Details

sample448.0ms

Algorithm

intervals

Results

156.0ms	68×	body	1280	valid
87.0ms	43×	body	640	valid
79.0ms	263×	body	80	valid
23.0ms	24×	body	320	valid
7.0ms	2×	body	2560	valid
7.0ms	7×	body	160	valid

simplify785.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2008
5	823
4	210
3	95
2	62
1	35
0	19

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.3b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y.re (log (hypot x.re x.im)))
1.5b	(* (atan2 x.im x.re) y.im)
1.7b	(* (atan2 x.im x.re) y.re)
29.9b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite37.0ms

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` `insert-posit16` `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 → 81

Calls

4 calls:

6.0ms	(* y.re (log (hypot x.re x.im)))
13.0ms	(* (atan2 x.im x.re) y.im)
8.0ms	(* (atan2 x.im x.re) y.re)
7.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* y.re (log (hypot x.re x.im)))
33.0ms	(* (atan2 x.im x.re) y.im)
33.0ms	(* (atan2 x.im x.re) y.re)
181.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify923.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	2000
3	1362
2	599
1	268
0	142

prune886.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize100.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.re)
1.5b	(* (atan2 x.im x.re) y.im)
1.5b	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
29.7b	(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `pow1` `add-exp-log`
9×	`add-cbrt-cube`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
2×	`*-commutative` `unswap-sqr`
1×	`sin-sum` `pow1/3` `fma-udef`

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt y.re)
11.0ms	(* (atan2 x.im x.re) y.im)
34.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
5.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series524.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(cbrt y.re)
30.0ms	(* (atan2 x.im x.re) y.im)
111.0ms	(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
180.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify1.0s

Counts

80 → 80

Iterations

Iter	Nodes
done	2001
3	1724
2	662
1	273
0	130

prune689.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.2b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`sin-sum` `fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
2.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

series364.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(cbrt (atan2 x.im x.re))
75.0ms	(cbrt (atan2 x.im x.re))
71.0ms	(cbrt (atan2 x.im x.re))
165.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

simplify801.0ms

Counts

65 → 65

Iterations

Iter	Nodes
done	2001
4	969
3	365
2	178
1	101
0	61

prune633.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.2b

localize87.0ms

Local error

Found 4 expressions with local error:

6.5b	(cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))
6.5b	(cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))
6.5b	(cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))
29.6b	(sin (fma y.im (log (hypot x.re x.im)) (* (* (* (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))) (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))) (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))) (cbrt y.re))))

rewrite41.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`sin-sum` `fma-udef`

Counts

4 → 47

Calls

4 calls:

11.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))
16.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))
11.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))
3.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (* (* (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))) (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))) (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))) (cbrt y.re))))

series868.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))
231.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))
224.0ms	(cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))
209.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (* (* (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))) (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))) (cbrt (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))))) (cbrt y.re))))

simplify838.0ms

Counts

59 → 59

Iterations

Iter	Nodes
done	2000
4	944
3	409
2	231
1	124
0	72

prune719.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 3.2b

regimes647.0ms

Accuracy

0% (0.3b remaining)

Error of 3.7b against oracle of 3.4b and baseline of 3.7b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	23
1	23
0	18

end0.0ms

sample11.9s

Algorithm

intervals

Results

5.1s	2268×	body	1280	valid
2.8s	1424×	body	640	valid
2.6s	7950×	body	80	valid
617.0ms	562×	body	320	valid
126.0ms	214×	body	160	valid
124.0ms	42×	body	2560	valid