.0ms	508×	body	80	invalid

Details

analyze571.0ms

sample24.0ms

simplify162.0ms

prune4.0ms

localize10.0ms

rewrite13.0ms

series40.0ms

simplify42.0ms

prune98.0ms

localize13.0ms

rewrite25.0ms

series55.0ms

simplify48.0ms

prune130.0ms

localize14.0ms

rewrite25.0ms

series32.0ms

simplify37.0ms

prune121.0ms

localize14.0ms

rewrite31.0ms

series55.0ms

simplify58.0ms

prune123.0ms

regimes485.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample638.0ms

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