Details

sample466.0ms

Algorithm

intervals

Results

54.0ms	85×	body	1280	valid
44.0ms	250×	body	80	valid
23.0ms	54×	body	640	valid
7.0ms	24×	body	320	valid
3.0ms	15×	body	160	valid
2.0ms	1×	body	2560	valid

simplify37.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20
done	5001	20

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.7b

localize26.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (atan2 x.im x.re) y.im)
31.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite51.0ms

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×	`sin-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.im)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
172.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	196	425
1	506	388
2	1139	386
3	2509	386
4	5001	386
done	5001	386

prune331.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.7b

localize32.0ms

Local error

Found 4 expressions with local error:

6.9b	(cbrt (atan2 x.im x.re))
31.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(cbrt (atan2 x.im x.re))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
159.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Counts

61 → 61

Iterations

Useful iterations: 4 (60.0ms)

Iter	Nodes	Cost
0	160	405
1	334	373
2	731	371
3	1992	371
4	5002	369
done	5002	369

prune345.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.7b

localize35.0ms

Local error

Found 4 expressions with local error:

31.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite63.0ms

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×	`sin-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 39

Calls

4 calls:

8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
19.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
18.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series504.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
156.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
154.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
158.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify160.0ms

Counts

51 → 51

Iterations

Useful iterations: 4 (51.0ms)

Iter	Nodes	Cost
0	142	553
1	288	487
2	611	487
3	1523	487
4	4766	486
5	5002	486
done	5002	486

prune385.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.7b

localize44.0ms

Local error

Found 4 expressions with local error:

35.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
35.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `sin-sum` `add-cbrt-cube` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
19.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series624.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
155.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
159.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
152.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify44.0ms

Counts

44 → 44

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	65	604
1	86	520
2	122	520
3	273	520
4	554	520
5	5001	520
done	5001	520

prune338.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.7b

regimes320.0ms

Accuracy

72.4% (4.0b remaining)

Error of 23.1b against oracle of 19.1b and baseline of 33.7b

bsearch344.0ms

Steps

Iters	Range	Point
6	-1.4959250046215287e-302	-2.567506762143674e-303	-2.5962338926543545e-303
8	-1.6719419556606264e-258	-6.066143731619887e-262	-1.6487457515453153e-258
8	-3.994344838543798e-116	-7.483129203032891e-120	-1.0326540582516197e-119

Iters

Range

Point

-1.4959250046215287e-302

-2.567506762143674e-303

-2.5962338926543545e-303

-1.6719419556606264e-258

-6.066143731619887e-262

-1.6487457515453153e-258

-3.994344838543798e-116

-7.483129203032891e-120

-1.0326540582516197e-119

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	104
1	67	104
done	67	104

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	2234×	body	1280	valid
711.0ms	7938×	body	80	valid
582.0ms	1365×	body	640	valid
157.0ms	543×	body	320	valid
66.0ms	44×	body	2560	valid
45.0ms	238×	body	160	valid