Details

sample604.0ms

Algorithm

intervals

Results

246.0ms	43×	body	1280	valid
110.0ms	256×	body	80	valid
73.0ms	53×	body	640	valid
15.0ms	16×	body	320	valid
4.0ms	6×	body	160	valid

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
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: 31.9b

localize78.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.re)
29.7b	(cos (+ (* (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)))

rewrite72.0ms

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.re)
21.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (atan2 x.im x.re) y.re)
173.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
54.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
70.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
4	2035
3	854
2	413
1	198
0	97

prune624.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.7b

localize47.0ms

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)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.9b	(* (atan2 x.im x.re) y.im)
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite85.0ms

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:

33.0ms	(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)
12.0ms	(* (atan2 x.im x.re) y.im)
19.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
133.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
49.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.8s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
4	4812
3	1753
2	685
1	297
0	137

prune570.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.1b

localize92.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b	(cos (+ (* (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))))

rewrite68.0ms

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×	`cos-sum` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

24.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0ms	(cos (+ (* (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))))

series469.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
259.0ms	(cos (+ (* (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))))

simplify2.6s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
4	3340
3	1122
2	519
1	240
0	110

prune764.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.1b

localize118.0ms

Local error

Found 4 expressions with local error:

29.7b	(cos (+ (* (log (posit16->real (real->posit16 (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)))
59.9b	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

rewrite57.0ms

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:

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)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(cos (+ (* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
58.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
58.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

simplify2.9s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
5	3694
4	1215
3	548
2	276
1	152
0	79

prune816.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.1b

regimes526.0ms

Accuracy

63.4% (5.8b remaining)

Error of 9.3b against oracle of 3.5b and baseline of 19.4b

bsearch400.0ms

Steps

Iters	Range		Point
6	6.2956859368800825e-205	2.6609176224936472e-204	7.402062416285907e-205
8	-1.1392530337654849e-282	-2.574729366748541e-287	-8.138202357158243e-284

simplify7.0ms

Iterations

Iter	Nodes
done	43
1	43
0	33

end0.0ms

sample10.8s

Algorithm

intervals

Results

4.9s	1961×	body	1280	valid
2.5s	8009×	body	80	valid
2.0s	1444×	body	640	valid
646.0ms	638×	body	320	valid
186.0ms	291×	body	160	valid