Details

Time bar (total: 24.8s)

sample596.0ms

Algorithm
intervals
Results
144.0ms57×body1280valid
120.0ms42×body640valid
119.0ms249×body80valid
16.0ms25×body320valid
3.0ms7×body160valid

simplify2.3s

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: 5.5b

localize49.0ms

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)
1.7b
(* (atan2 x.im x.re) y.im)
33.2b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite36.0ms

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)))
7.0ms
(* (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)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* y.re (log (hypot x.re x.im)))
18.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
249.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify961.0ms

Counts
89 → 89
Iterations
IterNodes
done5001
21097
1298
0146

prune811.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize81.0ms

Local error

Found 4 expressions with local error:

0.5b
(expm1 (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)
1.7b
(* (atan2 x.im x.re) y.im)
33.2b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
5×log1p-expm1-u
4×expm1-log1p-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum expm1-log1p fma-udef expm1-udef
Counts
4 → 61
Calls
4 calls:
0.0ms
(expm1 (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)))

series490.0ms

Counts
4 → 12
Calls
4 calls:
252.0ms
(expm1 (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
31.0ms
(* (atan2 x.im x.re) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)
187.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.0s

Counts
73 → 73
Iterations
IterNodes
done5000
2966
1261
0125

prune788.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize128.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
33.2b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.2b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.2b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite13.0ms

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)
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)))

series572.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.im)
150.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
208.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
195.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.9s

Counts
62 → 62
Iterations
IterNodes
done5000
34338
2585
1158
080

prune932.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize98.0ms

Local error

Found 4 expressions with local error:

0.5b
(expm1 (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)
1.7b
(* (atan2 x.im x.re) y.im)
33.2b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
5×log1p-expm1-u
4×expm1-log1p-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum expm1-log1p fma-udef expm1-udef
Counts
4 → 61
Calls
4 calls:
0.0ms
(expm1 (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)
11.0ms
(* (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)))

series491.0ms

Counts
4 → 12
Calls
4 calls:
273.0ms
(expm1 (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)
19.0ms
(* (atan2 x.im x.re) y.im)
166.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts
73 → 73
Iterations
IterNodes
done5000
2966
1261
0125

prune777.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

regimes706.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done27
127
022

end0.0ms

sample8.1s

Algorithm
intervals
Results
2.8s2090×body1280valid
2.1s8037×body80valid
1.8s1444×body640valid
424.0ms646×body320valid
107.0ms318×body160valid