Details

sample345.0ms

Algorithm

intervals

Results

31.0ms	52×	body	1280	valid
23.0ms	250×	body	80	valid
21.0ms	52×	body	640	valid
5.0ms	18×	body	320	valid
2.0ms	10×	body	160	valid

simplify660.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	19	37
1	31	37
2	53	36
3	84	36
4	201	36
5	851	36
done	5000	36

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize24.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) y.im)
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b	(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)))

rewrite21.0ms

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:

3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
156.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.5s

Counts

68 → 68

Iterations

Useful iterations: 3 (155.0ms)

Iter	Nodes	Cost
0	95	836
1	193	778
2	438	690
3	879	677
4	1750	677
5	4882	677
done	5000	677

prune323.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 18.4b

localize16.0ms

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)
1.5b	(* (atan2 x.im x.re) y.im)
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

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:

3.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
5.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
92.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.1s

Counts

78 → 78

Iterations

Useful iterations: 3 (320.0ms)

Iter	Nodes	Cost
0	130	1070
1	292	990
2	770	908
3	2031	892
done	5000	892

prune274.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.8b

localize29.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) y.im)
29.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b	(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)))

rewrite17.0ms

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:

3.0ms	(* (atan2 x.im x.re) y.im)
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
136.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.4s

Counts

68 → 68

Iterations

Useful iterations: 3 (148.0ms)

Iter	Nodes	Cost
0	95	836
1	193	778
2	438	690
3	879	677
4	1750	677
5	4882	677
done	5000	677

prune339.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 2.8b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.1b	(* (log (- x.re)) y.re)
1.5b	(* (atan2 x.im x.re) y.im)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`pow1`
7×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `add-cbrt-cube`
6×	`associate-r`
5×	`add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `log-pow` `flip--`

Counts

3 → 49

Calls

3 calls:

3.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
3.0ms	(* (log (- x.re)) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)

series196.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
71.0ms	(* (log (- x.re)) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)

simplify2.6s

Counts

58 → 58

Iterations

Useful iterations: 3 (255.0ms)

Iter	Nodes	Cost
0	103	598
1	222	556
2	584	513
3	1580	510
4	3760	510
done	5000	510

prune156.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 2.8b

regimes228.0ms

Accuracy

65.1% (5.7b remaining)

Error of 9.3b against oracle of 3.6b and baseline of 19.8b

bsearch367.0ms

Steps

Iters	Range		Point
8	1.8793537737921384e-32	3.9771376544151965e-29	5.924531193162435e-30
9	5.073148275473809e-159	2.88733846674046e-150	8.899433436760234e-153
9	-6.152941817396574e-304	2.4251123973937145e-305	2.98637517902405e-310
5	-3.595439683671731e-80	-1.748986179357307e-80	-1.9930388043660413e-80

simplify8.0ms

Iterations

Useful iterations: done (7.0ms)

Iter	Nodes	Cost
0	39	96
1	52	76
2	55	59
3	58	59
done	58	58

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	2039×	body	1280	valid
674.0ms	7988×	body	80	valid
620.0ms	1558×	body	640	valid
185.0ms	664×	body	320	valid
51.0ms	284×	body	160	valid