Details

sample499.0ms

Algorithm

intervals

Results

138.0ms	66×	body	1280	valid
129.0ms	253×	body	80	valid
56.0ms	42×	body	640	valid
11.0ms	11×	body	320	valid
5.0ms	1×	body	2560	valid
5.0ms	8×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	880
4	215
3	96
2	63
1	35
0	19

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.2b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
0.6b	(* (atan2 x.im x.re) y.im)
0.9b	(* (atan2 x.im x.re) y.re)
30.5b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite41.0ms

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:

14.0ms	(* y.re (log (hypot x.re x.im)))
6.0ms	(* (atan2 x.im x.re) y.im)
12.0ms	(* (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)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* y.re (log (hypot x.re x.im)))
18.0ms	(* (atan2 x.im x.re) y.im)
24.0ms	(* (atan2 x.im x.re) y.re)
190.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.8s

Counts

93 → 93

Iterations

Iter	Nodes
done	5002
4	3756
3	1726
2	679
1	268
0	142

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.1b

localize49.0ms

Local error

Found 4 expressions with local error:

4.8b	(cbrt (* (atan2 x.im x.re) y.im))
4.8b	(cbrt (* (atan2 x.im x.re) y.im))
4.8b	(cbrt (* (atan2 x.im x.re) y.im))
30.5b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

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:

6.0ms	(cbrt (* (atan2 x.im x.re) y.im))
6.0ms	(cbrt (* (atan2 x.im x.re) y.im))
6.0ms	(cbrt (* (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)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(cbrt (* (atan2 x.im x.re) y.im))
105.0ms	(cbrt (* (atan2 x.im x.re) y.im))
92.0ms	(cbrt (* (atan2 x.im x.re) y.im))
157.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts

59 → 59

Iterations

Iter	Nodes
done	5001
5	2619
4	901
3	398
2	202
1	123
0	74

prune748.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.1b

localize53.0ms

Local error

Found 4 expressions with local error:

4.8b	(cbrt (* (atan2 x.im x.re) y.im))
4.8b	(cbrt (* (atan2 x.im x.re) y.im))
4.8b	(cbrt (* (atan2 x.im x.re) y.im))
30.5b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

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:

3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
3.0ms	(cbrt (* (atan2 x.im x.re) y.im))
9.0ms	(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)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(cbrt (* (atan2 x.im x.re) y.im))
67.0ms	(cbrt (* (atan2 x.im x.re) y.im))
75.0ms	(cbrt (* (atan2 x.im x.re) y.im))
172.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.8s

Counts

59 → 59

Iterations

Iter	Nodes
done	5001
5	2619
4	901
3	398
2	202
1	123
0	74

prune885.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.1b

localize100.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y.im)
0.7b	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
0.9b	(* (atan2 x.im x.re) y.re)
30.5b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

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.im)
17.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
6.0ms	(* (atan2 x.im x.re) y.re)
2.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series592.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(cbrt y.im)
100.0ms	(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
29.0ms	(* (atan2 x.im x.re) y.re)
168.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
3	1989
2	698
1	263
0	126

prune765.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.1b

regimes897.0ms

Accuracy

0% (0.1b remaining)

Error of 3.6b against oracle of 3.5b and baseline of 3.6b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	27
1	27
0	21

end0.0ms

sample11.8s

Algorithm

intervals

Results

5.3s	2232×	body	1280	valid
3.1s	7967×	body	80	valid
1.9s	1424×	body	640	valid
660.0ms	584×	body	320	valid
175.0ms	244×	body	160	valid
136.0ms	45×	body	2560	valid