Details

sample512.0ms

Algorithm

intervals

Results

226.0ms	45×	body	640	valid
73.0ms	69×	body	1280	valid
72.0ms	257×	body	80	valid
8.0ms	19×	body	320	valid
4.0ms	14×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

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

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize71.0ms

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)
29.4b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite35.0ms

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×	`cos-sum` `log-pow` `fma-udef`

Counts

4 → 77

Calls

4 calls:

7.0ms	(* y.re (log (hypot x.re x.im)))
15.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* y.re (log (hypot x.re x.im)))
30.0ms	(* (atan2 x.im x.re) y.re)
26.0ms	(* (atan2 x.im x.re) y.im)
231.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.0s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1097
1	298
0	146

prune814.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.6b

localize80.0ms

Local error

Found 4 expressions with local error:

3.3b	(cbrt (atan2 x.im x.re))
3.3b	(cbrt (atan2 x.im x.re))
3.3b	(cbrt (atan2 x.im x.re))
29.4b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite9.0ms

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` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 49

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	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(cbrt (atan2 x.im x.re))
44.0ms	(cbrt (atan2 x.im x.re))
51.0ms	(cbrt (atan2 x.im x.re))
237.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
3	1255
2	313
1	119
0	66

prune659.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.6b

localize131.0ms

Local error

Found 4 expressions with local error:

3.3b	(cbrt (atan2 x.im x.re))
3.3b	(cbrt (atan2 x.im x.re))
3.3b	(cbrt (atan2 x.im x.re))
29.4b	(cos (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` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 49

Calls

4 calls:

2.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
1.0ms	(cbrt (atan2 x.im x.re))
4.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(cbrt (atan2 x.im x.re))
52.0ms	(cbrt (atan2 x.im x.re))
49.0ms	(cbrt (atan2 x.im x.re))
179.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
3	1255
2	313
1	119
0	66

prune696.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 3.6b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
0.9b	(* (atan2 x.im x.re) y.re)
1.2b	(* (atan2 x.im x.re) y.im)
29.4b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 68

Calls

4 calls:

4.0ms	(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
6.0ms	(* (atan2 x.im x.re) y.re)
6.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
33.0ms	(* (atan2 x.im x.re) y.re)
35.0ms	(* (atan2 x.im x.re) y.im)
152.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	847
1	243
0	129

prune801.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.6b

regimes469.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	23
1	23
0	19

end0.0ms

sample8.2s

Algorithm

intervals

Results

3.2s	2050×	body	1280	valid
1.6s	7984×	body	80	valid
1.3s	1496×	body	640	valid
1.3s	660×	body	320	valid
156.0ms	295×	body	160	valid