Details

sample509.0ms

Algorithm

intervals

Results

204.0ms	85×	body	1280	valid
89.0ms	46×	body	640	valid
74.0ms	254×	body	80	valid
14.0ms	14×	body	320	valid
6.0ms	2×	body	2560	valid
3.0ms	5×	body	160	valid

simplify4.3s

Counts

1 → 1

Iterations

Iter	Nodes
6	5698
5	805
4	195
3	82
2	53
1	31
0	19

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize98.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (atan2 x.im x.re) y.im)
34.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(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)))

rewrite76.0ms

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:

12.0ms	(* (atan2 x.im x.re) y.im)
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (atan2 x.im x.re) y.im)
49.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
245.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts

72 → 72

Iterations

Iter	Nodes
5	4090
4	1666
3	854
2	430
1	206
0	102

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.1b

localize99.0ms

Local error

Found 4 expressions with local error:

34.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.1b	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

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)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
146.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
72.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
226.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

69 → 69

Iterations

Iter	Nodes
5	4382
4	1355
3	595
2	283
1	151
0	75

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.1b

localize133.0ms

Local error

Found 4 expressions with local error:

34.0b	(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)))
34.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.1b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite114.0ms

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:

12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
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)))
37.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series690.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
219.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
184.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
223.0ms	(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
5	3217
4	1145
3	535
2	268
1	145
0	73

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 20.1b

localize48.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) y.re)
2.3b	(* (atan2 x.im x.re) y.im)
18.3b	(sin (+ (* (log x.im) y.im) (* (atan2 x.im x.re) y.re)))
34.0b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite55.0ms

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:

17.0ms	(* (atan2 x.im x.re) y.re)
11.0ms	(* (atan2 x.im x.re) y.im)
19.0ms	(sin (+ (* (log x.im) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (atan2 x.im x.re) y.re)
18.0ms	(* (atan2 x.im x.re) y.im)
123.0ms	(sin (+ (* (log x.im) y.im) (* (atan2 x.im x.re) y.re)))
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.3s

Counts

75 → 75

Iterations

Iter	Nodes
4	2089
3	1076
2	548
1	254
0	126

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.8b

regimes833.0ms

Accuracy

35.5% (12.6b remaining)

Error of 25.9b against oracle of 13.3b and baseline of 32.8b

bsearch905.0ms

Steps

Iters	Range		Point
4	7.957893929761558e-17	1.578644681612568e-16	1.544354402853649e-16
10	2.1120502566707385e-82	5.585328319567324e-72	5.3514152020060203e-79
7	8.715913468109951e-246	4.909230640994137e-244	1.4263058830387834e-245
9	-2.585959330048096e-19	-7.954193926627051e-25	-2.5472724614357004e-19

simplify23.0ms

Iterations

Iter	Nodes
2	70
1	70
0	54

end0.0ms

sample11.8s

Algorithm

intervals

Results

4.4s	2234×	body	1280	valid
2.9s	7947×	body	80	valid
2.6s	1395×	body	640	valid
1.1s	558×	body	320	valid
212.0ms	42×	body	2560	valid
123.0ms	223×	body	160	valid