Details

sample65.0ms

Algorithm

intervals

Results

44.0ms

280×

body

valid

simplify10.0ms

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: 24.9b

localize54.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.4b	(+ (* x.re y.re) (* x.im y.im))
24.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite790.0ms

Algorithm

rewrite-expression-head

Rules

208×	`*-un-lft-identity`
85×	`distribute-lft-out`
76×	`associate-l`
56×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`swap-sqr`
8×	`associate-/r*`
7×	`associate-/l*` `add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `flip-+`
3×	`pow1` `insert-posit16`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 121

Calls

3 calls:

75.0ms	(+ (* y.re y.re) (* y.im y.im))
42.0ms	(+ (* x.re y.re) (* x.im y.im))
660.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series215.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* y.re y.re) (* y.im y.im))
45.0ms	(+ (* x.re y.re) (* x.im y.im))
130.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.3s

Counts

130 → 130

Iterations

Iter	Nodes
done	5011
3	4467
2	1114
1	292
0	106

prune339.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 24.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* x.re y.re) (* x.im y.im))
15.0b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite426.0ms

Algorithm

rewrite-expression-head

Rules

258×	`*-un-lft-identity`
102×	`distribute-lft-out`
92×	`associate-l`
80×	`sqrt-prod`
77×	`times-frac`
36×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
20×	`swap-sqr`
11×	`associate-/r*`
7×	`associate-/l*`
6×	`pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`insert-posit16`
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 → 170

Calls

4 calls:

53.0ms	(+ (* x.re y.re) (* x.im y.im))
220.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
79.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
66.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* x.re y.re) (* x.im y.im))
135.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
51.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts

182 → 182

Iterations

Iter	Nodes
done	5003
3	2704
2	891
1	293
0	126

prune572.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* x.re y.re) (* x.im y.im))
15.0b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite398.0ms

Algorithm

rewrite-expression-head

Rules

258×	`*-un-lft-identity`
102×	`distribute-lft-out`
92×	`associate-l`
80×	`sqrt-prod`
77×	`times-frac`
36×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
20×	`swap-sqr`
11×	`associate-/r*`
7×	`associate-/l*`
6×	`pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`insert-posit16`
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 → 170

Calls

4 calls:

46.0ms	(+ (* x.re y.re) (* x.im y.im))
189.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
81.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
70.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* x.re y.re) (* x.im y.im))
134.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts

182 → 182

Iterations

Iter	Nodes
done	5003
3	2704
2	891
1	293
0	126

prune574.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.4b	(+ (* x.re y.re) (* x.im y.im))
0.7b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
24.5b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite613.0ms

Algorithm

rewrite-expression-head

Rules

959×	`*-un-lft-identity`
466×	`times-frac`
366×	`distribute-lft-out`
328×	`associate-l`
150×	`add-sqr-sqrt` `add-cube-cbrt`
76×	`associate-/r*` `swap-sqr`
30×	`associate-/r/`
24×	`associate-/l*`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`flip3-+` `flip-+`
8×	`div-exp` `add-log-exp`
6×	`div-inv` `remove-double-div`
5×	`pow1`
4×	`cbrt-undiv` `clear-num` `insert-posit16` `associate-/l/`
3×	`frac-2neg`
2×	`+-commutative` `rec-exp` `sum-log` `1-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 419

Calls

4 calls:

55.0ms	(+ (* y.re y.re) (* y.im y.im))
53.0ms	(+ (* x.re y.re) (* x.im y.im))
284.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
182.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (* y.re y.re) (* y.im y.im))
50.0ms	(+ (* x.re y.re) (* x.im y.im))
152.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
71.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify1.4s

Counts

431 → 431

Iterations

Iter	Nodes
done	5002
2	1817
1	621
0	230

prune786.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 23.1b

regimes236.0ms

Accuracy

0% (1.9b remaining)

Error of 25.2b against oracle of 23.3b and baseline of 25.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample1.2s

Algorithm

intervals

Results

924.0ms

8478×

body

valid