Details

sample33.0ms

Algorithm

intervals

Results

23.0ms

271×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
24.1b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

9.0ms	(+ (* x.re y.re) (* x.im y.im))
27.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series149.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(+ (* x.re y.re) (* x.im y.im))
99.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts

50 → 50

Iterations

Iter	Nodes
done	5002
3	2834
2	817
1	239
0	88

prune287.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* 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))))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite70.0ms

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))
42.0ms	(/ (+ (* 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)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series578.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* x.re y.re) (* x.im y.im))
137.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
355.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts

100 → 100

Iterations

Iter	Nodes
done	5044
3	2874
2	944
1	283
0	120

prune506.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
15.8b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite85.0ms

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` `insert-posit16`
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` `sum-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 98

Calls

4 calls:

7.0ms	(+ (* x.re y.re) (* x.im y.im))
56.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* x.re y.re) (* x.im y.im))
108.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify3.0s

Counts

110 → 110

Iterations

Iter	Nodes
done	5003
3	4119
2	1270
1	403
0	149

prune587.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 22.2b

localize50.0ms

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)))))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite61.0ms

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:

32.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
68.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
53.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.9s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
3	2240
2	791
1	306
0	145

prune742.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 22.2b

regimes536.0ms

Accuracy

0% (2.4b remaining)

Error of 25.8b against oracle of 23.3b and baseline of 25.8b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	22
1	22
0	15

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8459×

body

valid