Details

sample1.0s

Algorithm

intervals

Results

715.0ms	255×	body	80	valid
123.0ms	61×	body	1280	valid
36.0ms	37×	body	640	valid
14.0ms	19×	body	320	valid
9.0ms	2×	body	2560	valid
1.0ms	3×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

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

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.4b

localize108.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (atan2 x.im x.re) y.im)
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite53.0ms

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:

10.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(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)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (atan2 x.im x.re) y.im)
58.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
222.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
3	3046
2	577
1	204
0	99

prune715.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.2b

localize89.0ms

Local error

Found 4 expressions with local error:

5.3b	(cbrt (* (atan2 x.im x.re) y.im))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `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))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms	(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)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (* (atan2 x.im x.re) y.im))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
195.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify5.7s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
4	3170
3	953
2	401
1	197
0	100

prune719.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.2b

localize145.0ms

Local error

Found 4 expressions with local error:

5.3b	(cbrt (* y.im (atan2 x.im x.re)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `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 (* y.im (atan2 x.im x.re)))
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (* y.im (atan2 x.im x.re)))
54.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
42.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
191.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify5.9s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
4	3170
3	953
2	401
1	197
0	100

prune729.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.2b

localize173.0ms

Local error

Found 4 expressions with local error:

5.3b	(cbrt (* y.im (atan2 x.im x.re)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b	(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

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

5.0ms	(cbrt (* y.im (atan2 x.im x.re)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (* y.im (atan2 x.im x.re)))
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
59.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
225.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify5.4s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
4	3170
3	953
2	401
1	197
0	100

prune800.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.2b

regimes815.0ms

Accuracy

65.3% (4.8b remaining)

Error of 24.2b against oracle of 19.4b and baseline of 33.2b

bsearch815.0ms

Steps

Iters	Range		Point
7	9.365269763508214e-129	2.8759051065913875e-127	1.8089899081997888e-128
9	-3.6833268119706894e-236	-9.18030811337958e-246	-5.907306680385344e-241

simplify22.0ms

Iterations

Iter	Nodes
done	74
3	74
2	72
1	69
0	53

end0.0ms

sample8.0s

Algorithm

intervals

Results

2.7s	2184×	body	1280	valid
2.3s	7979×	body	80	valid
1.3s	1363×	body	640	valid
504.0ms	44×	body	2560	valid
283.0ms	564×	body	320	valid
82.0ms	242×	body	160	valid