Details

sample551.0ms

Algorithm

intervals

Results

153.0ms	80×	body	1280	valid
98.0ms	254×	body	80	valid
89.0ms	48×	body	640	valid
13.0ms	15×	body	320	valid
5.0ms	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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize63.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (atan2 x.im x.re) y.im)
34.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.3b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite38.0ms

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

series304.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (atan2 x.im x.re) y.im)
45.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
184.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

72 → 72

Iterations

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

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.1b

localize50.0ms

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)
2.3b	(* (atan2 x.im x.re) y.im)
34.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite48.0ms

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)))
10.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
108.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
20.0ms	(* (atan2 x.im x.re) y.im)
60.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.9s

Counts

85 → 85

Iterations

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

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.3b	(* 3 (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
2.3b	(* (atan2 x.im x.re) y.im)
34.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`pow1`
12×	`associate-l`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-r`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `log-pow` `*-commutative` `sqrt-prod` `cbrt-unprod` `unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sqrt-div` `associate-*r/`
1×	`rem-sqrt-square` `flip3-+` `flip3--` `flip-+` `flip--`

Counts

4 → 82

Calls

4 calls:

20.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
57.0ms	(* 3 (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
11.0ms	(* (atan2 x.im x.re) y.im)
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
186.0ms	(* 3 (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
33.0ms	(* (atan2 x.im x.re) y.im)
46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.4s

Counts

94 → 94

Iterations

Iter	Nodes
3	2710
2	933
1	376
0	160

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

localize103.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.3b	(* (atan2 x.im x.re) y.im)
34.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.4b	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

rewrite32.0ms

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:

12.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms	(* (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)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
32.0ms	(* (atan2 x.im x.re) y.im)
56.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(posit16->real (real->posit16 (* (atan2 x.im x.re) y.im)))

simplify1.8s

Counts

78 → 78

Iterations

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

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

regimes791.0ms

Accuracy

74.2% (5.4b remaining)

Error of 9.1b against oracle of 3.8b and baseline of 24.6b

bsearch220.0ms

Steps

Iters	Range		Point
8	-5.580170670220212e-306	9.89762762130257e-309	-3.19554071954375e-310

simplify8.0ms

Iterations

Iter	Nodes
2	30
1	30
0	24

end0.0ms

sample11.4s

Algorithm

intervals

Results

4.3s	2042×	body	1280	valid
3.2s	7968×	body	80	valid
2.5s	1466×	body	640	valid
707.0ms	627×	body	320	valid
218.0ms	296×	body	160	valid