Details

Time bar (total: 25.7s)

sample269.0ms

Algorithm
intervals
Results
108.0ms77×body1280valid
38.0ms259×body80valid
30.0ms48×body640valid
10.0ms27×body320valid
1.0ms4×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
01937
13137
25336
38536
422036
5102336
done500036

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.0b

localize32.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.re)
28.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.9b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log sqrt-prod add-cbrt-cube
4×sqrt-div add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
14.0ms
(* (atan2 x.im x.re) y.re)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (atan2 x.im x.re) y.re)
56.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
254.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.0s

Counts
68 → 68
Iterations

Useful iterations: 3 (645.0ms)

IterNodesCost
094836
1195778
2545692
32847677
done5000677

prune565.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.5b
(* (atan2 x.im x.re) y.im)
28.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-*r* add-log-exp
3×sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-sqrt-square flip3-- flip3-+ diff-log flip-- flip-+
Counts
4 → 66
Calls
4 calls:
9.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
24.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
14.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
120.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
35.0ms
(* (atan2 x.im x.re) y.im)
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify983.0ms

Counts
78 → 78
Iterations

Useful iterations: done (980.0ms)

IterNodesCost
01301070
1300990
21018908
done5000899

prune468.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.5b
(* (atan2 x.im x.re) y.im)
5.0b
(log (exp (* (atan2 x.im x.re) y.im)))
28.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×pow1
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-*r* log-pow
5×add-log-exp
3×log-prod sqrt-prod
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square exp-prod exp-to-pow flip3-+ rem-log-exp flip-+
Counts
4 → 68
Calls
4 calls:
25.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
14.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(log (exp (* (atan2 x.im x.re) y.im)))
18.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
22.0ms
(* (atan2 x.im x.re) y.im)
23.0ms
(log (exp (* (atan2 x.im x.re) y.im)))
55.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify677.0ms

Counts
80 → 80
Iterations

Useful iterations: done (675.0ms)

IterNodesCost
0124858
1260791
2843699
done5001693

prune469.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.6b

localize57.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) y.im)
4.9b
(log (cbrt (exp (* (atan2 x.im x.re) y.im))))
4.9b
(log (cbrt (exp (* (atan2 x.im x.re) y.im))))
28.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×log-prod
11×add-cube-cbrt *-un-lft-identity
9×pow1
8×add-exp-log
6×cbrt-prod add-cbrt-cube
4×log-pow add-log-exp
3×associate-*r* associate-*l* sqrt-prod
2×pow1/3 sqrt-div rem-log-exp
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 65
Calls
4 calls:
14.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(log (cbrt (exp (* (atan2 x.im x.re) y.im))))
8.0ms
(log (cbrt (exp (* (atan2 x.im x.re) y.im))))
15.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (atan2 x.im x.re) y.im)
74.0ms
(log (cbrt (exp (* (atan2 x.im x.re) y.im))))
74.0ms
(log (cbrt (exp (* (atan2 x.im x.re) y.im))))
59.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify6.9s

Counts
77 → 77
Iterations

Useful iterations: 3 (755.0ms)

IterNodesCost
095816
1187772
2572692
34231676
done5000676

prune515.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.6b

regimes388.0ms

Accuracy

67.9% (6.1b remaining)

Error of 9.8b against oracle of 3.7b and baseline of 22.7b

bsearch479.0ms

Steps
ItersRangePoint
10
-3.547288156007854e-304
2.2136711423479e-301
3.3491475839482e-310
7
-4.730577659665696e-107
-1.9943167595264697e-109
-1.975264043799633e-108
8
-0.000687340213703477
-8.195787992305643e-08
-8.347507979969241e-08

simplify10.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
04698
16392
26792
done6792

end0.0ms

sample7.8s

Algorithm
intervals
Results
2.9s1968×body1280valid
2.3s7978×body80valid
1.2s1484×body640valid
459.0ms632×body320valid
91.0ms283×body160valid