Details

sample586.0ms

Algorithm

intervals

Results

170.0ms	70×	body	1280	valid
159.0ms	53×	body	640	valid
56.0ms	255×	body	80	valid
41.0ms	11×	body	320	valid
3.0ms	8×	body	160	valid
3.0ms	1×	body	2560	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	808
4	197
3	82
2	53
1	31
0	19

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize75.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.im)
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite101.0ms

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:

14.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (atan2 x.im x.re) y.im)
50.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
62.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
270.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
4	2127
3	906
2	432
1	207
0	102

prune682.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.6b

localize97.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(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)))

rewrite210.0ms

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:

16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
168.0ms	(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)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
62.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
70.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
222.0ms	(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)))

simplify3.0s

Counts

69 → 69

Iterations

Iter	Nodes
done	5004
5	4381
4	1428
3	609
2	285
1	152
0	75

prune710.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.6b

localize70.0ms

Local error

Found 4 expressions with local error:

4.2b	(log (exp (* (atan2 x.im x.re) y.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(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

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

Counts

4 → 56

Calls

4 calls:

6.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(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)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
57.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
213.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.1s

Counts

68 → 68

Iterations

Iter	Nodes
done	5006
5	4469
4	1414
3	626
2	315
1	171
0	94

prune761.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.6b

localize66.0ms

Local error

Found 4 expressions with local error:

4.3b	(log (cbrt (exp (* (atan2 x.im x.re) y.im))))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b	(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

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

Counts

4 → 58

Calls

4 calls:

4.0ms	(log (cbrt (exp (* (atan2 x.im x.re) y.im))))
8.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms	(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)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(log (cbrt (exp (* (atan2 x.im x.re) y.im))))
55.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
60.0ms	(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)))

simplify3.1s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
5	3995
4	1313
3	622
2	323
1	184
0	105

prune733.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 19.6b

regimes608.0ms

Accuracy

76.2% (3.4b remaining)

Error of 22.1b against oracle of 18.7b and baseline of 32.9b

bsearch654.0ms

Steps

Iters	Range	Point
8	-5.100675455252401e-306	1.585521898477689e-306	-1.2253344719312e-312
8	-7.841047903969177e-156	-1.4042593121131706e-158	-4.748647839754185e-157
9	-4.352162551169737e-30	-1.4851173002701437e-39	-1.2685618014437514e-33

Iters

Range

Point

-5.100675455252401e-306

1.585521898477689e-306

-1.2253344719312e-312

-7.841047903969177e-156

-1.4042593121131706e-158

-4.748647839754185e-157

-4.352162551169737e-30

-1.4851173002701437e-39

-1.2685618014437514e-33

simplify28.0ms

Iterations

Iter	Nodes
done	61
1	61
0	47

end0.0ms

sample9.2s

Algorithm

intervals

Results

4.3s	2218×	body	1280	valid
1.9s	1428×	body	640	valid
1.9s	7923×	body	80	valid
388.0ms	570×	body	320	valid
148.0ms	52×	body	2560	valid
86.0ms	229×	body	160	valid