Details

sample361.0ms

Algorithm

intervals

Results

84.0ms	255×	body	80	valid
70.0ms	55×	body	1280	valid
40.0ms	47×	body	640	valid
6.0ms	10×	body	320	valid
2.0ms	6×	body	160	valid
2.0ms	1×	body	2560	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	808
4	197
3	82
2	53
1	31
0	19

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize83.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.re)
29.6b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite316.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

8.0ms	(* (atan2 x.im x.re) y.re)
128.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
106.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
68.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (atan2 x.im x.re) y.re)
274.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
74.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
61.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.3s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
4	1995
3	870
2	420
1	206
0	104

prune667.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.6b

localize93.0ms

Local error

Found 4 expressions with local error:

8.0b	(cbrt (* (atan2 x.im x.re) y.re))
29.5b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
16×	`sqrt-prod`
13×	`add-sqr-sqrt`
12×	`cbrt-prod`
11×	`associate-l`
10×	`distribute-lft-out`
9×	`add-cube-cbrt`
6×	`pow1`
4×	`add-cbrt-cube` `sqrt-div` `swap-sqr` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`associate-r`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sin-sum` `flip-+`
1×	`+-commutative` `pow1/3` `*-commutative` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

9.0ms	(cbrt (* (atan2 x.im x.re) y.re))
1.6s	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))
82.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(cbrt (* (atan2 x.im x.re) y.re))
238.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))
52.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
5	4836
4	1614
3	770
2	420
1	234
0	130

prune776.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.6b

localize107.0ms

Local error

Found 4 expressions with local error:

29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
32×	`sqrt-prod`
20×	`distribute-lft-out`
16×	`associate-l`
12×	`add-sqr-sqrt`
8×	`pow1` `sqrt-div` `swap-sqr` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 84

Calls

4 calls:

75.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
70.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
76.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
59.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
47.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
66.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5004
5	3202
4	991
3	432
2	200
1	95
0	41

prune891.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.6b

localize104.0ms

Local error

Found 4 expressions with local error:

29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
59.9b	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

rewrite276.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
24×	`sqrt-prod`
15×	`distribute-lft-out`
12×	`associate-l`
10×	`add-sqr-sqrt`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div` `swap-sqr`
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 → 72

Calls

4 calls:

112.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
83.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
78.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
1.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

series223.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
63.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

simplify2.8s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
5	3325
4	1003
3	441
2	211
1	106
0	50

prune1.4s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 18.6b

regimes630.0ms

Accuracy

76.1% (3.3b remaining)

Error of 22.2b against oracle of 18.9b and baseline of 32.6b

bsearch314.0ms

Steps

Iters	Range		Point
10	-6.011308145746772e-298	1.697267822885472e-307	-1.39623527537587e-310

simplify7.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample11.5s

Algorithm

intervals

Results

5.1s	2157×	body	1280	valid
2.6s	7975×	body	80	valid
2.4s	1384×	body	640	valid
534.0ms	555×	body	320	valid
185.0ms	230×	body	160	valid
154.0ms	42×	body	2560	valid