Details

sample54.0ms

Algorithm

intervals

Results

19.0ms

269×

body

valid

simplify23.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize26.0ms

Local error

Found 2 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
25.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite61.0ms

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:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
49.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series257.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(+ (* x.re y.re) (* x.im y.im))
186.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify4.1s

Counts

50 → 50

Iterations

Iter	Nodes
done	5001
3	2585
2	803
1	239
0	88

prune919.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 25.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
14.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite83.0ms

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:

9.0ms	(+ (* x.re y.re) (* x.im y.im))
44.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (* x.re y.re) (* x.im y.im))
317.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
50.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
57.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify4.4s

Counts

100 → 100

Iterations

Iter	Nodes
done	5002
3	2505
2	874
1	284
0	120

prune1.5s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 22.3b

localize68.0ms

Local error

Found 4 expressions with local error:

7.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite106.0ms

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:

51.0ms	(/ (+ (* 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)))
17.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series677.0ms

Counts

4 → 12

Calls

4 calls:

471.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
80.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
57.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
69.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify4.5s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
3	2148
2	762
1	306
0	145

prune2.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 22.3b

localize125.0ms

Local error

Found 4 expressions with local error:

29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

21.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
23.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
19.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
11.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
48.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
76.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
62.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify6.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
5	3240
4	991
3	433
2	196
1	92
0	39

prune1.3s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 22.3b

regimes1.9s

Accuracy

0% (3.1b remaining)

Error of 26.6b against oracle of 23.5b and baseline of 26.6b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample1.3s

Algorithm

intervals

Results

774.0ms

8499×

body

valid