Details

sample827.0ms

Algorithm

intervals

Results

657.0ms	75×	body	1280	valid
45.0ms	257×	body	80	valid
36.0ms	45×	body	640	valid
8.0ms	18×	body	320	valid
3.0ms	9×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1130
4	249
3	99
2	63
1	35
0	19

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
0.9b	(* (atan2 x.im x.re) y.re)
1.2b	(* (atan2 x.im x.re) y.im)
29.6b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
10×	`add-cbrt-cube` `associate-r` `add-exp-log`
9×	`associate-l`
6×	`log-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sin-sum` `log-pow` `fma-udef`

Counts

4 → 77

Calls

4 calls:

7.0ms	(* y.re (log (hypot x.re x.im)))
11.0ms	(* (atan2 x.im x.re) y.re)
8.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* y.re (log (hypot x.re x.im)))
34.0ms	(* (atan2 x.im x.re) y.re)
33.0ms	(* (atan2 x.im x.re) y.im)
207.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify876.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	871
1	270
0	138

prune827.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize68.0ms

Local error

Found 4 expressions with local error:

5.5b	(cbrt (* (atan2 x.im x.re) y.im))
5.5b	(cbrt (* (atan2 x.im x.re) y.im))
5.5b	(cbrt (* (atan2 x.im x.re) y.im))
29.6b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

5.0ms	(cbrt (* (atan2 x.im x.re) y.im))
5.0ms	(cbrt (* (atan2 x.im x.re) y.im))
4.0ms	(cbrt (* (atan2 x.im x.re) y.im))
2.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (* (atan2 x.im x.re) y.im))
101.0ms	(cbrt (* (atan2 x.im x.re) y.im))
102.0ms	(cbrt (* (atan2 x.im x.re) y.im))
222.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.5s

Counts

55 → 55

Iterations

Iter	Nodes
done	5002
4	1845
3	485
2	209
1	121
0	72

prune745.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize169.0ms

Local error

Found 4 expressions with local error:

5.5b	(cbrt (* (atan2 x.im x.re) y.im))
5.5b	(cbrt (* (atan2 x.im x.re) y.im))
5.5b	(cbrt (* (atan2 x.im x.re) y.im))
29.6b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
2.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (* (atan2 x.im x.re) y.im))
98.0ms	(cbrt (* (atan2 x.im x.re) y.im))
93.0ms	(cbrt (* (atan2 x.im x.re) y.im))
164.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts

55 → 55

Iterations

Iter	Nodes
done	5002
4	1845
3	485
2	209
1	121
0	72

prune731.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize108.0ms

Local error

Found 4 expressions with local error:

5.5b	(cbrt (* (atan2 x.im x.re) y.im))
5.5b	(cbrt (* (atan2 x.im x.re) y.im))
5.5b	(cbrt (* (atan2 x.im x.re) y.im))
29.6b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
2.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (* (atan2 x.im x.re) y.im))
95.0ms	(cbrt (* (atan2 x.im x.re) y.im))
101.0ms	(cbrt (* (atan2 x.im x.re) y.im))
176.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts

55 → 55

Iterations

Iter	Nodes
done	5002
4	1845
3	485
2	209
1	121
0	72

prune727.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

regimes548.0ms

Accuracy

0% (0.1b remaining)

Error of 3.4b against oracle of 3.3b and baseline of 3.4b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.0s	2239×	body	1280	valid
2.6s	7959×	body	80	valid
1.9s	1448×	body	640	valid
343.0ms	580×	body	320	valid
97.0ms	40×	body	2560	valid
72.0ms	219×	body	160	valid