Details

sample467.0ms

Algorithm

intervals

Results

101.0ms	252×	body	80	valid
80.0ms	73×	body	1280	valid
69.0ms	21×	body	320	valid
34.0ms	9×	body	160	valid
26.0ms	39×	body	640	valid
7.0ms	2×	body	2560	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	808
4	197
3	82
2	53
1	31
0	19

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize111.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (atan2 x.im x.re) y.im)
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
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:

5.0ms	(* (atan2 x.im x.re) y.im)
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
47.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
73.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
247.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
4	2165
3	915
2	424
1	204
0	99

prune732.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.8b

localize164.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b	(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)))

rewrite604.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
570.0ms	(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)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
191.0ms	(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)))

simplify3.6s

Counts

65 → 65

Iterations

Iter	Nodes
done	5001
5	4588
4	1438
3	607
2	283
1	150
0	73

prune759.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.7b

localize161.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `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:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
14.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series754.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
216.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
237.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
245.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.1s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
5	3680
4	1190
3	540
2	268
1	144
0	71

prune628.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.7b

localize174.0ms

Local error

Found 4 expressions with local error:

31.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.0b	(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×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `sin-sum` `add-exp-log` `add-cube-cbrt` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

24.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
20.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
14.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series868.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
221.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
220.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
220.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.9s

Counts

44 → 44

Iterations

Iter	Nodes
done	5004
9	2804
8	1835
7	1411
6	991
5	402
4	214
3	127
2	86
1	65
0	42

prune657.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 19.7b

regimes610.0ms

Accuracy

63.3% (5.0b remaining)

Error of 24.8b against oracle of 19.7b and baseline of 33.4b

bsearch426.0ms

Steps

Iters	Range		Point
9	4.8838286355542577e+107	5.435673689154424e+114	4.9510282086413965e+107
7	-7.483069171419468e-243	-4.482378503574263e-244	-4.528905539070836e-244

simplify43.0ms

Iterations

Iter	Nodes
done	54
1	54
0	41

end0.0ms

sample9.0s

Algorithm

intervals

Results

4.5s	2141×	body	1280	valid
1.7s	7945×	body	80	valid
1.5s	1418×	body	640	valid
431.0ms	621×	body	320	valid
175.0ms	51×	body	2560	valid
84.0ms	228×	body	160	valid