Details

sample364.0ms

Algorithm

intervals

Results

50.0ms	77×	body	1280	valid
25.0ms	265×	body	80	valid
17.0ms	41×	body	640	valid
4.0ms	15×	body	320	valid
2.0ms	11×	body	160	valid
2.0ms	1×	body	2560	valid

simplify344.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	19	37
1	35	26
2	63	25
3	98	25
4	215	25
5	882	25
done	5000	25

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (pow (hypot x.re x.im) y.re) (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
1.1b	(* (atan2 x.im x.re) y.im)
1.2b	(* (atan2 x.im x.re) y.re)
32.1b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-sqr-sqrt`
13×	`add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow-to-exp` `frac-2neg` `sin-sum` `pow-exp` `clear-num` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 75

Calls

4 calls:

6.0ms	(/ (* (pow (hypot x.re x.im) y.re) (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
3.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series602.0ms

Counts

4 → 12

Calls

4 calls:

397.0ms	(/ (* (pow (hypot x.re x.im) y.re) (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
16.0ms	(* (atan2 x.im x.re) y.im)
20.0ms	(* (atan2 x.im x.re) y.re)
169.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify442.0ms

Counts

87 → 87

Iterations

Useful iterations: done (439.0ms)

Iter	Nodes	Cost
0	153	1462
1	337	1430
2	1140	1222
done	5001	1215

prune408.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.4b

localize30.0ms

Local error

Found 4 expressions with local error:

17.8b	(sin (* (atan2 x.im x.re) y.re))
17.8b	(cos (* (atan2 x.im x.re) y.re))
21.8b	(cos (* (log (hypot x.re x.im)) y.im))
21.9b	(sin (* (log (hypot x.re x.im)) y.im))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

2.0ms	(sin (* (atan2 x.im x.re) y.re))
2.0ms	(cos (* (atan2 x.im x.re) y.re))
2.0ms	(cos (* (log (hypot x.re x.im)) y.im))
2.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series329.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sin (* (atan2 x.im x.re) y.re))
44.0ms	(cos (* (atan2 x.im x.re) y.re))
123.0ms	(cos (* (log (hypot x.re x.im)) y.im))
124.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify3.8s

Counts

48 → 48

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	65	431
1	89	425
2	131	371
3	198	368
4	396	368
5	1166	368
done	5001	368

prune358.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize31.0ms

Local error

Found 4 expressions with local error:

17.8b	(sin (* (atan2 x.im x.re) y.re))
17.8b	(cos (* (atan2 x.im x.re) y.re))
21.8b	(cos (* (log (hypot x.re x.im)) y.im))
21.9b	(sin (* (log (hypot x.re x.im)) y.im))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

2.0ms	(sin (* (atan2 x.im x.re) y.re))
2.0ms	(cos (* (atan2 x.im x.re) y.re))
2.0ms	(cos (* (log (hypot x.re x.im)) y.im))
2.0ms	(sin (* (log (hypot x.re x.im)) y.im))

series335.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sin (* (atan2 x.im x.re) y.re))
44.0ms	(cos (* (atan2 x.im x.re) y.re))
125.0ms	(cos (* (log (hypot x.re x.im)) y.im))
129.0ms	(sin (* (log (hypot x.re x.im)) y.im))

simplify3.8s

Counts

48 → 48

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	65	431
1	89	425
2	131	371
3	198	368
4	396	368
5	1166	368
done	5001	368

prune384.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.4b

localize23.0ms

Local error

Found 4 expressions with local error:

8.1b	(cbrt (* (atan2 x.im x.re) y.im))
8.1b	(cbrt (* (atan2 x.im x.re) y.im))
8.1b	(cbrt (* (atan2 x.im x.re) y.im))
32.1b	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`sin-sum` `fma-udef`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt (* (atan2 x.im x.re) y.im))
1.0ms	(cbrt (* (atan2 x.im x.re) y.im))
1.0ms	(cbrt (* (atan2 x.im x.re) y.im))
1.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(cbrt (* (atan2 x.im x.re) y.im))
58.0ms	(cbrt (* (atan2 x.im x.re) y.im))
63.0ms	(cbrt (* (atan2 x.im x.re) y.im))
159.0ms	(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.6s

Counts

55 → 55

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	72	601
1	121	596
2	192	533
3	331	513
4	697	486
5	2184	486
done	5001	483

prune417.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.4b

regimes460.0ms

Accuracy

50.9% (2.5b remaining)

Error of 6.0b against oracle of 3.5b and baseline of 8.6b

bsearch4.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	121
1	50	121
done	50	121

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2221×	body	1280	valid
717.0ms	7941×	body	80	valid
604.0ms	1418×	body	640	valid
158.0ms	550×	body	320	valid
64.0ms	43×	body	2560	valid
44.0ms	234×	body	160	valid