Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

277×

body

valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7
done	15	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.4b	(+ (* x.re y.re) (* x.im y.im))
25.0b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite40.0ms

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:

7.0ms	(+ (* x.re y.re) (* x.im y.im))
32.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series113.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(+ (* x.re y.re) (* x.im y.im))
81.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify77.0ms

Counts

48 → 48

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	231	450
1	847	413
2	2851	412
3	5003	412
done	5003	412

prune118.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 24.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* x.re y.re) (* x.im y.im))
15.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite56.0ms

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:

7.0ms	(+ (* x.re y.re) (* x.im y.im))
32.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* x.re y.re) (* x.im y.im))
109.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify78.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2693	828
3	5001	828
done	5001	828

prune267.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* x.re y.re) (* x.im y.im))
15.7b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
30.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite48.0ms

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` `add-cbrt-cube` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/r*`
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:

7.0ms	(+ (* x.re y.re) (* x.im y.im))
24.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series186.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* x.re y.re) (* x.im y.im))
82.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify66.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	263	883
1	831	838
2	2301	833
3	5001	833
done	5001	833

prune261.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.4b	(+ (* x.re y.re) (* x.im y.im))
0.6b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
24.6b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 126

Calls

3 calls:

7.0ms	(+ (* x.re y.re) (* x.im y.im))
22.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
31.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series229.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (* x.re y.re) (* x.im y.im))
135.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
59.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify58.0ms

Counts

135 → 135

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	480	1744
1	2237	1592
2	5003	1505
done	5003	1505

prune229.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 22.1b

regimes120.0ms

Accuracy

0% (3.0b remaining)

Error of 26.0b against oracle of 23.0b and baseline of 26.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14
done	21	14

end0.0ms

sample576.0ms

Algorithm

intervals

Results

281.0ms

8508×

body

valid