Details

sample33.0ms

Algorithm

intervals

Results

17.0ms

265×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	15	15
done	15	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize23.0ms

Local error

Found 2 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
27.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite58.0ms

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:

12.0ms	(+ (* x.re y.re) (* x.im y.im))
45.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series143.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(+ (* x.re y.re) (* x.im y.im))
101.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.4s

Counts

48 → 48

Iterations

Useful iterations: 3 (558.0ms)

Iter	Nodes	Cost
0	86	924
1	232	906
2	767	824
3	2337	820
done	5000	820

prune156.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
16.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
33.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite87.0ms

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:

13.0ms	(+ (* x.re y.re) (* x.im y.im))
54.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(+ (* x.re y.re) (* x.im y.im))
161.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
61.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts

96 → 96

Iterations

Useful iterations: 3 (562.0ms)

Iter	Nodes	Cost
0	117	1780
1	275	1649
2	775	1541
3	2060	1525
done	5000	1525

prune355.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 26.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
16.3b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
33.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
33.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

9.0ms	(+ (* x.re y.re) (* x.im y.im))
72.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* x.re y.re) (* x.im y.im))
134.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
46.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.8s

Counts

106 → 106

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	146	1886
1	378	1642
2	1154	1474
3	3751	1458
done	5001	1458

prune532.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 26.2b

localize35.0ms

Local error

Found 3 expressions with local error:

0.6b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
0.7b	(+ (* x.re y.re) (* x.im y.im))
27.4b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite126.0ms

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:

36.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
17.0ms	(+ (* x.re y.re) (* x.im y.im))
66.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series351.0ms

Counts

3 → 9

Calls

3 calls:

202.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
57.0ms	(+ (* x.re y.re) (* x.im y.im))
92.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify3.4s

Counts

135 → 135

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	194	3510
1	468	3261
2	1271	2982
3	4125	2954
done	5000	2954

prune791.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 26.2b

regimes213.0ms

Accuracy

0% (2.7b remaining)

Error of 25.8b against oracle of 23.1b and baseline of 25.8b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	25
1	17	25
done	17	25

end0.0ms

sample1.1s

Algorithm

intervals

Results

726.0ms

8453×

body

valid