Details

sample29.0ms

Algorithm

intervals

Results

12.0ms

269×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	15	15
done	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: 28.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
27.8b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite18.0ms

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

Counts

3 → 53

Calls

3 calls:

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

series50.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* y.re y.re) (* y.im y.im))
11.0ms	(+ (* x.re y.re) (* x.im y.im))
34.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.6s

Counts

62 → 62

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	99	1090
1	270	1067
2	932	951
3	3227	951
done	5000	951

prune125.0ms

Filtered

50 candidates to 62 candidates (-24.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	52	10	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	10	63

Merged error: 27.5b

Counts

63 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
17.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b	(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`
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:

4.0ms	(+ (* x.re y.re) (* x.im y.im))
10.0ms	(/ (+ (* x.re y.re) (* x.im 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)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
37.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.3s

Counts

96 → 96

Iterations

Useful iterations: 3 (383.0ms)

Iter	Nodes	Cost
0	117	1780
1	274	1649
2	751	1541
3	2024	1525
done	5001	1525

prune130.0ms

Filtered

75 candidates to 96 candidates (-28.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	96	10	106

Merged error: 23.8b

Counts

106 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
17.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b	(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`
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:

4.0ms	(+ (* x.re y.re) (* x.im y.im))
11.0ms	(/ (+ (* x.re y.re) (* x.im 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)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.3s

Counts

96 → 96

Iterations

Useful iterations: 3 (390.0ms)

Iter	Nodes	Cost
0	117	1780
1	274	1649
2	751	1541
3	2024	1525
done	5001	1525

prune130.0ms

Filtered

75 candidates to 96 candidates (-28.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	96	10	106

Merged error: 23.8b

Counts

106 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.im y.im) (pow y.re 2))
0.5b	(+ (* y.re x.re) (* y.im x.im))
1.0b	(/ 1 (/ (+ (* y.im y.im) (pow y.re 2)) (+ (* y.re x.re) (* y.im x.im))))
27.1b	(/ (+ (* y.im y.im) (pow y.re 2)) (+ (* y.re x.re) (* y.im x.im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`+-commutative` `rec-exp` `frac-2neg` `1-exp` `clear-num` `sum-log` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 137

Calls

4 calls:

6.0ms	(+ (* y.im y.im) (pow y.re 2))
4.0ms	(+ (* y.re x.re) (* y.im x.im))
12.0ms	(/ 1 (/ (+ (* y.im y.im) (pow y.re 2)) (+ (* y.re x.re) (* y.im x.im))))
11.0ms	(/ (+ (* y.im y.im) (pow y.re 2)) (+ (* y.re x.re) (* y.im x.im)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* y.im y.im) (pow y.re 2))
11.0ms	(+ (* y.re x.re) (* y.im x.im))
29.0ms	(/ 1 (/ (+ (* y.im y.im) (pow y.re 2)) (+ (* y.re x.re) (* y.im x.im))))
23.0ms	(/ (+ (* y.im y.im) (pow y.re 2)) (+ (* y.re x.re) (* y.im x.im)))

simplify743.0ms

Counts

149 → 149

Iterations

Useful iterations: done (738.0ms)

Iter	Nodes	Cost
0	203	3676
1	505	3418
2	1419	3113
done	5001	3111

prune169.0ms

Filtered

89 candidates to 149 candidates (-67.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	149	10	159

Merged error: 23.8b

Counts

159 → 10

regimes472.0ms

Accuracy

40.8% (1.9b remaining)

Error of 25.6b against oracle of 23.7b and baseline of 27.0b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	83
1	31	83
done	31	83

end0.0ms

sample825.0ms

Algorithm

intervals

Results

405.0ms

8479×

body

valid

Details

sample29.0ms

simplify4.0ms

prune3.0ms

localize10.0ms

rewrite18.0ms

series50.0ms

simplify1.6s

prune125.0ms

localize12.0ms

rewrite25.0ms

series62.0ms

simplify1.3s

prune130.0ms

localize17.0ms

rewrite25.0ms

series60.0ms

simplify1.3s

prune130.0ms

localize12.0ms

rewrite39.0ms

series68.0ms

simplify743.0ms

prune169.0ms

regimes472.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample825.0ms

Profiling