Details

sample669.0ms

Algorithm

intervals

Results

175.0ms	254×	body	80	valid
159.0ms	71×	body	1280	valid
67.0ms	39×	body	640	valid
43.0ms	8×	body	160	valid
15.0ms	14×	body	320	valid
14.0ms	4×	body	2560	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2059
6	2059
5	808
4	197
3	82
2	53
1	31
0	19

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize70.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (atan2 x.im x.re) y.im)
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite52.0ms

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` `insert-posit16` `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 → 60

Calls

4 calls:

11.0ms	(* (atan2 x.im x.re) y.im)
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(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)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
59.0ms	(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)))

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	2004
4	2004
3	906
2	432
1	207
0	102

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.0b

localize119.0ms

Local error

Found 4 expressions with local error:

31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`sin-sum` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 43

Calls

4 calls:

6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series661.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
227.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
199.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
173.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts

55 → 55

Iterations

Iter	Nodes
done	2002
5	2002
4	1189
3	531
2	270
1	146
0	73

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 17.0b

localize74.0ms

Local error

Found 4 expressions with local error:

2.1b	(* y.re (atan2 x.im x.re))
2.7b	(* (atan2 x.im x.re) y.im)
18.5b	(sin (+ (* y.re (atan2 x.im x.re)) (* (log x.re) y.im)))
31.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
9×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`sqrt-prod`
2×	`sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sin-sum` `flip-+`

Counts

4 → 63

Calls

4 calls:

11.0ms	(* y.re (atan2 x.im x.re))
17.0ms	(* (atan2 x.im x.re) y.im)
28.0ms	(sin (+ (* y.re (atan2 x.im x.re)) (* (log x.re) y.im)))
11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* y.re (atan2 x.im x.re))
22.0ms	(* (atan2 x.im x.re) y.im)
147.0ms	(sin (+ (* y.re (atan2 x.im x.re)) (* (log x.re) y.im)))
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.1s

Counts

75 → 75

Iterations

Iter	Nodes
done	2046
4	2046
3	1285
2	565
1	262
0	128

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log x.re) y.im)
2.1b	(* y.re (atan2 x.im x.re))
2.7b	(* (atan2 x.im x.re) y.im)
18.5b	(sin (+ (* y.re (atan2 x.im x.re)) (* (log x.re) y.im)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`pow1`
10×	`-un-lft-identity` `add-cbrt-cube` `associate-l*` `add-exp-log` `add-cube-cbrt`
9×	`associate-r`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-sum` `log-pow`

Counts

4 → 67

Calls

4 calls:

19.0ms	(* (log x.re) y.im)
11.0ms	(* y.re (atan2 x.im x.re))
7.0ms	(* (atan2 x.im x.re) y.im)
14.0ms	(sin (+ (* y.re (atan2 x.im x.re)) (* (log x.re) y.im)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (log x.re) y.im)
20.0ms	(* y.re (atan2 x.im x.re))
37.0ms	(* (atan2 x.im x.re) y.im)
121.0ms	(sin (+ (* y.re (atan2 x.im x.re)) (* (log x.re) y.im)))

simplify1.2s

Counts

79 → 79

Iterations

Iter	Nodes
done	2000
4	2000
3	1468
2	544
1	240
0	117

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 12.2b

regimes1.3s

Accuracy

62.1% (7.6b remaining)

Error of 20.7b against oracle of 13.1b and baseline of 33.2b

bsearch1.6s

Steps

Iters	Range		Point
8	8718.24681470488	215118504.3831951	9416.095709505209
9	4.195508089265745e-85	1.0563696146442309e-79	3.9300468248158223e-82
9	4.902448394715273e-304	1.536716652908975e-296	3.7259888111147467e-302
9	-5.0845109697337885e-102	-6.772238160253083e-107	-2.8995865521776026e-105

simplify61.0ms

Iterations

Iter	Nodes
done	72
1	72
0	55

end0.0ms

sample12.1s

Algorithm

intervals

Results

4.9s	2155×	body	1280	valid
3.1s	7955×	body	80	valid
2.6s	1395×	body	640	valid
566.0ms	542×	body	320	valid
210.0ms	252×	body	160	valid
156.0ms	49×	body	2560	valid