Details

sample1.3s

Algorithm

intervals

Results

743.0ms	248×	body	80	valid
103.0ms	61×	body	1280	valid
45.0ms	42×	body	640	valid
15.0ms	21×	body	320	valid
4.0ms	8×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	19	784
1	31	784
2	53	784
3	85	784
4	236	784
5	1115	784
done	5000	784

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize125.0ms

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)))

rewrite58.0ms

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:

11.0ms	(* (atan2 x.im x.re) y.im)
6.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series412.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (atan2 x.im x.re) y.im)
67.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
255.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.7s

Counts

68 → 68

Iterations

Useful iterations: 3 (802.0ms)

Iter	Nodes	Cost
0	99	20213
1	204	19175
2	577	19175
3	3046	19055
done	5001	19055

prune735.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.5b

localize95.0ms

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)))

rewrite88.0ms

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:

35.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
43.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
204.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts

69 → 69

Iterations

Useful iterations: 3 (680.0ms)

Iter	Nodes	Cost
0	108	24053
1	238	21910
2	595	21830
3	1765	21510
done	5000	21510

prune727.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.5b

localize212.0ms

Local error

Found 4 expressions with local error:

5.8b	(cbrt (* (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)))

rewrite48.0ms

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:

13.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
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)))

series578.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
58.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
218.0ms	(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: 3 (364.0ms)

Iter	Nodes	Cost
0	95	21513
1	193	19510
2	430	19510
3	1135	19310
4	3937	19310
done	5002	19310

prune877.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.5b

localize232.0ms

Local error

Found 4 expressions with local error:

5.8b	(cbrt (* (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)))

rewrite79.0ms

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:

26.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
12.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
63.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
209.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts

59 → 59

Iterations

Useful iterations: 3 (363.0ms)

Iter	Nodes	Cost
0	95	21513
1	193	19510
2	430	19510
3	1135	19310
4	3937	19310
done	5002	19310

prune778.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.5b

regimes773.0ms

Accuracy

78.5% (3.1b remaining)

Error of 22.1b against oracle of 19.1b and baseline of 33.3b

bsearch207.0ms

Steps

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

simplify13.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	29	1275
1	39	1275
done	39	1275

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.9s	2261×	body	1280	valid
2.3s	8009×	body	80	valid
1.3s	1409×	body	640	valid
390.0ms	558×	body	320	valid
135.0ms	54×	body	2560	valid
124.0ms	244×	body	160	valid