Details

analyze537.0ms

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	9×	body	80	invalid

simplify164.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (163.0ms)

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: 31.9b

Counts

2 → 1

localize10.0ms

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))
31.2b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite20.0ms

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))
11.0ms	(/ (- (* 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))
27.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5785	976

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: 26.6b

Counts

64 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
18.4b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
32.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

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

series59.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
37.0ms	(/ (- (* 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)))

simplify47.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5760	1553

prune113.0ms

Filtered

77 candidates to 97 candidates (-26.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	98	7	105

Merged error: 26.6b

Counts

105 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

8.7b	(* y.im (/ x.re (sqrt (+ (* y.re y.re) (* y.im y.im)))))
32.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.6b	(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.im (/ x.re (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)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* y.im (/ x.re (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)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify35.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4989	1084
1	4989	1084

prune139.0ms

Filtered

75 candidates to 101 candidates (-34.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	101	7	108

Merged error: 26.6b

Counts

108 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

10.2b	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
11.0b	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
11.4b	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))
11.6b	(* y.im (/ x.re (+ (* 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.re (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))
9.0ms	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
14.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
15.0ms	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))
13.0ms	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))

simplify56.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5147	1682

prune114.0ms

Filtered

104 candidates to 138 candidates (-32.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	2	3
Picked	1	0	1
Done	0	3	3
Total	139	6	145

Merged error: 26.6b

Counts

145 → 6

regimes367.0ms

Accuracy

0% (1.0b remaining)

Error of 23.4b against oracle of 22.4b and baseline of 23.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	34
1	50	34

end0.0ms

sample630.0ms

Algorithm

intervals

Results

382.0ms	8000×	body	80	valid
21.0ms	449×	body	80	invalid

Details

analyze537.0ms

sample22.0ms

simplify164.0ms

prune4.0ms

localize10.0ms

rewrite20.0ms

series43.0ms

simplify46.0ms

prune100.0ms

localize12.0ms

rewrite22.0ms

series59.0ms

simplify47.0ms

prune113.0ms

localize13.0ms

rewrite25.0ms

series33.0ms

simplify35.0ms

prune139.0ms

localize11.0ms

rewrite31.0ms

series55.0ms

simplify56.0ms

prune114.0ms

regimes367.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample630.0ms

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