Details

sample908.0ms

Algorithm

intervals

Results

138.0ms	75×	body	1280	valid
65.0ms	255×	body	80	valid
63.0ms	50×	body	640	valid
14.0ms	17×	body	320	valid
9.0ms	3×	body	2560	valid
6.0ms	11×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
6	5780
5	821
4	208
3	95
2	62
1	35
0	19

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(* y.re (log (hypot x.re x.im)))
1.3b	(* (atan2 x.im x.re) y.re)
2.0b	(* (atan2 x.im x.re) y.im)
29.4b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite57.0ms

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:

24.0ms	(* y.re (log (hypot x.re x.im)))
11.0ms	(* (atan2 x.im x.re) y.re)
11.0ms	(* (atan2 x.im x.re) y.im)
7.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* y.re (log (hypot x.re x.im)))
31.0ms	(* (atan2 x.im x.re) y.re)
31.0ms	(* (atan2 x.im x.re) y.im)
156.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.7s

Counts

93 → 93

Iterations

Iter	Nodes
5	3262
4	1626
3	898
2	525
1	256
0	142

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize49.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (atan2 x.im x.re))
5.7b	(cbrt (atan2 x.im x.re))
5.7b	(cbrt (atan2 x.im x.re))
29.4b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite11.0ms

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

series273.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(cbrt (atan2 x.im x.re))
48.0ms	(cbrt (atan2 x.im x.re))
48.0ms	(cbrt (atan2 x.im x.re))
130.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify8.7s

Counts

65 → 65

Iterations

Iter	Nodes
6	9836
5	1856
4	544
3	245
2	148
1	92
0	59

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

localize95.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (atan2 x.im x.re))
5.7b	(cbrt (atan2 x.im x.re))
5.7b	(cbrt (atan2 x.im x.re))
29.4b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite6.0ms

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

series360.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(cbrt (atan2 x.im x.re))
64.0ms	(cbrt (atan2 x.im x.re))
76.0ms	(cbrt (atan2 x.im x.re))
163.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify9.2s

Counts

65 → 65

Iterations

Iter	Nodes
6	9836
5	1856
4	544
3	245
2	148
1	92
0	59

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

localize89.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (atan2 x.im x.re))
5.7b	(cbrt (atan2 x.im x.re))
5.7b	(cbrt (atan2 x.im x.re))
29.4b	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite10.0ms

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

series333.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(cbrt (atan2 x.im x.re))
41.0ms	(cbrt (atan2 x.im x.re))
52.0ms	(cbrt (atan2 x.im x.re))
172.0ms	(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify8.6s

Counts

65 → 65

Iterations

Iter	Nodes
6	9836
5	1856
4	544
3	245
2	148
1	92
0	59

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

regimes535.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
2	28
1	28
0	21

end0.0ms

sample11.7s

Algorithm

intervals

Results

5.4s	2205×	body	1280	valid
3.1s	7955×	body	80	valid
1.9s	1403×	body	640	valid
541.0ms	545×	body	320	valid
146.0ms	45×	body	2560	valid
126.0ms	236×	body	160	valid