Details

sample275.0ms

Algorithm

intervals

Results

126.0ms	63×	body	1280	valid
40.0ms	253×	body	80	valid
26.0ms	38×	body	640	valid
10.0ms	20×	body	320	valid
3.0ms	8×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	823
4	210
3	95
2	62
1	35
0	19

prune47.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.6b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y.re (log (hypot x.re x.im)))
1.6b	(* (atan2 x.im x.re) y.re)
2.4b	(* (atan2 x.im x.re) y.im)
31.7b	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite26.0ms

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)))
6.0ms	(* (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)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* y.re (log (hypot x.re x.im)))
22.0ms	(* (atan2 x.im x.re) y.re)
26.0ms	(* (atan2 x.im x.re) y.im)
229.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.5s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
3	2437
2	751
1	298
0	146

prune879.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.6b

localize102.0ms

Local error

Found 4 expressions with local error:

0.4b	(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
1.6b	(* (atan2 x.im x.re) y.re)
2.4b	(* (atan2 x.im x.re) y.im)
31.7b	(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)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
34.0ms	(* (atan2 x.im x.re) y.re)
28.0ms	(* (atan2 x.im x.re) y.im)
161.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
3	1418
2	543
1	241
0	129

prune946.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize100.0ms

Local error

Found 4 expressions with local error:

5.9b	(cbrt (atan2 x.im x.re))
5.9b	(cbrt (atan2 x.im x.re))
5.9b	(cbrt (atan2 x.im x.re))
31.7b	(cos (fma y.im (log (hypot x.re x.im)) (* (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` `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))
2.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(cbrt (atan2 x.im x.re))
72.0ms	(cbrt (atan2 x.im x.re))
59.0ms	(cbrt (atan2 x.im x.re))
173.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.5s

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
4	2360
3	638
2	248
1	119
0	66

prune692.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

localize161.0ms

Local error

Found 4 expressions with local error:

5.9b	(cbrt (atan2 x.im x.re))
5.9b	(cbrt (atan2 x.im x.re))
5.9b	(cbrt (atan2 x.im x.re))
31.7b	(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)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(cbrt (atan2 x.im x.re))
57.0ms	(cbrt (atan2 x.im x.re))
59.0ms	(cbrt (atan2 x.im x.re))
213.0ms	(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
4	2360
3	638
2	248
1	119
0	66

prune683.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

regimes955.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample7.8s

Algorithm

intervals

Results

3.2s	2037×	body	1280	valid
1.7s	7989×	body	80	valid
1.3s	1493×	body	640	valid
842.0ms	621×	body	320	valid
119.0ms	363×	body	160	valid