Details

sample356.0ms

Algorithm

intervals

Results

38.0ms	59×	body	1280	valid
23.0ms	250×	body	80	valid
21.0ms	50×	body	640	valid
4.0ms	16×	body	320	valid
2.0ms	1×	body	2560	valid
1.0ms	6×	body	160	valid

simplify661.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	19	37
1	31	37
2	53	36
3	84	36
4	201	36
5	851	36
done	5000	36

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize23.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) y.im)
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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×	`sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
163.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.5s

Counts

68 → 68

Iterations

Useful iterations: 3 (155.0ms)

Iter	Nodes	Cost
0	98	845
1	198	787
2	439	699
3	871	686
4	1747	686
5	4898	686
done	5000	686

prune341.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.7b

localize28.0ms

Local error

Found 4 expressions with local error:

29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
66.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
145.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.5s

Counts

65 → 65

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	73	1155
1	150	1073
2	293	767
3	587	718
4	1459	718
5	4820	718
done	5000	718

prune364.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.6b

localize29.0ms

Local error

Found 4 expressions with local error:

29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

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×	`sin-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 39

Calls

4 calls:

3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
147.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
142.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
145.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts

51 → 51

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	71	1005
1	144	975
2	278	851
3	561	842
4	1234	842
5	3231	842
done	5000	842

prune359.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 18.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (atan2 x.im x.re) y.re)
1.5b	(* (atan2 x.im x.re) y.im)
18.2b	(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series188.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
117.0ms	(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.2s

Counts

73 → 73

Iterations

Useful iterations: 3 (214.0ms)

Iter	Nodes	Cost
0	124	797
1	256	761
2	590	675
3	1176	666
4	2152	666
done	5000	666

prune308.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 11.9b

regimes369.0ms

Accuracy

76.8% (4.9b remaining)

Error of 17.6b against oracle of 12.7b and baseline of 33.8b

bsearch284.0ms

Steps

Iters	Range		Point
9	-6.152941817396574e-304	2.4251123973937145e-305	-5.514399990102696e-309
10	-7.520341406059738e-16	-6.032254327786318e-27	-6.956422000428077e-25

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	96
1	50	96
done	50	96

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	2240×	body	1280	valid
820.0ms	7959×	body	80	valid
613.0ms	1492×	body	640	valid
168.0ms	577×	body	320	valid
65.0ms	42×	body	2560	valid
41.0ms	223×	body	160	valid