Details

sample340.0ms

Algorithm

intervals

Results

107.0ms	257×	body	80	valid
85.0ms	73×	body	1280	valid
44.0ms	53×	body	640	valid
13.0ms	20×	body	320	valid
5.0ms	14×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	19	37
1	31	37
2	53	36
3	85	36
4	220	36
5	1023	36
done	5000	36

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.0b

localize38.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (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)))
33.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite62.0ms

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:

7.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (atan2 x.im x.re) y.im)
55.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
226.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.9s

Counts

68 → 68

Iterations

Useful iterations: 3 (626.0ms)

Iter	Nodes	Cost
0	95	836
1	197	778
2	554	692
3	2818	677
done	5000	677

prune663.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.2b

localize43.0ms

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)
1.9b	(* (atan2 x.im x.re) y.im)
25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite64.0ms

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:

22.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
13.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
10.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
120.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
35.0ms	(* (atan2 x.im x.re) y.im)
73.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify844.0ms

Counts

81 → 81

Iterations

Useful iterations: done (841.0ms)

Iter	Nodes	Cost
0	132	1042
1	290	985
2	920	871
done	5000	867

prune527.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.0b

localize44.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (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)))
33.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite59.0ms

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:

8.0ms	(* (atan2 x.im x.re) y.im)
15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (atan2 x.im x.re) y.im)
54.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
198.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.5s

Counts

68 → 68

Iterations

Useful iterations: 3 (525.0ms)

Iter	Nodes	Cost
0	95	836
1	197	778
2	554	692
3	2818	677
done	5000	677

prune556.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.0b

localize48.0ms

Local error

Found 4 expressions with local error:

25.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.0b	(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

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:

16.0ms	(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)))
31.0ms	(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)))

series767.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
261.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
202.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
237.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.1s

Counts

51 → 51

Iterations

Useful iterations: 3 (159.0ms)

Iter	Nodes	Cost
0	68	978
1	139	948
2	289	824
3	651	815
4	1869	815
done	5001	815

prune529.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.0b

regimes604.0ms

Accuracy

75.1% (7.2b remaining)

Error of 11.3b against oracle of 4.1b and baseline of 33.0b

bsearch191.0ms

Steps

Iters	Range		Point
11	-2.8777477469784756e-294	1.4337929867489595e-303	-2.19425972553957e-310

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	22	32
1	32	28
2	36	28
done	36	28

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.0s	2030×	body	1280	valid
1.7s	7968×	body	80	valid
1.3s	1460×	body	640	valid
381.0ms	662×	body	320	valid
104.0ms	313×	body	160	valid