Details

sample30.0ms

Algorithm

intervals

Results

20.0ms

268×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	15
1	15
0	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.5b	(+ (* x.re y.re) (* x.im y.im))
24.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 56

Calls

3 calls:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
7.0ms	(+ (* x.re y.re) (* x.im y.im))
38.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series176.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* y.re y.re) (* y.im y.im))
40.0ms	(+ (* x.re y.re) (* x.im y.im))
105.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.4s

Counts

65 → 65

Iterations

Iter	Nodes
3	4231
2	1139
1	285
0	101

prune754.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 24.0b

localize30.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (* x.re y.re) (* x.im y.im))
16.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`insert-posit16`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
28.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (* x.re y.re) (* x.im y.im))
159.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
57.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
43.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify994.0ms

Counts

100 → 100

Iterations

Iter	Nodes
3	2624
2	906
1	283
0	120

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.9b

localize35.0ms

Local error

Found 4 expressions with local error:

9.3b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
10×	`sqrt-div`
9×	`associate-/r*`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
5×	`flip3-+` `flip-+`
4×	`insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 104

Calls

4 calls:

39.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
42.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
60.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify678.0ms

Counts

116 → 116

Iterations

Iter	Nodes
3	2153
2	767
1	306
0	145

prune1.9s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 22.9b

localize62.0ms

Local error

Found 4 expressions with local error:

16.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
21×	`sqrt-prod`
18×	`times-frac`
8×	`sqrt-div`
7×	`pow1`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`flip3-+` `flip-+`
4×	`insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 92

Calls

4 calls:

58.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
51.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.6s

Counts

104 → 104

Iterations

Iter	Nodes
4	5666
3	1989
2	661
1	251
0	107

prune1.4s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 22.9b

regimes543.0ms

Accuracy

-4.7% (2.8b remaining)

Error of 26.3b against oracle of 23.5b and baseline of 26.2b

bsearch2.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	23
1	23
0	17

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8470×

body

valid