Details

sample387.0ms

Algorithm

intervals

Results

116.0ms	59×	body	640	valid
81.0ms	59×	body	1280	valid
55.0ms	257×	body	80	valid
10.0ms	14×	body	320	valid
4.0ms	9×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	808
4	197
3	82
2	53
1	31
0	19

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize69.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite83.0ms

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:

13.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (atan2 x.im x.re) y.im)
47.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
73.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
245.0ms	(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
done	5000
4	2216
3	911
2	425
1	202
0	99

prune614.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.7b

localize61.0ms

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)
1.6b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite82.0ms

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:

41.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
14.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
11.0ms	(* (atan2 x.im x.re) y.im)
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
139.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
19.0ms	(* (atan2 x.im x.re) y.im)
67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.3s

Counts

85 → 85

Iterations

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

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))) y.re)
1.6b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.6b	(cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

38.0ms	(* (log (cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms	(cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (log (cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))) y.re)
30.0ms	(* (atan2 x.im x.re) y.im)
70.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
45.0ms	(cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))

simplify2.1s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
3	2463
2	858
1	345
0	149

prune711.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.4b

localize95.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite85.0ms

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:

23.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
60.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
208.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.0s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
4	3927
3	1141
2	512
1	236
0	108

prune692.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.4b

regimes586.0ms

Accuracy

73.7% (5.4b remaining)

Error of 9.1b against oracle of 3.7b and baseline of 24.2b

bsearch208.0ms

Steps

Iters	Range		Point
8	-5.100675455252401e-306	1.585521898477689e-306	-1.2253344719312e-312

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample8.2s

Algorithm

intervals

Results

2.8s	7949×	body	80	valid
2.7s	2049×	body	1280	valid
1.7s	1462×	body	640	valid
400.0ms	656×	body	320	valid
106.0ms	304×	body	160	valid