Details

sample426.0ms

Algorithm

intervals

Results

137.0ms	60×	body	1280	valid
53.0ms	50×	body	640	valid
50.0ms	255×	body	80	valid
47.0ms	16×	body	320	valid
3.0ms	7×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	19	37
1	31	37
2	53	36
3	82	36
4	201	36
5	829	36
done	5000	36

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize38.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (atan2 x.im x.re) y.re)
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `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 → 56

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (atan2 x.im x.re) y.re)
56.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
66.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
223.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.2s

Counts

68 → 68

Iterations

Useful iterations: 3 (293.0ms)

Iter	Nodes	Cost
0	94	836
1	191	778
2	430	690
3	823	677
4	1660	677
5	4102	677
done	5000	677

prune530.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (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)
1.4b	(* (atan2 x.im x.re) y.im)
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`pow1`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `add-log-exp`
3×	`sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

4 → 66

Calls

4 calls:

15.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
12.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms	(* (atan2 x.im x.re) y.im)
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
113.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
27.0ms	(* (atan2 x.im x.re) y.im)
46.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify4.7s

Counts

78 → 78

Iterations

Useful iterations: 3 (693.0ms)

Iter	Nodes	Cost
0	130	1070
1	292	990
2	760	908
3	1848	892
4	4492	892
done	5000	892

prune452.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.8b

localize56.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (atan2 x.im x.re) y.re)
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `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 → 56

Calls

4 calls:

7.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (atan2 x.im x.re) y.re)
63.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
236.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.3s

Counts

68 → 68

Iterations

Useful iterations: 3 (401.0ms)

Iter	Nodes	Cost
0	94	836
1	191	778
2	430	690
3	823	677
4	1660	677
5	4102	677
done	5000	677

prune581.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.8b

localize54.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (atan2 x.im x.re) y.re)
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.1b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.6b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`sqrt-div` `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 → 56

Calls

4 calls:

14.0ms	(* (atan2 x.im x.re) y.re)
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (atan2 x.im x.re) y.re)
67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
72.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
166.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.7s

Counts

68 → 68

Iterations

Useful iterations: 3 (316.0ms)

Iter	Nodes	Cost
0	94	836
1	191	778
2	430	690
3	823	677
4	1660	677
5	4102	677
done	5000	677

prune584.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.8b

regimes618.0ms

Accuracy

83.1% (5.0b remaining)

Error of 8.5b against oracle of 3.5b and baseline of 33.2b

bsearch185.0ms

Steps

Iters	Range		Point
8	-1.4022111336343335e-302	-1.2051837121686706e-306	-1.2239707999231867e-306

simplify8.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	33
1	34	29
2	47	29
done	47	29

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.7s	2058×	body	1280	valid
2.3s	8031×	body	80	valid
1.4s	1437×	body	640	valid
428.0ms	607×	body	320	valid
96.0ms	264×	body	160	valid