Details

sample297.0ms

Algorithm

intervals

Results

105.0ms	57×	body	1280	valid
39.0ms	249×	body	80	valid
32.0ms	42×	body	640	valid
15.0ms	25×	body	320	valid
2.0ms	7×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize119.0ms

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)))
33.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite58.0ms

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×	`cos-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)
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (atan2 x.im x.re) y.im)
48.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
223.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
3	2779
2	562
1	199
0	96

prune726.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

16.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
16.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
10.0ms	(* (atan2 x.im x.re) y.im)
19.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
113.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
19.0ms	(* (atan2 x.im x.re) y.im)
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.2s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	953
1	293
0	133

prune707.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))) y.re)
1.7b	(* (atan2 x.im x.re) y.im)
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.2b	(cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

38.0ms	(* (log (cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))) y.re)
10.0ms	(* (atan2 x.im x.re) y.im)
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms	(cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (log (cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))) y.re)
33.0ms	(* (atan2 x.im x.re) y.im)
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
71.0ms	(cbrt (* (sqrt (+ (* x.re x.re) (* x.im x.im))) (+ (* x.re x.re) (* x.im x.im))))

simplify1.1s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	1121
1	342
0	145

prune706.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

localize159.0ms

Local error

Found 4 expressions with local error:

28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.2b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite55.0ms

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×	`cos-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)))
13.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
19.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
15.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series712.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
195.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
215.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
241.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
4	1878
3	652
2	289
1	139
0	68

prune663.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.8b

regimes1.0s

Accuracy

73.8% (5.7b remaining)

Error of 9.1b against oracle of 3.4b and baseline of 25.2b

bsearch707.0ms

Steps

Iters	Range		Point
9	5.1798647897020696e-05	7.830610238325062	0.033937663748779164
10	1.0104396359133627e-102	3.059160399966502e-92	2.3540707404960833e-92
9	-3.405412354409858e-300	-2.1744703393091546e-306	-2.2031366962120984e-306

simplify352.0ms

Iterations

Iter	Nodes
done	55
2	55
1	52
0	38

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.7s	2090×	body	1280	valid
2.6s	8037×	body	80	valid
1.4s	1444×	body	640	valid
368.0ms	646×	body	320	valid
102.0ms	318×	body	160	valid