Details

Time bar (total: 30.7s)

sample581.0ms

Algorithm
intervals
Results
149.0ms258×body80valid
109.0ms55×body1280valid
41.0ms32×body640valid
16.0ms17×body320valid
6.0ms9×body160valid

simplify2.5s

Counts
1 → 1
Iterations
IterNodes
done5000
5823
4210
395
262
135
019

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b
(* y.re (log (hypot x.re x.im)))
1.0b
(* (atan2 x.im x.re) y.re)
1.3b
(* (atan2 x.im x.re) y.im)
32.6b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

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×cos-sum log-pow fma-udef
Counts
4 → 81
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)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(* y.re (log (hypot x.re x.im)))
25.0ms
(* (atan2 x.im x.re) y.re)
30.0ms
(* (atan2 x.im x.re) y.im)
175.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts
93 → 93
Iterations
IterNodes
done5001
32037
2736
1298
0150

prune855.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.0b

localize101.0ms

Local error

Found 4 expressions with local error:

3.8b
(cbrt (atan2 x.im x.re))
3.8b
(cbrt (atan2 x.im x.re))
3.8b
(cbrt (atan2 x.im x.re))
32.3b
(cos (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))))

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×cos-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
(cos (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))))

series374.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(cbrt (atan2 x.im x.re))
48.0ms
(cbrt (atan2 x.im x.re))
64.0ms
(cbrt (atan2 x.im x.re))
194.0ms
(cos (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))))

simplify2.5s

Counts
65 → 65
Iterations
IterNodes
done5002
42544
3718
2278
1129
070

prune694.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.0b

localize113.0ms

Local error

Found 4 expressions with local error:

18.7b
(sin (* (atan2 x.im x.re) y.re))
19.1b
(cos (* (atan2 x.im x.re) y.re))
22.9b
(sin (* y.im (log (hypot x.re x.im))))
23.0b
(cos (* y.im (log (hypot x.re x.im))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
12×log-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×distribute-rgt-in cos-sum distribute-lft-in sin-sum
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 52
Calls
4 calls:
16.0ms
(sin (* (atan2 x.im x.re) y.re))
16.0ms
(cos (* (atan2 x.im x.re) y.re))
20.0ms
(sin (* y.im (log (hypot x.re x.im))))
27.0ms
(cos (* y.im (log (hypot x.re x.im))))

series407.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sin (* (atan2 x.im x.re) y.re))
66.0ms
(cos (* (atan2 x.im x.re) y.re))
139.0ms
(sin (* y.im (log (hypot x.re x.im))))
159.0ms
(cos (* y.im (log (hypot x.re x.im))))

simplify2.0s

Counts
64 → 64
Iterations
IterNodes
done5000
41441
3559
2280
1188
0134

prune779.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.9b

localize160.0ms

Local error

Found 4 expressions with local error:

22.4b
(cos (* (log (cbrt (hypot x.re x.im))) y.im))
22.4b
(sin (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
22.5b
(sin (* (log (cbrt (hypot x.re x.im))) y.im))
22.9b
(sin (* y.im (log (hypot x.re x.im))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt log-prod *-un-lft-identity sin-sum add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in
Counts
4 → 46
Calls
4 calls:
17.0ms
(cos (* (log (cbrt (hypot x.re x.im))) y.im))
12.0ms
(sin (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
8.0ms
(sin (* (log (cbrt (hypot x.re x.im))) y.im))
14.0ms
(sin (* y.im (log (hypot x.re x.im))))

series914.0ms

Counts
4 → 12
Calls
4 calls:
262.0ms
(cos (* (log (cbrt (hypot x.re x.im))) y.im))
293.0ms
(sin (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.im))
255.0ms
(sin (* (log (cbrt (hypot x.re x.im))) y.im))
105.0ms
(sin (* y.im (log (hypot x.re x.im))))

simplify3.4s

Counts
58 → 58
Iterations
IterNodes
done5000
54832
41621
3688
2340
1201
0136

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.9b

regimes858.0ms

Accuracy

0% (0.2b remaining)

Error of 3.4b against oracle of 3.2b and baseline of 3.4b

bsearch0.0ms

simplify10.0ms

Iterations
IterNodes
done31
131
024

end0.0ms

sample10.6s

Algorithm
intervals
Results
3.9s2023×body1280valid
3.3s7979×body80valid
2.2s1440×body640valid
538.0ms665×body320valid
171.0ms325×body160valid