Details

sample641.0ms

Algorithm

intervals

Results

198.0ms	58×	body	640	valid
137.0ms	70×	body	1280	valid
83.0ms	252×	body	80	valid
64.0ms	27×	body	320	valid
7.0ms	12×	body	160	valid

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
6	5698
5	805
4	195
3	82
2	53
1	31
0	19

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize79.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
30.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.1b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite46.0ms

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:

7.0ms	(* (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)))
24.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (atan2 x.im x.re) y.im)
68.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
66.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
227.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts

72 → 72

Iterations

Iter	Nodes
5	4104
4	1667
3	856
2	423
1	201
0	99

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.7b

localize39.0ms

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)
30.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite77.0ms

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:

25.0ms	(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)
18.0ms	(* (atan2 x.im x.re) y.im)
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series318.0ms

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)
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.3s

Counts

85 → 85

Iterations

Iter	Nodes
4	4065
3	1573
2	686
1	296
0	137

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize94.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
30.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
60.0b	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

14.0ms	(* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
1.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

series244.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
22.0ms	(* (atan2 x.im x.re) y.im)
56.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

simplify1.4s

Counts

76 → 76

Iterations

Iter	Nodes
4	2185
3	1168
2	591
1	251
0	118

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize89.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
30.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.3b	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))
60.0b	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

11.0ms	(* (atan2 x.im x.re) y.im)
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
0.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))
1.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

series589.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (atan2 x.im x.re) y.im)
479.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))
50.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

simplify2.0s

Counts

65 → 65

Iterations

Iter	Nodes
5	3808
4	1516
3	778
2	383
1	176
0	88

prune2.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

regimes891.0ms

Accuracy

74.5% (5.4b remaining)

Error of 9.0b against oracle of 3.6b and baseline of 24.8b

bsearch628.0ms

Steps

Iters	Range		Point
9	-8.73966273530909e-305	7.937286160023527e-307	-4.9836048998994e-312
8	-1.866965122026238e-68	-6.225449561958971e-72	-2.301028981933872e-69
7	-3.6834593536443994e-36	-1.5297920754102757e-37	-1.7493329460610796e-37

simplify10.0ms

Iterations

Iter	Nodes
2	48
1	48
0	40

end0.0ms

sample10.2s

Algorithm

intervals

Results

3.3s	1947×	body	1280	valid
3.1s	7954×	body	80	valid
2.5s	1467×	body	640	valid
575.0ms	581×	body	320	valid
220.0ms	303×	body	160	valid