Details

sample437.0ms

Algorithm

intervals

Results

57.0ms	57×	body	1280	valid
21.0ms	257×	body	80	valid
19.0ms	40×	body	640	valid
5.0ms	18×	body	320	valid
2.0ms	10×	body	160	valid
2.0ms	1×	body	2560	valid

simplify932.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.1b

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.re)
28.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite47.0ms

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:

6.0ms	(* (atan2 x.im x.re) y.re)
22.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.re)
161.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
47.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.6s

Counts

68 → 68

Iterations

Useful iterations: 3 (216.0ms)

Iter	Nodes	Cost
0	97	845
1	196	787
2	435	699
3	833	686
4	1667	686
5	4105	686
done	5001	686

prune375.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.2b

localize30.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
28.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
32.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`add-exp-log`
7×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`sqrt-prod`
4×	`sqrt-div` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

23.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
25.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
177.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.6s

Counts

69 → 69

Iterations

Useful iterations: 4 (847.0ms)

Iter	Nodes	Cost
0	109	1040
1	242	979
2	543	815
3	1144	768
4	2506	754
done	5001	754

prune365.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.2b

localize28.0ms

Local error

Found 4 expressions with local error:

32.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.0s

Counts

72 → 72

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	38	852
1	91	744
2	205	680
3	444	656
4	1114	656
5	3182	656
done	5001	656

prune464.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 22.2b

localize27.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (atan2 x.im x.re) y.re)
28.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite39.0ms

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.re)
17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (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)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.5s

Counts

68 → 68

Iterations

Useful iterations: 3 (212.0ms)

Iter	Nodes	Cost
0	97	845
1	196	787
2	435	699
3	833	686
4	1667	686
5	4105	686
done	5001	686

prune304.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 22.2b

regimes401.0ms

Accuracy

72.7% (3.9b remaining)

Error of 22.8b against oracle of 18.9b and baseline of 33.1b

bsearch286.0ms

Steps

Iters	Range	Point
9	-7.480505059669827e-308	8.87221607667086e-302	-5.732555556840644e-309
7	-3.0300923306794334e-295	-6.868082273891393e-297	-2.9056593112647014e-295
5	-2.4132217880656314e-158	-7.832699049707167e-159	-8.17511038994222e-159

Iters

Range

Point

-7.480505059669827e-308

8.87221607667086e-302

-5.732555556840644e-309

-3.0300923306794334e-295

-6.868082273891393e-297

-2.9056593112647014e-295

-2.4132217880656314e-158

-7.832699049707167e-159

-8.17511038994222e-159

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	150
1	58	150
done	58	150

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	2268×	body	1280	valid
662.0ms	7982×	body	80	valid
519.0ms	1328×	body	640	valid
152.0ms	547×	body	320	valid
69.0ms	46×	body	2560	valid
48.0ms	271×	body	160	valid