Details

Time bar (total: 25.1s)

sample510.0ms

Algorithm
intervals
Results
166.0ms260×body80valid
99.0ms44×body640valid
72.0ms56×body1280valid
10.0ms18×body320valid
4.0ms8×body160valid

simplify2.6s

Counts
1 → 1
Iterations
IterNodes
done5001
51130
4249
399
263
135
019

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b
(* y.re (log (hypot x.re x.im)))
0.8b
(* (atan2 x.im x.re) y.re)
1.8b
(* (atan2 x.im x.re) y.im)
30.8b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite60.0ms

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:
13.0ms
(* y.re (log (hypot x.re x.im)))
10.0ms
(* (atan2 x.im x.re) y.re)
10.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(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:
104.0ms
(* y.re (log (hypot x.re x.im)))
18.0ms
(* (atan2 x.im x.re) y.re)
33.0ms
(* (atan2 x.im x.re) y.im)
218.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify898.0ms

Counts
89 → 89
Iterations
IterNodes
done5001
21097
1298
0146

prune809.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.1b

localize84.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.im)
30.8b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
30.8b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
30.8b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cos-sum associate-*r* associate-*l* fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 50
Calls
4 calls:
6.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series503.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (atan2 x.im x.re) y.im)
167.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
151.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
158.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.8s

Counts
62 → 62
Iterations
IterNodes
done5000
34338
2585
1158
080

prune789.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.1b

localize201.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
30.8b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
30.8b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
30.8b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log
7×add-cbrt-cube
6×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cos-sum associate-*l* pow-prod-down prod-exp cbrt-unprod fma-udef
1×associate-*r* *-commutative unswap-sqr
Counts
4 → 51
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series713.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
190.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
213.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
187.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts
63 → 63
Iterations
IterNodes
done5000
32128
2533
1187
088

prune741.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.0b

localize190.0ms

Local error

Found 4 expressions with local error:

4.4b
(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
30.8b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
30.8b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
30.8b
(cos (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 log1p-expm1-u add-log-exp
3×cos-sum fma-udef
1×cbrt-prod pow1/3
Counts
4 → 41
Calls
4 calls:
16.0ms
(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series768.0ms

Counts
4 → 12
Calls
4 calls:
217.0ms
(cbrt (* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im))))
156.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
224.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
171.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.1s

Counts
53 → 53
Iterations
IterNodes
done5000
31364
2356
1141
075

prune887.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.0b

regimes378.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify16.0ms

Iterations
IterNodes
done34
134
026

end0.0ms

sample8.1s

Algorithm
intervals
Results
2.9s2032×body1280valid
2.1s7972×body80valid
2.0s1517×body640valid
386.0ms679×body320valid
133.0ms309×body160valid