Details

Time bar (total: 24.8s)

sample728.0ms

Algorithm
intervals
Results
603.0ms73×body1280valid
30.0ms258×body80valid
17.0ms29×body640valid
9.0ms22×body320valid
4.0ms11×body160valid
2.0ms1×body2560valid

simplify2.3s

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

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* y.re (log (hypot x.re x.im)))
1.1b
(* (atan2 x.im x.re) y.im)
1.8b
(* (atan2 x.im x.re) y.re)
33.6b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite48.0ms

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×sin-sum log-pow fma-udef
Counts
4 → 77
Calls
4 calls:
24.0ms
(* y.re (log (hypot x.re x.im)))
5.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(* y.re (log (hypot x.re x.im)))
19.0ms
(* (atan2 x.im x.re) y.im)
23.0ms
(* (atan2 x.im x.re) y.re)
241.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify834.0ms

Counts
89 → 89
Iterations
IterNodes
done5000
2862
1270
0138

prune770.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.4b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
1.1b
(* (atan2 x.im x.re) y.im)
1.8b
(* (atan2 x.im x.re) y.re)
33.6b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

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×log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×log1p-udef sin-sum log1p-expm1 fma-udef
Counts
4 → 61
Calls
4 calls:
0.0ms
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
11.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series503.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
32.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(* (atan2 x.im x.re) y.re)
197.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts
73 → 73
Iterations
IterNodes
done5001
2777
1217
0114

prune699.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.3b

localize140.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.re)
33.6b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.6b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.6b
(sin (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×sin-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.re)
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series584.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (atan2 x.im x.re) y.re)
175.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
196.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
190.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts
62 → 62
Iterations
IterNodes
done5000
32357
2367
1124
069

prune911.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.3b

localize130.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.re)
33.6b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.6b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.6b
(sin (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 log1p-expm1-u add-log-exp
3×sin-sum associate-*r* associate-*l* fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 50
Calls
4 calls:
11.0ms
(* (atan2 x.im x.re) y.re)
10.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series600.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (atan2 x.im x.re) y.re)
191.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
190.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
190.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.5s

Counts
62 → 62
Iterations
IterNodes
done5000
32357
2367
1124
069

prune804.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.3b

regimes580.0ms

Accuracy

0% (0.2b remaining)

Error of 3.9b against oracle of 3.7b and baseline of 3.9b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done21
121
017

end0.0ms

sample8.5s

Algorithm
intervals
Results
3.7s2111×body1280valid
1.9s1489×body640valid
1.8s7906×body80valid
331.0ms558×body320valid
102.0ms40×body2560valid
99.0ms232×body160valid