Details

sample281.0ms

Algorithm

intervals

Results

83.0ms	257×	body	80	valid
75.0ms	65×	body	1280	valid
32.0ms	43×	body	640	valid
6.0ms	12×	body	320	valid
2.0ms	8×	body	160	valid
2.0ms	1×	body	2560	valid

simplify3.0s

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize65.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (atan2 x.im x.re) y.im)
31.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite79.0ms

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:

7.0ms	(* (atan2 x.im x.re) y.im)
25.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (atan2 x.im x.re) y.im)
207.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
58.0ms	(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

Iter	Nodes
done	5000
3	3204
2	580
1	204
0	99

prune683.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.4b

localize168.0ms

Local error

Found 4 expressions with local error:

31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
58.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
68.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
4	1462
3	528
2	220
1	91
0	38

prune893.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.4b

localize114.0ms

Local error

Found 4 expressions with local error:

3.3b	(log (exp (* (atan2 x.im x.re) y.im)))
31.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

2.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
21.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
226.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.6s

Counts

64 → 64

Iterations

Iter	Nodes
done	5002
4	3038
3	842
2	354
1	168
0	91

prune796.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.4b

localize139.0ms

Local error

Found 4 expressions with local error:

3.4b	(log (cbrt (exp (* (atan2 x.im x.re) y.im))))
31.3b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

3.0ms	(log (cbrt (exp (* (atan2 x.im x.re) y.im))))
20.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(log (cbrt (exp (* (atan2 x.im x.re) y.im))))
253.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
49.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.4s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
4	2207
3	758
2	351
1	181
0	102

prune669.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.4b

regimes798.0ms

Accuracy

79.8% (2.9b remaining)

Error of 22.5b against oracle of 19.6b and baseline of 34.0b

bsearch222.0ms

Steps

Iters	Range		Point
9	-1.8790274713376555e-304	4.616381127637937e-308	2.92295118775524e-310

simplify6.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.6s	2237×	body	1280	valid
2.0s	7951×	body	80	valid
1.8s	1455×	body	640	valid
434.0ms	584×	body	320	valid
138.0ms	235×	body	160	valid
129.0ms	47×	body	2560	valid