Details

Time bar (total: 42.3s)

sample419.0ms

Algorithm
intervals
Results
116.0ms71×body1280valid
71.0ms20×body320valid
56.0ms257×body80valid
51.0ms48×body640valid
6.0ms2×body2560valid
4.0ms9×body160valid

simplify3.7s

Counts
1 → 1
Iterations
IterNodes
done5001
5823
4210
395
262
135
019

prune73.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.4b

localize93.0ms

Local error

Found 4 expressions with local error:

0.3b
(* y.re (log (hypot x.re x.im)))
1.2b
(* y.re (atan2 x.im x.re))
1.7b
(* (atan2 x.im x.re) y.im)
36.6b
(sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×pow1
10×add-exp-log associate-*r* add-cbrt-cube
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:
18.0ms
(* y.re (log (hypot x.re x.im)))
15.0ms
(* y.re (atan2 x.im x.re))
15.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

series481.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(* y.re (log (hypot x.re x.im)))
21.0ms
(* y.re (atan2 x.im x.re))
33.0ms
(* (atan2 x.im x.re) y.im)
288.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

simplify3.2s

Counts
89 → 89
Iterations
IterNodes
done5001
31928
2633
1266
0138

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

localize103.0ms

Local error

Found 4 expressions with local error:

0.3b
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re)))))
1.2b
(* y.re (atan2 x.im x.re))
1.7b
(* (atan2 x.im x.re) y.im)
36.6b
(sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
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)) (* y.re (atan2 x.im x.re)))))
10.0ms
(* y.re (atan2 x.im x.re))
25.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

series630.0ms

Counts
4 → 12
Calls
4 calls:
328.0ms
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re)))))
23.0ms
(* y.re (atan2 x.im x.re))
38.0ms
(* (atan2 x.im x.re) y.im)
241.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

simplify3.3s

Counts
73 → 73
Iterations
IterNodes
done5000
31617
2540
1224
0115

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.3b

localize118.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (cbrt y.re) (atan2 x.im x.re))
0.8b
(* (* (cbrt y.re) (cbrt y.re)) (* (cbrt y.re) (atan2 x.im x.re)))
1.7b
(* (atan2 x.im x.re) y.im)
36.2b
(sin (fma y.im (log (hypot x.re x.im)) (* (* (cbrt y.re) (cbrt y.re)) (* (cbrt y.re) (atan2 x.im x.re)))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-exp-log
15×add-sqr-sqrt
13×add-cbrt-cube
10×associate-*l* pow-prod-down prod-exp cbrt-unprod
9×add-cube-cbrt *-un-lft-identity
7×associate-*r*
4×cbrt-prod expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative unswap-sqr
1×sin-sum fma-udef
Counts
4 → 78
Calls
4 calls:
18.0ms
(* (cbrt y.re) (atan2 x.im x.re))
81.0ms
(* (* (cbrt y.re) (cbrt y.re)) (* (cbrt y.re) (atan2 x.im x.re)))
14.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (cbrt y.re) (cbrt y.re)) (* (cbrt y.re) (atan2 x.im x.re)))))

series488.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(* (cbrt y.re) (atan2 x.im x.re))
58.0ms
(* (* (cbrt y.re) (cbrt y.re)) (* (cbrt y.re) (atan2 x.im x.re)))
34.0ms
(* (atan2 x.im x.re) y.im)
269.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (cbrt y.re) (cbrt y.re)) (* (cbrt y.re) (atan2 x.im x.re)))))

simplify5.1s

Counts
90 → 90
Iterations
IterNodes
done5001
32519
2841
1294
0131

prune1.2s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.3b

localize134.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
0.7b
(* (cbrt y.re) (atan2 x.im x.re))
1.7b
(* (atan2 x.im x.re) y.im)
36.7b
(sin (fma y.im (log (hypot x.re x.im)) (* (cbrt y.re) (* (cbrt y.re) (* (cbrt y.re) (atan2 x.im x.re))))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
8×pow1 add-exp-log
7×cbrt-prod add-cbrt-cube
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unswap-sqr
2×pow-prod-down prod-exp *-commutative cbrt-unprod
1×sin-sum pow1/3 fma-udef
Counts
4 → 67
Calls
4 calls:
2.0ms
(cbrt y.re)
18.0ms
(* (cbrt y.re) (atan2 x.im x.re))
14.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (cbrt y.re) (* (cbrt y.re) (* (cbrt y.re) (atan2 x.im x.re))))))

series866.0ms

Counts
4 → 12
Calls
4 calls:
403.0ms
(cbrt y.re)
144.0ms
(* (cbrt y.re) (atan2 x.im x.re))
34.0ms
(* (atan2 x.im x.re) y.im)
284.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (cbrt y.re) (* (cbrt y.re) (* (cbrt y.re) (atan2 x.im x.re))))))

simplify5.4s

Counts
79 → 79
Iterations
IterNodes
done5000
43186
31372
2602
1236
0121

prune1.1s

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 3.3b

regimes1.5s

Accuracy

0% (0.2b remaining)

Error of 3.5b against oracle of 3.3b and baseline of 3.5b

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done21
121
017

end0.0ms

sample11.8s

Algorithm
intervals
Results
6.1s2194×body1280valid
2.2s7938×body80valid
2.0s1396×body640valid
412.0ms538×body320valid
230.0ms45×body2560valid
97.0ms225×body160valid