Details

sample2.5s

Algorithm

intervals

Results

596.0ms	62×	body	1280	valid
556.0ms	259×	body	80	valid
280.0ms	52×	body	640	valid
58.0ms	23×	body	320	valid
28.0ms	11×	body	160	valid

simplify14.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	809
4	197
3	82
2	53
1	31
0	19

prune255.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize257.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `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 → 56

Calls

4 calls:

13.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series1.9s

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (atan2 x.im x.re) y.im)
276.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
119.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
1.4s	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify9.0s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
4	2021
3	927
2	418
1	197
0	95

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.5b

localize613.0ms

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)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite389.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

90.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
51.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
22.0ms	(* (atan2 x.im x.re) y.im)
27.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series1.4s

Counts

4 → 12

Calls

4 calls:

529.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
579.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
91.0ms	(* (atan2 x.im x.re) y.im)
218.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify20.9s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
4	4953
3	1676
2	674
1	290
0	132

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize164.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `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 → 56

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
19.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series590.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (atan2 x.im x.re) y.im)
73.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
71.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
402.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify11.8s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
4	2021
3	927
2	418
1	197
0	95

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.4b

localize397.0ms

Local error

Found 4 expressions with local error:

28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
36.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
36.7b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
108.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
41.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
80.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series2.0s

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
446.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
965.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
519.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify15.6s

Counts

51 → 51

Iterations

Iter	Nodes
done	5006
5	3645
4	1185
3	524
2	263
1	139
0	68

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.4b

regimes1.2s

Accuracy

58.4% (6.8b remaining)

Error of 10.5b against oracle of 3.7b and baseline of 20.0b

bsearch486.0ms

Steps

Iters	Range		Point
10	1.8596140179382357e-41	1.4483518605695575e-31	1.3597552282580733e-34
6	-9.370678333643723e-70	-1.3034971086952715e-70	-8.732803126791036e-70

simplify64.0ms

Iterations

Iter	Nodes
done	43
1	43
0	34

end0.0ms

sample47.5s

Algorithm

intervals

Results

18.6s	7964×	body	80	valid
12.7s	2015×	body	1280	valid
12.7s	1450×	body	640	valid
2.0s	625×	body	320	valid
244.0ms	282×	body	160	valid