Details

sample451.0ms

Algorithm

intervals

Results

184.0ms	67×	body	1280	valid
126.0ms	261×	body	80	valid
40.0ms	28×	body	640	valid
20.0ms	19×	body	320	valid
5.0ms	8×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize73.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.im)
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b	(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:

12.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(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)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (atan2 x.im x.re) y.im)
66.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
272.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	2004
4	2004
3	906
2	432
1	207
0	102

prune875.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.1b

localize93.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite95.0ms

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:

37.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series521.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
61.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
251.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.5s

Counts

73 → 73

Iterations

Iter	Nodes
done	2105
4	2105
3	1151
2	517
1	241
0	111

prune657.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 18.1b

localize111.0ms

Local error

Found 4 expressions with local error:

29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`sin-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 43

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
24.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series678.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(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) y.re)))
183.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
203.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts

55 → 55

Iterations

Iter	Nodes
done	2002
5	2002
4	1189
3	531
2	270
1	146
0	73

prune910.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 18.1b

localize153.0ms

Local error

Found 4 expressions with local error:

29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
54.6b	(posit16->real (real->posit16 (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))))

rewrite36.0ms

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×	`sin-sum` `remove-posit16`

Counts

4 → 50

Calls

4 calls:

7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
0.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
68.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
209.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
106.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))))

simplify1.4s

Counts

62 → 62

Iterations

Iter	Nodes
done	2001
4	2001
3	936
2	408
1	189
0	94

prune1.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 18.1b

regimes827.0ms

Accuracy

77.8% (3.0b remaining)

Error of 22.5b against oracle of 19.5b and baseline of 33.1b

bsearch814.0ms

Steps

Iters	Range		Point
7	6.170731853765547e-18	2.346430924670633e-16	1.0982082920283287e-17
7	2.177847256718336e-142	3.3045862892917206e-140	2.1755487114248848e-140
10	-7.58300102256568e-301	1.7759471587980432e-306	-2.86513786455634e-310

simplify23.0ms

Iterations

Iter	Nodes
done	63
1	63
0	45

end0.0ms

sample13.0s

Algorithm

intervals

Results

4.5s	2148×	body	1280	valid
3.8s	7979×	body	80	valid
2.7s	1436×	body	640	valid
1.1s	562×	body	320	valid
161.0ms	259×	body	160	valid
139.0ms	42×	body	2560	valid