Details

Time bar (total: 27.3s)

sample348.0ms

Algorithm
intervals
Results
112.0ms260×body80valid
72.0ms56×body1280valid
35.0ms37×body640valid
12.0ms21×body320valid
4.0ms9×body160valid

simplify2.5s

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.9b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b
(* y.re (log (hypot x.re x.im)))
1.7b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
33.7b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite41.0ms

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:
9.0ms
(* y.re (log (hypot x.re x.im)))
17.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* y.re (log (hypot x.re x.im)))
20.0ms
(* (atan2 x.im x.re) y.re)
24.0ms
(* (atan2 x.im x.re) y.im)
197.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts
93 → 93
Iterations
IterNodes
done5001
32037
2736
1298
0150

prune742.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(* y.re (log (hypot x.re x.im)))
1.7b
(* y.re (atan2 x.im x.re))
2.2b
(* (atan2 x.im x.re) y.im)
33.7b
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.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 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:
17.0ms
(* y.re (log (hypot x.re x.im)))
14.0ms
(* y.re (atan2 x.im x.re))
8.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

series372.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(* y.re (log (hypot x.re x.im)))
12.0ms
(* y.re (atan2 x.im x.re))
19.0ms
(* (atan2 x.im x.re) y.im)
227.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

simplify2.3s

Counts
93 → 93
Iterations
IterNodes
done5001
32653
2759
1303
0151

prune824.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.9b

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b
(log1p (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
1.7b
(* (atan2 x.im x.re) y.re)
2.2b
(* (atan2 x.im x.re) y.im)
33.7b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite37.0ms

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×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum log1p-udef log1p-expm1 fma-udef
Counts
4 → 65
Calls
4 calls:
0.0ms
(log1p (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
10.0ms
(* (atan2 x.im x.re) y.re)
23.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series492.0ms

Counts
4 → 12
Calls
4 calls:
282.0ms
(log1p (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
27.0ms
(* (atan2 x.im x.re) y.re)
22.0ms
(* (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)))

simplify2.5s

Counts
77 → 77
Iterations
IterNodes
done5000
31752
2570
1247
0126

prune727.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.9b

localize91.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (atan2 x.im x.re) y.im)
33.7b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.7b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.7b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite30.0ms

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 insert-posit16 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 → 54
Calls
4 calls:
13.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
6.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series537.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (atan2 x.im x.re) y.im)
173.0ms
(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)))
184.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.7s

Counts
66 → 66
Iterations
IterNodes
done5000
44720
31088
2368
1160
082

prune865.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.9b

regimes474.0ms

Accuracy

0% (0.0b remaining)

Error of 3.4b against oracle of 3.3b and baseline of 3.4b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done28
128
023

end0.0ms

sample8.0s

Algorithm
intervals
Results
2.9s1985×body1280valid
1.9s7951×body80valid
1.7s1414×body640valid
924.0ms637×body320valid
95.0ms275×body160valid