Details

sample365.0ms

Algorithm

intervals

Results

112.0ms	72×	body	1280	valid
91.0ms	257×	body	80	valid
37.0ms	44×	body	640	valid
17.0ms	26×	body	320	valid
2.0ms	4×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2059
6	2059
5	808
4	197
3	82
2	53
1	31
0	19

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize99.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (atan2 x.im x.re) y.re)
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite83.0ms

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:

19.0ms	(* (atan2 x.im x.re) y.re)
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.re)
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
203.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	2014
4	2014
3	870
2	412
1	198
0	97

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.7b

localize38.0ms

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)
0.7b	(* (atan2 x.im x.re) y.im)
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite41.0ms

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:

17.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
10.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
133.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.4s

Counts

85 → 85

Iterations

Iter	Nodes
done	2005
4	2005
3	1753
2	685
1	297
0	137

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.7b	(* (atan2 x.im x.re) y.im)
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.1b	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
13.0ms	(* (atan2 x.im x.re) y.im)
23.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
1.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
37.0ms	(* (atan2 x.im x.re) y.im)
67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

simplify1.1s

Counts

78 → 78

Iterations

Iter	Nodes
done	2000
4	2000
3	1360
2	587
1	255
0	120

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize88.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (atan2 x.im x.re) y.re)
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite36.0ms

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:

6.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.re)
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
152.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	2014
4	2014
3	870
2	412
1	198
0	97

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.4b

regimes722.0ms

Accuracy

74.2% (5.3b remaining)

Error of 8.9b against oracle of 3.5b and baseline of 24.2b

bsearch293.0ms

Steps

Iters	Range		Point
10	-2.0138937375136724e-306	1.6865852339130767e-299	-1.7421973940893e-310

simplify3.0ms

Iterations

Iter	Nodes
done	28
1	28
0	21

end0.0ms

sample10.7s

Algorithm

intervals

Results

4.2s	1909×	body	1280	valid
3.2s	8008×	body	80	valid
2.0s	1502×	body	640	valid
661.0ms	641×	body	320	valid
219.0ms	327×	body	160	valid