Details

sample345.0ms

Algorithm

intervals

Results

90.0ms	53×	body	1280	valid
85.0ms	256×	body	80	valid
39.0ms	16×	body	320	valid
36.0ms	50×	body	640	valid
3.0ms	10×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (66.0ms)

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize69.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.re)
26.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite59.0ms

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:

13.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(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)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (atan2 x.im x.re) y.re)
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(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)))

simplify3.8s

Counts

68 → 68

Iterations

Useful iterations: 3 (345.0ms)

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

prune526.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.8b

localize35.0ms

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))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.8b	(* (atan2 x.im x.re) y.im)
26.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite74.0ms

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:

28.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
25.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
10.0ms	(* (atan2 x.im x.re) y.im)
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
124.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
36.0ms	(* (atan2 x.im x.re) y.im)
69.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify4.4s

Counts

78 → 78

Iterations

Useful iterations: 3 (788.0ms)

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

prune460.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.3b

localize40.0ms

Local error

Found 4 expressions with local error:

26.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cos-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 39

Calls

4 calls:

17.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
37.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
49.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series680.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
232.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
195.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
214.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.4s

Counts

51 → 51

Iterations

Useful iterations: 3 (195.0ms)

Iter	Nodes	Cost
0	68	978
1	139	948
2	274	824
3	543	815
4	1283	815
5	3415	815
done	5001	815

prune525.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.2b

localize56.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (atan2 x.im x.re) y.re)
26.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.8b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.8b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite64.0ms

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:

25.0ms	(* (atan2 x.im x.re) y.re)
10.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(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)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (atan2 x.im x.re) y.re)
42.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
190.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.4s

Counts

68 → 68

Iterations

Useful iterations: 3 (370.0ms)

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

prune527.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 2.2b

regimes461.0ms

Accuracy

68.3% (5.2b remaining)

Error of 8.7b against oracle of 3.6b and baseline of 19.9b

bsearch517.0ms

Steps

Iters	Range	Point
8	-1.7207244416510206e-306	1.6239292071936692e-306	-1.32640354580753e-310
9	-8.166542778182519e-199	-4.731679254084688e-207	-6.9768505035799e-201
7	-8.298483853091135e-39	-3.9783290244921013e-41	-1.279984231756221e-39

Iters

Range

Point

-1.7207244416510206e-306

1.6239292071936692e-306

-1.32640354580753e-310

-8.166542778182519e-199

-4.731679254084688e-207

-6.9768505035799e-201

-8.298483853091135e-39

-3.9783290244921013e-41

-1.279984231756221e-39

simplify9.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	38	77
1	52	69
2	54	69
done	54	69

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.1s	2082×	body	1280	valid
2.0s	7986×	body	80	valid
2.0s	1444×	body	640	valid
366.0ms	687×	body	320	valid
138.0ms	322×	body	160	valid