Details

sample711.0ms

Algorithm

intervals

Results

473.0ms	264×	body	80	valid
82.0ms	64×	body	1280	valid
48.0ms	24×	body	320	valid
42.0ms	45×	body	640	valid
4.0ms	10×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize50.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.re)
30.0b	(cos (+ (* (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)))

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:

9.0ms	(* (atan2 x.im x.re) y.re)
22.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (atan2 x.im x.re) y.re)
188.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
55.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
79.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify913.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	2000
3	854
2	413
1	198
0	97

prune628.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 23.5b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (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)
1.5b	(* (atan2 x.im x.re) y.im)
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite40.0ms

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` `add-log-exp`
4×	`insert-posit16`
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` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

4 → 70

Calls

4 calls:

7.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
9.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
5.0ms	(* (atan2 x.im x.re) y.im)
17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
125.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
22.0ms	(* (atan2 x.im x.re) y.im)
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify638.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	2000
2	752
1	307
0	135

prune525.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.5b	(* (atan2 x.im x.re) y.im)
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.7b	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

rewrite23.0ms

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:

10.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
5.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
24.0ms	(* (atan2 x.im x.re) y.im)
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

simplify902.0ms

Counts

78 → 78

Iterations

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

prune934.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

localize81.0ms

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)))
31.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `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 → 64

Calls

4 calls:

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

series246.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
68.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify799.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	2002
4	995
3	435
2	196
1	92
0	39

prune762.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.3b

regimes775.0ms

Accuracy

75.7% (5.2b remaining)

Error of 8.8b against oracle of 3.6b and baseline of 25.0b

bsearch208.0ms

Steps

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

simplify3.0ms

Iterations

Iter	Nodes
done	28
1	28
0	21

end0.0ms

sample11.2s

Algorithm

intervals

Results

4.4s	2044×	body	1280	valid
2.8s	1473×	body	640	valid
2.7s	7974×	body	80	valid
679.0ms	674×	body	320	valid
159.0ms	295×	body	160	valid