Details

sample366.0ms

Algorithm

intervals

Results

45.0ms	69×	body	1280	valid
25.0ms	263×	body	80	valid
23.0ms	55×	body	640	valid
5.0ms	17×	body	320	valid
2.0ms	11×	body	160	valid
1.0ms	1×	body	2560	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	19	37
1	31	37
2	53	36
3	84	36
4	201	36
5	841	36
done	5000	36

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b	(sin (+ (* (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×	`sin-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)))
8.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
163.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

68 → 68

Iterations

Useful iterations: 3 (182.0ms)

Iter	Nodes	Cost
0	98	845
1	198	787
2	439	699
3	874	686
4	1607	686
5	3657	686
done	5000	686

prune341.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.1b

localize28.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
67.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (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:

35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
145.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.3s

Counts

65 → 65

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	73	1155
1	150	1073
2	293	767
3	583	718
4	1414	718
5	4405	718
done	5001	718

prune356.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.1b

localize26.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

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:

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

series463.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
140.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
142.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
143.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.7s

Counts

51 → 51

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	71	1005
1	144	975
2	278	851
3	557	842
4	1193	842
5	2892	842
done	5000	842

prune350.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 17.1b

localize25.0ms

Local error

Found 4 expressions with local error:

9.8b	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `cube-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cube-mult` `sin-sum` `pow1/3` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 59

Calls

4 calls:

5.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
144.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.7s

Counts

71 → 71

Iterations

Useful iterations: 3 (151.0ms)

Iter	Nodes	Cost
0	96	1505
1	192	1290
2	409	1146
3	929	1132
4	2658	1132
done	5000	1132

prune329.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 17.1b

regimes254.0ms

Accuracy

77.9% (3.1b remaining)

Error of 22.3b against oracle of 19.2b and baseline of 33.3b

bsearch170.0ms

Steps

Iters	Range		Point
11	-1.0078999971950184e-293	6.598713796727423e-304	-5.36935851968977e-309

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	66
1	39	66
done	39	66

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.4s	2157×	body	1280	valid
706.0ms	8048×	body	80	valid
573.0ms	1370×	body	640	valid
152.0ms	530×	body	320	valid
73.0ms	45×	body	2560	valid
44.0ms	231×	body	160	valid