Details

sample765.0ms

Algorithm

intervals

Results

134.0ms	68×	body	1280	valid
92.0ms	43×	body	640	valid
73.0ms	263×	body	80	valid
21.0ms	24×	body	320	valid
7.0ms	2×	body	2560	valid
3.0ms	7×	body	160	valid

simplify876.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize75.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.re)
29.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite68.0ms

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:

11.0ms	(* (atan2 x.im x.re) y.re)
32.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (atan2 x.im x.re) y.re)
200.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
63.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
69.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify728.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	2000
3	861
2	414
1	203
0	100

prune821.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.5b

localize81.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
29.7b	(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))))
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite81.0ms

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:

17.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
39.0ms	(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))))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
254.0ms	(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))))
62.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
59.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify826.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	2000
3	1117
2	523
1	245
0	113

prune655.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.5b

localize131.0ms

Local error

Found 4 expressions with local error:

29.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
60.1b	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

rewrite58.0ms

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:

32.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
1.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

series389.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
69.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
69.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

simplify867.0ms

Counts

62 → 62

Iterations

Iter	Nodes
done	2002
4	1207
3	559
2	281
1	157
0	82

prune946.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.5b

localize112.0ms

Local error

Found 4 expressions with local error:

31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
60.1b	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

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)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

series234.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
70.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

simplify741.0ms

Counts

69 → 69

Iterations

Iter	Nodes
done	2002
4	1006
3	447
2	207
1	103
0	48

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.5b

regimes716.0ms

Accuracy

74.7% (3.5b remaining)

Error of 22.9b against oracle of 19.4b and baseline of 33.1b

bsearch362.0ms

Steps

Iters	Range		Point
9	-9.43756197114394e-304	9.26555058109245e-307	2.7722046200884e-310

simplify7.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample12.2s

Algorithm

intervals

Results

5.5s	2268×	body	1280	valid
2.8s	1424×	body	640	valid
2.5s	7950×	body	80	valid
587.0ms	562×	body	320	valid
173.0ms	214×	body	160	valid
130.0ms	42×	body	2560	valid