Details

Time bar (total: 32.0s)

sample1.0s

Algorithm
intervals
Results
688.0ms257×body80valid
162.0ms69×body1280valid
38.0ms45×body640valid
9.0ms19×body320valid
4.0ms14×body160valid

simplify2.2s

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

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.6b

localize46.0ms

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)))

rewrite45.0ms

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:
14.0ms
(* 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
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(* y.re (log (hypot x.re x.im)))
19.0ms
(* (atan2 x.im x.re) y.re)
29.0ms
(* (atan2 x.im x.re) y.im)
210.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts
89 → 89
Iterations
IterNodes
done5000
32437
2751
1298
0146

prune931.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.6b

localize125.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

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:
5.0ms
(* (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)))
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)))

series599.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.im)
207.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
193.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
179.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.6s

Counts
62 → 62
Iterations
IterNodes
done5005
44310
31085
2373
1158
080

prune864.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.6b

localize183.0ms

Local error

Found 4 expressions with local error:

29.4b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
29.4b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
29.4b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.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
4×add-sqr-sqrt expm1-log1p-u pow1 cos-sum *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef log1p-expm1-u add-log-exp
Counts
4 → 40
Calls
4 calls:
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)))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series803.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
180.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
203.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
218.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.6s

Counts
52 → 52
Iterations
IterNodes
done5001
54139
41481
3488
2195
195
050

prune879.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.6b

localize244.0ms

Local error

Found 4 expressions with local error:

29.4b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
29.4b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
29.4b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.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
4×add-sqr-sqrt expm1-log1p-u pow1 cos-sum *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef log1p-expm1-u add-log-exp
Counts
4 → 40
Calls
4 calls:
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)))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series673.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
180.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
161.0ms
(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)))

simplify3.5s

Counts
52 → 52
Iterations
IterNodes
done5001
54139
41481
3488
2195
195
050

prune830.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.6b

regimes476.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done27
127
021

end0.0ms

sample8.6s

Algorithm
intervals
Results
2.8s2050×body1280valid
2.6s7984×body80valid
1.8s1496×body640valid
585.0ms660×body320valid
163.0ms295×body160valid