Details

Time bar (total: 29.7s)

sample1.0s

Algorithm
intervals
Results
678.0ms38×body640valid
127.0ms63×body1280valid
59.0ms253×body80valid
31.0ms8×body160valid
14.0ms20×body320valid

simplify2.8s

Counts
1 → 1
Iterations
IterNodes
done5001
5808
4197
382
253
131
019

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize92.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (atan2 x.im x.re) y.im)
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite52.0ms

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:
6.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(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)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (atan2 x.im x.re) y.im)
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
67.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
265.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts
68 → 68
Iterations
IterNodes
done5001
42098
3914
2415
1199
096

prune544.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 19.6b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (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)
2.4b
(* (atan2 x.im x.re) y.im)
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1
10×*-un-lft-identity add-cube-cbrt
9×associate-*l*
8×add-cbrt-cube add-exp-log
7×add-log-exp
6×associate-*r*
3×exp-prod log-pow sqrt-prod
2×sqrt-pow1 pow1/2 sqrt-div exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
1×rem-sqrt-square sub-neg flip3-+ exp-diff diff-log flip-+
Counts
4 → 69
Calls
4 calls:
32.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
18.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
121.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
33.0ms
(* (atan2 x.im x.re) y.im)
68.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.3s

Counts
81 → 81
Iterations
IterNodes
done5001
44960
31755
2699
1293
0133

prune619.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.4b

localize66.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (atan2 x.im x.re) y.im)
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
6×add-cbrt-cube sqrt-div add-exp-log
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r* associate-*l* flip-+
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 63
Calls
4 calls:
5.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series202.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* (atan2 x.im x.re) y.im)
57.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
62.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.6s

Counts
75 → 75
Iterations
IterNodes
done5003
54886
41875
3815
2357
1153
068

prune792.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.4b

localize174.0ms

Local error

Found 4 expressions with local error:

30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.7b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.7b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log add-log-exp
3×cos-sum sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 39
Calls
4 calls:
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
27.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
15.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series720.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
239.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
205.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
214.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.9s

Counts
51 → 51
Iterations
IterNodes
done5001
53717
41186
3531
2263
1139
068

prune612.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.4b

regimes862.0ms

Accuracy

65.9% (5.4b remaining)

Error of 9.1b against oracle of 3.7b and baseline of 19.6b

bsearch106.0ms

Steps
ItersRangePoint
7
-1.7943355168458415e-304
-7.212192801442115e-306
-7.316830147106014e-306

simplify3.0ms

Iterations
IterNodes
done28
128
021

end0.0ms

sample8.1s

Algorithm
intervals
Results
3.1s2037×body1280valid
2.2s7989×body80valid
1.7s1493×body640valid
457.0ms621×body320valid
125.0ms363×body160valid