Details

sample718.0ms

Algorithm

intervals

Results

482.0ms	248×	body	80	valid
86.0ms	61×	body	1280	valid
39.0ms	42×	body	640	valid
13.0ms	21×	body	320	valid
3.0ms	8×	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

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.5b

localize85.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (atan2 x.im x.re) y.im)
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b	(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:

9.0ms	(* (atan2 x.im x.re) y.im)
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms	(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)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (atan2 x.im x.re) y.im)
44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
280.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

68 → 68

Iterations

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

prune710.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.5b

localize128.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

36.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms	(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)))

simplify1.1s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	1765
2	595
1	238
0	108

prune807.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.5b

localize196.0ms

Local error

Found 4 expressions with local error:

28.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b	(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
32.9b	(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
32.9b	(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

11.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms	(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
14.0ms	(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
23.0ms	(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

series719.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
205.0ms	(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
232.0ms	(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
240.0ms	(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

simplify872.0ms

Counts

51 → 51

Iterations

Iter	Nodes
done	5001
4	1883
3	654
2	294
1	144
0	71

prune908.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.5b

localize318.0ms

Local error

Found 4 expressions with local error:

32.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.9b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.9b	(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
32.9b	(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `sin-sum` `add-exp-log` `add-cube-cbrt` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

27.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
14.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
14.0ms	(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
23.0ms	(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

series973.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
241.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
237.0ms	(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
225.0ms	(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

simplify460.0ms

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
4	848
3	238
2	141
1	106
0	69

prune864.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.5b

regimes1.1s

Accuracy

78.3% (3.1b remaining)

Error of 22.1b against oracle of 19.0b and baseline of 33.3b

bsearch257.0ms

Steps

Iters	Range		Point
8	-2.1744703393091546e-306	1.1006474964727005e-306	-5.18925159072013e-310

simplify4.0ms

Iterations

Iter	Nodes
done	43
1	43
0	32

end0.0ms

sample8.7s

Algorithm

intervals

Results

4.2s	2261×	body	1280	valid
1.7s	8009×	body	80	valid
1.6s	1409×	body	640	valid
352.0ms	558×	body	320	valid
184.0ms	54×	body	2560	valid
87.0ms	244×	body	160	valid