Details

sample1.2s

Algorithm

intervals

Results

588.0ms	74×	body	1280	valid
277.0ms	260×	body	80	valid
120.0ms	41×	body	640	valid
20.0ms	21×	body	320	valid
6.0ms	9×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize79.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite48.0ms

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×	`cos-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.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (atan2 x.im x.re) y.im)
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
254.0ms	(cos (+ (* (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	911
2	425
1	202
0	99

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

41.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
20.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
11.0ms	(* (atan2 x.im x.re) y.im)
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
126.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
31.0ms	(* (atan2 x.im x.re) y.im)
67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.5s

Counts

85 → 85

Iterations

Iter	Nodes
done	2005
4	2005
3	1753
2	685
1	297
0	137

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.8b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.0b	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

11.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
12.0ms	(* (atan2 x.im x.re) y.im)
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
1.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

simplify1.4s

Counts

78 → 78

Iterations

Iter	Nodes
done	2000
4	2000
3	1360
2	587
1	255
0	120

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.8b

localize89.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0b	(cos (+ (* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
59.8b	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

rewrite63.0ms

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×	`cos-sum` `remove-posit16`

Counts

4 → 50

Calls

4 calls:

19.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0ms	(cos (+ (* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
1.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

series335.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
49.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
171.0ms	(cos (+ (* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
49.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

simplify1.2s

Counts

62 → 62

Iterations

Iter	Nodes
done	2006
5	2006
4	1172
3	542
2	277
1	153
0	79

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

regimes626.0ms

Accuracy

80.8% (5.4b remaining)

Error of 9.6b against oracle of 4.2b and baseline of 32.5b

bsearch561.0ms

Steps

Iters	Range		Point
4	4.4782309392589594e+88	6.748223417676591e+88	4.8030355459155164e+88
8	9.176816685230438e-43	6.631003097907421e-39	1.4989257856483083e-40
8	-6.245387472968191e-307	2.5049244080050127e-307	-4.1355045148069e-310

simplify11.0ms

Iterations

Iter	Nodes
done	56
1	56
0	40

end0.0ms

sample10.9s

Algorithm

intervals

Results

4.0s	2064×	body	1280	valid
2.9s	1426×	body	640	valid
2.5s	8007×	body	80	valid
702.0ms	632×	body	320	valid
262.0ms	303×	body	160	valid