Details

sample575.0ms

Algorithm

intervals

Results

182.0ms	74×	body	1280	valid
107.0ms	46×	body	640	valid
62.0ms	254×	body	80	valid
15.0ms	22×	body	320	valid
7.0ms	5×	body	160	valid
5.0ms	2×	body	2560	valid

simplify1.8s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize107.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (atan2 x.im x.re) y.re)
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) 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` `insert-posit16` `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 → 60

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
23.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (atan2 x.im x.re) y.re)
58.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
45.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
249.0ms	(sin (+ (* (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	860
2	413
1	203
0	100

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.8b

localize108.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.3b	(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))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`add-exp-log`
7×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
6×	`sqrt-prod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

21.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms	(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))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
62.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
237.0ms	(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))))

simplify1.2s

Counts

73 → 73

Iterations

Iter	Nodes
done	2001
4	2001
3	1098
2	518
1	245
0	113

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.8b

localize84.0ms

Local error

Found 4 expressions with local error:

5.3b	(cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (* (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))) (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))) (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))) (cbrt y.re))))

rewrite206.0ms

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` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cbrt-prod` `sin-sum` `pow1/3`

Counts

4 → 51

Calls

4 calls:

23.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
158.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (* (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))) (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))) (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))) (cbrt y.re))))

series600.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))
63.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
62.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
235.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (* (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))) (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))) (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))) (cbrt y.re))))

simplify1.0s

Counts

63 → 63

Iterations

Iter	Nodes
done	2000
4	2000
3	825
2	402
1	200
0	100

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.8b

localize136.0ms

Local error

Found 4 expressions with local error:

4.9b	(cbrt (atan2 x.im x.re))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.3b	(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)) (* (cbrt y.re) (cbrt y.re)))) (cbrt y.re))))

rewrite86.0ms

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` `insert-posit16` `add-log-exp`
3×	`cbrt-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `pow1/3`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms	(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)) (* (cbrt y.re) (cbrt y.re)))) (cbrt y.re))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(cbrt (atan2 x.im x.re))
55.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
268.0ms	(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)) (* (cbrt y.re) (cbrt y.re)))) (cbrt y.re))))

simplify1.8s

Counts

65 → 65

Iterations

Iter	Nodes
done	2043
4	2043
3	887
2	393
1	185
0	93

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.8b

regimes606.0ms

Accuracy

79.5% (2.9b remaining)

Error of 21.5b against oracle of 18.6b and baseline of 32.9b

bsearch298.0ms

Steps

Iters	Range		Point
10	-2.0138937375136724e-306	1.6865852339130767e-299	-1.7421973940893e-310

simplify6.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample11.3s

Algorithm

intervals

Results

5.0s	2079×	body	1280	valid
2.9s	7982×	body	80	valid
2.2s	1466×	body	640	valid
490.0ms	554×	body	320	valid
151.0ms	48×	body	2560	valid
147.0ms	258×	body	160	valid