Details

sample321.0ms

Algorithm

intervals

Results

70.0ms	42×	body	640	valid
59.0ms	61×	body	1280	valid
38.0ms	248×	body	80	valid
10.0ms	21×	body	320	valid
3.0ms	8×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1115
4	236
3	85
2	53
1	31
0	19

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize118.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite81.0ms

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:

10.0ms	(* (atan2 x.im x.re) y.im)
22.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (atan2 x.im x.re) y.im)
52.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
279.0ms	(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
3	3046
2	577
1	204
0	99

prune818.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.5b

localize76.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b	(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

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`add-exp-log`
7×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
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:

18.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
62.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
214.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	1765
2	595
1	238
0	108

prune772.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.5b

localize189.0ms

Local error

Found 4 expressions with local error:

5.8b	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

27.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series573.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
47.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
220.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts

59 → 59

Iterations

Iter	Nodes
done	5002
4	3937
3	1135
2	430
1	193
0	95

prune685.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.5b

localize241.0ms

Local error

Found 4 expressions with local error:

5.8b	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

24.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(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)))

series536.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
238.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

59 → 59

Iterations

Iter	Nodes
done	5002
4	3937
3	1135
2	430
1	193
0	95

prune789.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.5b

regimes1.2s

Accuracy

78.5% (3.1b remaining)

Error of 22.1b against oracle of 19.1b and baseline of 33.3b

bsearch236.0ms

Steps

Iters	Range		Point
8	-2.1744703393091546e-306	1.1006474964727005e-306	-5.18925159072013e-310

simplify8.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.3s	2261×	body	1280	valid
2.7s	8009×	body	80	valid
1.3s	1409×	body	640	valid
396.0ms	558×	body	320	valid
201.0ms	244×	body	160	valid
147.0ms	54×	body	2560	valid