Details

Time bar (total: 29.3s)

sample591.0ms

Algorithm
intervals
Results
118.0ms71×body1280valid
109.0ms258×body80valid
38.0ms47×body640valid
16.0ms26×body320valid
2.0ms7×body160valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
01937
13526
26325
39925
423225
5103425
done500025

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
1.0b
(* (atan2 x.im x.re) y.re)
2.1b
(* (atan2 x.im x.re) y.im)
31.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite23.0ms

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*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
1×cos-sum
Counts
4 → 60
Calls
4 calls:
0.0ms
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
7.0ms
(* (atan2 x.im x.re) y.re)
8.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series541.0ms

Counts
4 → 12
Calls
4 calls:
254.0ms
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
19.0ms
(* (atan2 x.im x.re) y.re)
23.0ms
(* (atan2 x.im x.re) y.im)
244.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify4.4s

Counts
72 → 72
Iterations

Useful iterations: 3 (988.0ms)

IterNodesCost
0101729
1182720
2576638
34394630
done5000630

prune738.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.0b

localize47.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (atan2 x.im x.re) y.re)
1.0b
(* (atan2 x.im x.re) y.re)
2.1b
(* (atan2 x.im x.re) y.im)
32.0b
(cos (* (* (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 69
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.re)
14.0ms
(* (atan2 x.im x.re) y.re)
14.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(cos (* (* (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))

series361.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.re)
37.0ms
(* (atan2 x.im x.re) y.re)
35.0ms
(* (atan2 x.im x.re) y.im)
269.0ms
(cos (* (* (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))

simplify6.1s

Counts
81 → 81
Iterations

Useful iterations: 3 (954.0ms)

IterNodesCost
0851008
1161998
2541624
34569588
done5000588

prune781.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.im)
1.0b
(* (atan2 x.im x.re) y.re)
1.9b
(* (* (cbrt y.im) (cbrt y.im)) (atan2 x.im x.re))
31.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-sqr-sqrt
9×add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×cbrt-prod
2×*-commutative unswap-sqr
1×cos-sum pow1/3 fma-udef
Counts
4 → 64
Calls
4 calls:
2.0ms
(cbrt y.im)
14.0ms
(* (atan2 x.im x.re) y.re)
64.0ms
(* (* (cbrt y.im) (cbrt y.im)) (atan2 x.im x.re))
5.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series704.0ms

Counts
4 → 12
Calls
4 calls:
277.0ms
(cbrt y.im)
38.0ms
(* (atan2 x.im x.re) y.re)
132.0ms
(* (* (cbrt y.im) (cbrt y.im)) (atan2 x.im x.re))
257.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts
76 → 76
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0121738
1269722
21372596
done5000589

prune770.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.0b

localize100.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (* (cbrt y.im) (cbrt y.im)) (atan2 x.im x.re))
31.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
31.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
31.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log
7×add-cbrt-cube
6×add-sqr-sqrt
5×add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cos-sum associate-*r* pow-prod-down prod-exp cbrt-unprod fma-udef
1×associate-*l* *-commutative unswap-sqr
Counts
4 → 51
Calls
4 calls:
34.0ms
(* (* (cbrt y.im) (cbrt y.im)) (atan2 x.im x.re))
5.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
5.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
5.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series843.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* (* (cbrt y.im) (cbrt y.im)) (atan2 x.im x.re))
246.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
258.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
231.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.0s

Counts
63 → 63
Iterations

Useful iterations: done (1.0s)

IterNodesCost
080922
1174911
2706796
done5000784

prune722.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.0b

regimes650.0ms

Accuracy

83.4% (0.5b remaining)

Error of 5.9b against oracle of 5.4b and baseline of 8.6b

bsearch4.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
037138
148138
done48138

end0.0ms

sample7.7s

Algorithm
intervals
Results
2.4s1993×body1280valid
2.2s8004×body80valid
1.2s1432×body640valid
894.0ms655×body320valid
144.0ms280×body160valid