Details

sample556.0ms

Algorithm

intervals

Results

200.0ms	74×	body	1280	valid
89.0ms	260×	body	80	valid
56.0ms	41×	body	640	valid
20.0ms	21×	body	320	valid
7.0ms	9×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

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

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize98.0ms

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)))

rewrite70.0ms

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:

12.0ms	(* (atan2 x.im x.re) y.im)
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(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) y.re)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.im)
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
204.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts

72 → 72

Iterations

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

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.4b

localize38.0ms

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)))

rewrite78.0ms

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:

42.0ms	(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)
8.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
147.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
23.0ms	(* (atan2 x.im x.re) y.im)
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.0s

Counts

85 → 85

Iterations

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

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.8b

localize80.0ms

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)))

rewrite22.0ms

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)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
30.0ms	(* (atan2 x.im x.re) y.im)
52.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

simplify1.3s

Counts

78 → 78

Iterations

Iter	Nodes
4	2188
3	1180
2	581
1	254
0	120

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.8b

localize120.0ms

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)))))

rewrite54.0ms

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:

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

series433.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
74.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
240.0ms	(cos (+ (* (log (posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))
75.0ms	(posit16->real (real->posit16 (sqrt (+ (* x.re x.re) (* x.im x.im)))))

simplify1.9s

Counts

62 → 62

Iterations

Iter	Nodes
5	3197
4	1146
3	536
2	275
1	152
0	79

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

regimes747.0ms

Accuracy

80.8% (5.4b remaining)

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

bsearch564.0ms

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

simplify18.0ms

Iterations

Iter	Nodes
2	54
1	54
0	40

end0.0ms

sample11.1s

Algorithm

intervals

Results

4.1s	2064×	body	1280	valid
3.3s	8007×	body	80	valid
2.0s	1426×	body	640	valid
1.0s	632×	body	320	valid
210.0ms	303×	body	160	valid