Details

sample464.0ms

Algorithm

intervals

Results

150.0ms	74×	body	1280	valid
87.0ms	46×	body	640	valid
69.0ms	254×	body	80	valid
19.0ms	22×	body	320	valid
10.0ms	2×	body	2560	valid
3.0ms	5×	body	160	valid

simplify4.1s

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize57.0ms

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)))

rewrite59.0ms

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:

6.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.re)
63.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
178.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.8s

Counts

72 → 72

Iterations

Iter	Nodes
5	4114
4	1670
3	851
2	415
1	202
0	100

prune651.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.8b

localize87.0ms

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))))

rewrite66.0ms

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:

19.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0ms	(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))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
55.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
227.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify1.3s

Counts

73 → 73

Iterations

Iter	Nodes
4	2569
3	1084
2	514
1	244
0	113

prune800.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.8b

localize117.0ms

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))))

rewrite211.0ms

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:

13.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
170.0ms	(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))))

series590.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
75.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
220.0ms	(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))))

simplify3.1s

Counts

63 → 63

Iterations

Iter	Nodes
5	6804
4	1924
3	812
2	392
1	199
0	100

prune828.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.8b

localize117.0ms

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))))

rewrite118.0ms

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))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
96.0ms	(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))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(cbrt (atan2 x.im x.re))
49.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
250.0ms	(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))))

simplify1.5s

Counts

65 → 65

Iterations

Iter	Nodes
4	2554
3	900
2	389
1	184
0	93

prune625.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.8b

regimes476.0ms

Accuracy

79.5% (2.9b remaining)

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

bsearch348.0ms

Steps

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

simplify12.0ms

Iterations

Iter	Nodes
2	39
1	39
0	29

end0.0ms

sample11.4s

Algorithm

intervals

Results

3.9s	2079×	body	1280	valid
3.1s	7982×	body	80	valid
3.1s	1466×	body	640	valid
500.0ms	554×	body	320	valid
205.0ms	258×	body	160	valid
186.0ms	48×	body	2560	valid