Details

analyze483.0ms

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

sample21.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	19×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	15
1	15	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: 31.3b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
30.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite12.0ms

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×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 42

Calls

2 calls:

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

series35.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(+ (* x.re y.re) (* x.im y.im))
26.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5273	820

prune80.0ms

Filtered

38 candidates to 48 candidates (-26.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	42	6	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	7	49

Merged error: 30.5b

Counts

49 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
18.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
32.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite20.0ms

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`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

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

series56.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* x.re y.re) (* x.im y.im))
33.0ms	(/ (+ (* x.re y.re) (* x.im 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)))

simplify35.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5044	1525

prune121.0ms

Filtered

76 candidates to 96 candidates (-26.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	93	10	103

Merged error: 28.2b

Counts

103 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
18.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
32.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite21.0ms

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`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

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

series56.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (* x.re y.re) (* x.im y.im))
35.0ms	(/ (+ (* x.re y.re) (* x.im 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)))

simplify36.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5044	1525

prune125.0ms

Filtered

76 candidates to 96 candidates (-26.3%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	94	12	106

Merged error: 28.2b

Counts

106 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))) 3)
0.7b	(+ (* x.re y.re) (* x.im y.im))
30.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
32.6b	(cbrt (pow (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))) 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`cbrt-prod`
30×	`unpow-prod-down` `cube-prod`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
5×	`pow1` `div-inv`
3×	`pow-unpow` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `sum-log` `rem-cbrt-cube`

Counts

4 → 138

Calls

4 calls:

8.0ms	(pow (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))) 3)
4.0ms	(+ (* x.re y.re) (* x.im y.im))
8.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(cbrt (pow (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))) 3))

series163.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(pow (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))) 3)
9.0ms	(+ (* x.re y.re) (* x.im y.im))
26.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
28.0ms	(cbrt (pow (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))) 3))

simplify40.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4983	3125
1	4983	3125

prune123.0ms

Filtered

79 candidates to 150 candidates (-89.9%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	150	12	162

Merged error: 28.2b

Counts

162 → 12

regimes472.0ms

Accuracy

4.6% (3.1b remaining)

Error of 26.4b against oracle of 23.3b and baseline of 26.5b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	53
1	22	53

end0.0ms

analyze493.0ms

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

sample567.0ms

Algorithm

intervals

Results

346.0ms	8000×	body	80	valid
19.0ms	459×	body	80	invalid

Details

analyze483.0ms

sample21.0ms

simplify3.0ms

prune3.0ms

localize11.0ms

rewrite12.0ms

series35.0ms

simplify57.0ms

prune80.0ms

localize11.0ms

rewrite20.0ms

series56.0ms

simplify35.0ms

prune121.0ms

localize13.0ms

rewrite21.0ms

series56.0ms

simplify36.0ms

prune125.0ms

localize12.0ms

rewrite32.0ms

series163.0ms

simplify40.0ms

prune123.0ms

regimes472.0ms

bsearch1.0ms

simplify1.0ms

end0.0ms

analyze493.0ms

sample567.0ms

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