Details

Time bar (total: 7.6s)

sample472.0ms

Algorithm
intervals
Results
53.0ms84×body1280valid
40.0ms50×body640valid
25.0ms254×body80valid
8.0ms26×body320valid
3.0ms15×body160valid

simplify37.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120
done500120

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.6b

localize31.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (atan2 x.im x.re) y.im)
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite51.0ms

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:
8.0ms
(* (atan2 x.im x.re) y.im)
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
23.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series264.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
168.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify73.0ms

Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191422
1501385
21134381
32496381
45001381
done5001381

prune335.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.7b

localize17.0ms

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)
2.4b
(* (atan2 x.im x.re) y.im)
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite44.0ms

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:
10.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
14.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
8.0ms
(* (atan2 x.im x.re) y.im)
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series285.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
95.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
22.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify77.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0290540
1897500
22667491
35002491
done5002491

prune286.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize28.0ms

Local error

Found 4 expressions with local error:

6.9b
(cbrt (atan2 x.im x.re))
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube 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))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms
(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)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(cbrt (atan2 x.im x.re))
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
147.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Counts
61 → 61
Iterations

Useful iterations: 4 (59.0ms)

IterNodesCost
0155400
1329368
2726366
31987366
45001364
done5001364

prune343.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

localize31.0ms

Local error

Found 4 expressions with local error:

6.9b
(cbrt (atan2 x.im x.re))
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube 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))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(cbrt (atan2 x.im x.re))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
150.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify63.0ms

Counts
61 → 61
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
0155400
1329368
2726366
31987366
45001366
done5001366

prune380.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.3b

regimes264.0ms

Accuracy

64% (5.8b remaining)

Error of 9.2b against oracle of 3.4b and baseline of 19.4b

bsearch453.0ms

Steps
ItersRangePoint
8
7.841361707165973e-118
1.1600926010518023e-113
2.3587395489387108e-116
10
-1.6589831606554724e-304
6.454285120993577e-301
-2.24511513455111e-307
10
-2.720601240866907e-151
-3.353823364696623e-167
-9.872887954978358e-158
9
-1.582446197482246e-05
-5.83695009860604e-12
-1.9709248512397297e-07

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05245
15845
25845
done5845

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.3s2066×body1280valid
718.0ms7962×body80valid
589.0ms1410×body640valid
182.0ms631×body320valid
56.0ms293×body160valid