Details

sample450.0ms

Algorithm

intervals

Results

51.0ms	81×	body	1280	valid
39.0ms	46×	body	640	valid
24.0ms	257×	body	80	valid
4.0ms	14×	body	320	valid
2.0ms	1×	body	2560	valid
1.0ms	7×	body	160	valid

simplify935.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	19	37
1	31	37
2	53	36
3	82	36
4	201	36
5	829	36
done	5000	36

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.1b

localize25.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (atan2 x.im x.re) y.im)
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.1b	(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

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
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)
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
23.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
175.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.5s

Counts

68 → 68

Iterations

Useful iterations: 3 (215.0ms)

Iter	Nodes	Cost
0	98	845
1	198	787
2	442	699
3	831	686
4	1663	686
5	4083	686
done	5001	686

prune313.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.0b

localize30.0ms

Local error

Found 4 expressions with local error:

6.0b	(cbrt (* (atan2 x.im x.re) y.im))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(cbrt (* (atan2 x.im x.re) y.im))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
156.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.5s

Counts

59 → 59

Iterations

Useful iterations: 4 (395.0ms)

Iter	Nodes	Cost
0	100	803
1	197	747
2	363	666
3	715	647
4	1657	638
5	4497	638
done	5001	638

prune313.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.0b

localize23.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (atan2 x.im x.re) y.im)
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
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)
9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
150.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.5s

Counts

68 → 68

Iterations

Useful iterations: 3 (221.0ms)

Iter	Nodes	Cost
0	98	845
1	198	787
2	442	699
3	831	686
4	1663	686
5	4083	686
done	5001	686

prune303.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 20.0b

localize28.0ms

Local error

Found 4 expressions with local error:

6.0b	(cbrt (* (atan2 x.im x.re) y.im))
6.0b	(cbrt (* (atan2 x.im x.re) y.im))
18.3b	(sin (+ (* (log x.im) y.im) (* (atan2 x.im x.re) y.re)))
30.9b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
15.0ms	(sin (+ (* (log x.im) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(cbrt (* (atan2 x.im x.re) y.im))
61.0ms	(cbrt (* (atan2 x.im x.re) y.im))
97.0ms	(sin (+ (* (log x.im) y.im) (* (atan2 x.im x.re) y.re)))
40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.5s

Counts

53 → 53

Iterations

Useful iterations: 5 (1.4s)

Iter	Nodes	Cost
0	103	624
1	200	594
2	371	530
3	731	509
4	1695	491
5	4650	486
done	5000	486

prune262.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.6b

regimes237.0ms

Accuracy

60.6% (9.0b remaining)

Error of 22.3b against oracle of 13.3b and baseline of 36.1b

bsearch151.0ms

Steps

Iters	Range		Point
10	-1.8181227697780049e-302	6.771944776546714e-304	-5.217492173167827e-309

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	96
1	43	96
done	43	96

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.3s	2164×	body	1280	valid
685.0ms	7971×	body	80	valid
549.0ms	1369×	body	640	valid
145.0ms	519×	body	320	valid
73.0ms	49×	body	2560	valid
42.0ms	233×	body	160	valid