Details

sample886.0ms

Algorithm

intervals

Results

220.0ms	42×	body	640	valid
201.0ms	68×	body	1280	valid
197.0ms	256×	body	80	valid
19.0ms	16×	body	320	valid
9.0ms	8×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize87.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (atan2 x.im x.re) y.im)
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite74.0ms

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:

11.0ms	(* (atan2 x.im x.re) y.im)
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (atan2 x.im x.re) y.im)
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
63.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
202.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	2001
4	2001
3	911
2	425
1	202
0	99

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 17.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (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)
2.7b	(* (atan2 x.im x.re) y.im)
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite57.0ms

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` `add-log-exp`
4×	`insert-posit16`
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` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

4 → 70

Calls

4 calls:

8.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
25.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
11.0ms	(* (atan2 x.im x.re) y.im)
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
132.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
19.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.2s

Counts

82 → 82

Iterations

Iter	Nodes
done	2000
3	2000
2	752
1	307
0	135

prune704.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.0b

localize95.0ms

Local error

Found 4 expressions with local error:

31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
27.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
172.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
153.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
156.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify997.0ms

Counts

55 → 55

Iterations

Iter	Nodes
done	2006
5	2006
4	1185
3	540
2	265
1	141
0	70

prune629.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.0b

localize66.0ms

Local error

Found 4 expressions with local error:

31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(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)))
17.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series504.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
206.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
190.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts

62 → 62

Iterations

Iter	Nodes
done	2006
5	2006
4	1185
3	540
2	265
1	141
0	70

prune707.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.0b

regimes711.0ms

Accuracy

58% (6.8b remaining)

Error of 10.2b against oracle of 3.4b and baseline of 19.6b

bsearch537.0ms

Steps

Iters	Range		Point
8	8718.24681470488	215118504.3831951	8950.863112971656
8	-3.4072473816268267e-77	-5.668439296253745e-80	-1.6474711713701992e-78

simplify9.0ms

Iterations

Iter	Nodes
done	43
1	43
0	33

end0.0ms

sample11.0s

Algorithm

intervals

Results

3.8s	1975×	body	1280	valid
3.3s	7979×	body	80	valid
2.0s	1448×	body	640	valid
1.0s	639×	body	320	valid
275.0ms	307×	body	160	valid