Details

sample42.0ms

Algorithm

intervals

Results

28.0ms

272×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize40.0ms

Local error

Found 3 expressions with local error:

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

rewrite45.0ms

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:

7.0ms	(+ (* x.re y.re) (* x.im y.im))
9.0ms	(+ (* y.re y.re) (* y.im y.im))
29.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series199.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(+ (* x.re y.re) (* x.im y.im))
44.0ms	(+ (* y.re y.re) (* y.im y.im))
99.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

65 → 65

Iterations

Iter	Nodes
done	2002
3	2002
2	1142
1	284
0	101

prune542.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`*-un-lft-identity` `add-cube-cbrt`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*` `flip3-+` `flip-+`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 268

Calls

4 calls:

42.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
32.0ms	(/ (+ (* 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)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
131.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
46.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts

280 → 280

Iterations

Iter	Nodes
done	2010
3	2010
2	1755
1	724
0	305

prune3.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.5b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite76.0ms

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:

15.0ms	(+ (* x.re y.re) (* x.im y.im))
20.0ms	(+ (* y.re y.re) (* y.im y.im))
40.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series216.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(+ (* x.re y.re) (* x.im y.im))
38.0ms	(+ (* y.re y.re) (* y.im y.im))
129.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

65 → 65

Iterations

Iter	Nodes
done	2002
3	2002
2	1142
1	284
0	101

prune775.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x.re y.re) (* x.im y.im))
0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
24.2b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16`
2×	`+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `1-exp` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 141

Calls

4 calls:

7.0ms	(+ (* x.re y.re) (* x.im y.im))
7.0ms	(+ (* y.re y.re) (* y.im y.im))
32.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
60.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* x.re y.re) (* x.im y.im))
41.0ms	(+ (* y.re y.re) (* y.im y.im))
223.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
73.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify1.3s

Counts

153 → 153

Iterations

Iter	Nodes
done	2007
3	2007
2	1770
1	576
0	210

prune1.8s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.5b

regimes559.0ms

Accuracy

15.8% (2.3b remaining)

Error of 25.7b against oracle of 23.4b and baseline of 26.1b

bsearch3.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.2s

8489×

body

valid