Details

sample288.0ms

Algorithm

intervals

Results

65.0ms	55×	body	1280	valid
50.0ms	258×	body	80	valid
23.0ms	32×	body	640	valid
9.0ms	17×	body	320	valid
4.0ms	9×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	808
4	197
3	82
2	53
1	31
0	19

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize79.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.im)
25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

5.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (atan2 x.im x.re) y.im)
48.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
157.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
4	2216
3	911
2	425
1	202
0	99

prune644.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.3b	(* (atan2 x.im x.re) y.im)
25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`pow1`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-l`
8×	`add-cbrt-cube` `add-exp-log`
7×	`add-log-exp`
6×	`associate-r`
4×	`insert-posit16`
3×	`exp-prod` `log-pow` `sqrt-prod`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`
1×	`rem-sqrt-square` `sub-neg` `flip3-+` `exp-diff` `diff-log` `flip-+`

Counts

4 → 73

Calls

4 calls:

39.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
9.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
5.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
122.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
24.0ms	(* (atan2 x.im x.re) y.im)
67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
4	4812
3	1753
2	685
1	297
0	137

prune569.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.9b

localize104.0ms

Local error

Found 4 expressions with local error:

23.0b	(cos (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 56

Calls

4 calls:

24.0ms	(cos (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cos (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
68.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.9s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
5	3766
4	1209
3	551
2	265
1	130
0	60

prune896.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.9b

localize165.0ms

Local error

Found 4 expressions with local error:

25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite26.0ms

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:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
60.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
5	3254
4	995
3	435
2	196
1	92
0	39

prune926.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.9b

regimes901.0ms

Accuracy

80.1% (5.7b remaining)

Error of 9.3b against oracle of 3.6b and baseline of 32.2b

bsearch176.0ms

Steps

Iters	Range		Point
9	-3.624048073274082e-307	9.672750817997472e-303	4.11803379523495e-310

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample7.9s

Algorithm

intervals

Results

3.1s	2023×	body	1280	valid
2.6s	7979×	body	80	valid
1.3s	1440×	body	640	valid
350.0ms	665×	body	320	valid
117.0ms	325×	body	160	valid