Details

sample415.0ms

Algorithm

intervals

Results

190.0ms	97×	body	1280	valid
43.0ms	254×	body	80	valid
35.0ms	46×	body	640	valid
14.0ms	24×	body	320	valid
4.0ms	9×	body	160	valid
3.0ms	1×	body	2560	valid

simplify1.3s

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: 31.8b

localize38.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (atan2 x.im x.re) y.re)
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite45.0ms

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:

5.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
24.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (atan2 x.im x.re) y.re)
68.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
64.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
228.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
3	2557
2	543
1	200
0	97

prune736.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.5b

localize108.0ms

Local error

Found 4 expressions with local error:

27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(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)))

rewrite159.0ms

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` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum`

Counts

4 → 53

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)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
137.0ms	(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)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
58.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
198.0ms	(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)))

simplify1.1s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
4	2349
3	732
2	308
1	150
0	73

prune745.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.5b

localize146.0ms

Local error

Found 4 expressions with local error:

27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (* (* (cbrt (sqrt (+ (pow x.re 2) (pow x.im 2)))) (cbrt (sqrt (+ (pow x.re 2) (pow x.im 2))))) (cbrt (sqrt (+ (pow x.re 2) (pow x.im 2)))))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite304.0ms

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` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sin-sum`

Counts

4 → 53

Calls

4 calls:

9.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
280.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (* (* (cbrt (sqrt (+ (pow x.re 2) (pow x.im 2)))) (cbrt (sqrt (+ (pow x.re 2) (pow x.im 2))))) (cbrt (sqrt (+ (pow x.re 2) (pow x.im 2)))))))) y.im) (* (atan2 x.im x.re) y.re)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
49.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
264.0ms	(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (* (* (cbrt (sqrt (+ (pow x.re 2) (pow x.im 2)))) (cbrt (sqrt (+ (pow x.re 2) (pow x.im 2))))) (cbrt (sqrt (+ (pow x.re 2) (pow x.im 2)))))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.0s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
3	4213
2	649
1	181
0	81

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.5b

localize500.0ms

Local error

Found 4 expressions with local error:

13.4b	(cbrt (pow (sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* y.re (atan2 x.im x.re)))) 3))
27.2b	(sqrt (+ (pow x.re 2) (pow x.im 2)))
27.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* y.re (atan2 x.im x.re))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`sqrt-prod`
6×	`pow1`
5×	`unpow-prod-down`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
3×	`cube-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out`
1×	`cube-mult` `sin-sum` `pow1/3` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 61

Calls

4 calls:

16.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* y.re (atan2 x.im x.re)))) 3))
29.0ms	(sqrt (+ (pow x.re 2) (pow x.im 2)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* y.re (atan2 x.im x.re))))

series540.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(cbrt (pow (sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* y.re (atan2 x.im x.re)))) 3))
70.0ms	(sqrt (+ (pow x.re 2) (pow x.im 2)))
42.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
227.0ms	(sin (+ (* (log (sqrt (+ (pow x.re 2) (pow x.im 2)))) y.im) (* y.re (atan2 x.im x.re))))

simplify745.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1206
1	282
0	128

prune581.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 17.5b

regimes968.0ms

Accuracy

77.7% (3.2b remaining)

Error of 22.7b against oracle of 19.6b and baseline of 33.7b

bsearch474.0ms

Steps

Iters	Range	Point
10	-2.631585147976807e-302	4.078675660601341e-299	2.1393293584853e-311
4	-9.659196323420146e-149	-4.978406214505162e-149	-5.801236634736126e-149
4	-8.717966691165857e-55	-5.552161494492505e-55	-5.6168325596515585e-55

Iters

Range

Point

-2.631585147976807e-302

4.078675660601341e-299

2.1393293584853e-311

-9.659196323420146e-149

-4.978406214505162e-149

-5.801236634736126e-149

-8.717966691165857e-55

-5.552161494492505e-55

-5.6168325596515585e-55

simplify32.0ms

Iterations

Iter	Nodes
done	68
1	68
0	52

end0.0ms

sample9.0s

Algorithm

intervals

Results

3.4s	2240×	body	1280	valid
1.9s	7952×	body	80	valid
1.7s	1444×	body	640	valid
585.0ms	50×	body	2560	valid
429.0ms	560×	body	320	valid
134.0ms	236×	body	160	valid