Details

Time bar (total: 21.5s)

sample472.0ms

Algorithm
intervals
Results
225.0ms67×body1280valid
78.0ms247×body80valid
44.0ms52×body640valid
16.0ms28×body320valid
4.0ms9×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01937
13137
25336
38536
423636
5111536
done500036

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize73.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (atan2 x.im x.re) y.im)
31.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log sqrt-prod
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:
20.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series338.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (atan2 x.im x.re) y.im)
47.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
207.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.7s

Counts
68 → 68
Iterations

Useful iterations: 3 (486.0ms)

IterNodesCost
096836
1199778
2562692
32779677
done5001677

prune636.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.8b

localize46.0ms

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))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.6b
(* (atan2 x.im x.re) y.im)
31.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×*-un-lft-identity associate-*l* add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×associate-*r* add-log-exp
3×log-pow sqrt-prod
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sub-neg flip3-+ flip3-- diff-log flip-+ flip--
Counts
4 → 66
Calls
4 calls:
6.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
10.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
5.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
152.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
27.0ms
(* (atan2 x.im x.re) y.im)
76.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify728.0ms

Counts
78 → 78
Iterations

Useful iterations: done (723.0ms)

IterNodesCost
01311070
1303990
21066908
done5000899

prune661.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
2.6b
(* (atan2 x.im x.re) y.im)
31.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.6b
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×cbrt-prod
14×*-un-lft-identity add-cube-cbrt
10×pow1
9×sqrt-prod
8×add-cbrt-cube associate-*l* add-exp-log
6×unpow-prod-down cube-prod associate-*r*
4×sqrt-div add-log-exp
2×cube-div cbrt-div flip3-+ pow1/3 pow-prod-down prod-exp log-pow *-commutative cbrt-unprod flip-+ unswap-sqr
1×cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 82
Calls
4 calls:
14.0ms
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
10.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series270.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
38.0ms
(* (atan2 x.im x.re) y.im)
48.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
58.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify1.3s

Counts
94 → 94
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01471404
13661042
21788960
done5000956

prune734.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.5b

localize45.0ms

Local error

Found 4 expressions with local error:

7.4b
(cbrt (atan2 x.im x.re))
31.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×pow1 sqrt-prod
4×add-cbrt-cube sqrt-div add-exp-log add-log-exp
3×cbrt-prod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow1/3
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt (atan2 x.im x.re))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series415.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(cbrt (atan2 x.im x.re))
62.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
69.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
221.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.3s

Counts
61 → 61
Iterations

Useful iterations: 3 (169.0ms)

IterNodesCost
082777
1161718
2356638
3851622
42626622
done5002622

prune581.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.5b

regimes828.0ms

Accuracy

73.8% (5.7b remaining)

Error of 9.1b against oracle of 3.5b and baseline of 25.1b

bsearch442.0ms

Steps
ItersRangePoint
9
-2.2002539390802092e-300
5.436781484594434e-309
1.619465862676e-311
4
-7.481903444527903e-59
-3.8127051615001333e-59
-7.361927728922943e-59
6
-6.822245010336324e-16
-1.3563033996188634e-16
-5.135876824507383e-16

simplify17.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
04280
15572
27172
done7172

end0.0ms

sample8.4s

Algorithm
intervals
Results
3.7s2027×body1280valid
2.2s7967×body80valid
1.2s1404×body640valid
378.0ms647×body320valid
105.0ms299×body160valid