Details

sample426.0ms

Algorithm

intervals

Results

103.0ms	58×	body	1280	valid
99.0ms	37×	body	640	valid
85.0ms	260×	body	80	valid
15.0ms	15×	body	320	valid
5.0ms	9×	body	160	valid

simplify3.8s

Counts

1 → 1

Iterations

Iter	Nodes
6	5698
5	805
4	195
3	82
2	53
1	31
0	19

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize58.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.re)
31.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sin (+ (* (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` `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:

10.0ms	(* (atan2 x.im x.re) y.re)
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (atan2 x.im x.re) y.re)
46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
210.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

68 → 68

Iterations

Iter	Nodes
5	4028
4	1641
3	834
2	411
1	199
0	97

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.2b

localize93.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
31.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite45.0ms

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` `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:

6.0ms	(* (atan2 x.im x.re) y.im)
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (atan2 x.im x.re) y.im)
72.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
47.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
244.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify2.6s

Counts

68 → 68

Iterations

Iter	Nodes
5	4287
4	1778
3	918
2	449
1	213
0	103

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 21.2b

localize70.0ms

Local error

Found 4 expressions with local error:

4.9b	(cbrt (atan2 x.im x.re))
31.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

series380.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(cbrt (atan2 x.im x.re))
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
226.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

simplify2.9s

Counts

61 → 61

Iterations

Iter	Nodes
5	5548
4	1715
3	737
2	346
1	173
0	87

prune1.4s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 21.2b

localize91.0ms

Local error

Found 4 expressions with local error:

31.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))
33.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))
33.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `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:

5.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))
40.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))
25.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

series714.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
227.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))
199.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))
234.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

simplify1.3s

Counts

51 → 51

Iterations

Iter	Nodes
5	3245
4	1165
3	549
2	283
1	153
0	75

prune1.2s

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 21.2b

regimes858.0ms

Accuracy

77.8% (3.0b remaining)

Error of 22.3b against oracle of 19.3b and baseline of 32.7b

bsearch348.0ms

Steps

Iters	Range		Point
10	-1.0906968289144063e-304	2.8714006224246324e-294	1.04726288994103e-310

simplify12.0ms

Iterations

Iter	Nodes
2	39
1	39
0	30

end0.0ms

sample11.5s

Algorithm

intervals

Results

4.6s	2174×	body	1280	valid
2.9s	1484×	body	640	valid
2.6s	7993×	body	80	valid
550.0ms	576×	body	320	valid
204.0ms	58×	body	2560	valid
183.0ms	239×	body	160	valid