Details

sample47.0ms

Algorithm

intervals

Results

33.0ms

271×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	15
1	15
0	11

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize35.0ms

Local error

Found 2 expressions with local error:

0.4b	(+ (* x.re y.re) (* x.im y.im))
27.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite54.0ms

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:

8.0ms	(+ (* 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)))

series152.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(+ (* 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)))

simplify883.0ms

Counts

50 → 50

Iterations

Iter	Nodes
3	2585
2	802
1	238
0	88

prune530.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 27.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* x.re y.re) (* x.im y.im))
15.2b	(/ (+ (* 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)))

rewrite55.0ms

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:

8.0ms	(+ (* x.re y.re) (* x.im y.im))
33.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (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)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* x.re y.re) (* x.im y.im))
158.0ms	(/ (+ (* 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)))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

100 → 100

Iterations

Iter	Nodes
3	2632
2	899
1	282
0	120

prune1.4s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 24.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* x.re y.re) (* x.im y.im))
15.2b	(/ (+ (* 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)))

rewrite98.0ms

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:

13.0ms	(+ (* x.re y.re) (* x.im y.im))
64.0ms	(/ (+ (* 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)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (* x.re y.re) (* x.im y.im))
175.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
48.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
48.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify946.0ms

Counts

100 → 100

Iterations

Iter	Nodes
3	2632
2	899
1	282
0	120

prune1.4s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 24.3b

localize66.0ms

Local error

Found 4 expressions with local error:

8.5b	(/ (+ (* 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)))

rewrite80.0ms

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:

54.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
12.0ms	(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)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

272.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
62.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
56.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
50.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify738.0ms

Counts

116 → 116

Iterations

Iter	Nodes
3	2090
2	753
1	305
0	145

prune1.7s

Pruning

14 alts after pruning (10 fresh and 4 done)

Merged error: 24.3b

regimes778.0ms

Accuracy

8.1% (2.4b remaining)

Error of 25.7b against oracle of 23.2b and baseline of 25.9b

bsearch4.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	22
1	22
0	18

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

8497×

body

valid