Details

sample45.0ms

Algorithm

intervals

Results

23.0ms

267×

body

valid

simplify70.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	70
5	70
4	66
3	48
2	36
1	19
0	11

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
25.0b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite60.0ms

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`
3×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

3 → 58

Calls

3 calls:

12.0ms	(+ (* y.re y.re) (* y.im y.im))
8.0ms	(- (* x.im y.re) (* x.re y.im))
38.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
64.0ms	(- (* x.im y.re) (* x.re y.im))
103.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
2	1186
1	305
0	104

prune331.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
16.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite43.0ms

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`
4×	`insert-posit16`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 90

Calls

4 calls:

8.0ms	(- (* x.im y.re) (* x.re y.im))
22.0ms	(/ (- (* x.im y.re) (* x.re 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)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* x.im y.re) (* x.re y.im))
156.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
42.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
51.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	5006
3	2657
2	934
1	315
0	124

prune519.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
16.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite63.0ms

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`
4×	`insert-posit16`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 90

Calls

4 calls:

14.0ms	(- (* x.im y.re) (* x.re y.im))
34.0ms	(/ (- (* x.im y.re) (* x.re 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)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (* x.im y.re) (* x.re y.im))
153.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
46.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
68.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.3s

Counts

102 → 102

Iterations

Iter	Nodes
done	5006
3	2657
2	934
1	315
0	124

prune704.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.6b

localize75.0ms

Local error

Found 4 expressions with local error:

9.2b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite54.0ms

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`
4×	`flip3-+` `flip-+` `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` `flip3--` `div-sub` `div-exp` `div-inv` `flip--`

Counts

4 → 105

Calls

4 calls:

29.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (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)))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
44.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
48.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.2s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
3	2471
2	909
1	341
0	147

prune756.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.6b

regimes459.0ms

Accuracy

0% (2.5b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	21
1	21
0	15

end0.0ms

sample986.0ms

Algorithm

intervals

Results

739.0ms

8448×

body

valid