Details

sample50.0ms

Algorithm

intervals

Results

27.0ms

271×

body

valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.8b	(+ (* x.re y.re) (* x.im y.im))
23.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite81.0ms

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:

16.0ms	(+ (* y.re y.re) (* y.im y.im))
17.0ms	(+ (* x.re y.re) (* x.im y.im))
47.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series226.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (* y.re y.re) (* y.im y.im))
54.0ms	(+ (* x.re y.re) (* x.im y.im))
134.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.9s

Counts

62 → 62

Iterations

Useful iterations: 2 (164.0ms)

Iter	Nodes	Cost
0	99	1090
1	270	1067
2	866	951
3	2515	951
done	5001	951

prune257.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* x.re y.re) (* x.im y.im))
13.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite71.0ms

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:

8.0ms	(+ (* x.re y.re) (* x.im y.im))
43.0ms	(/ (+ (* 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)))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* x.re y.re) (* x.im y.im))
136.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
43.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.9s

Counts

96 → 96

Iterations

Useful iterations: 3 (622.0ms)

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

prune604.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 22.0b

localize30.0ms

Local error

Found 4 expressions with local error:

8.3b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`sqrt-div`
9×	`associate-/r*`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

41.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
17.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
14.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

321.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
53.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
58.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts

112 → 112

Iterations

Useful iterations: 3 (557.0ms)

Iter	Nodes	Cost
0	142	2329
1	296	2120
2	761	2007
3	1900	1980
done	5000	1980

prune581.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 22.0b

localize64.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

12.0ms	(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)))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
65.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.9s

Counts

72 → 72

Iterations

Useful iterations: 3 (162.0ms)

Iter	Nodes	Cost
0	38	852
1	91	744
2	205	680
3	444	656
4	1114	656
5	3182	656
done	5001	656

prune498.0ms

Pruning

13 alts after pruning (9 fresh and 4 done)

Merged error: 22.0b

regimes386.0ms

Accuracy

0% (2.9b remaining)

Error of 26.5b against oracle of 23.6b and baseline of 26.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	27
1	22	27
done	22	27

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

8458×

body

valid