Details

Time bar (total: 10.1s)

sample264.0ms

Algorithm
intervals
Results
69.0ms247×body80valid
50.0ms65×body1280valid
28.0ms55×body640valid
13.0ms27×body320valid
3.0ms11×body160valid

simplify37.0ms

Counts
1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize59.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (atan2 x.im x.re) y.im)
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.5b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite60.0ms

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:
18.0ms
(* (atan2 x.im x.re) y.im)
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series277.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.im)
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
45.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
172.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Counts
68 → 68

prune337.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.4b

localize19.0ms

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)
1.0b
(* (atan2 x.im x.re) y.im)
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite43.0ms

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:
14.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
12.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
101.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify78.0ms

Counts
78 → 78

prune283.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.4b

localize33.0ms

Local error

Found 4 expressions with local error:

28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.5b
(cos (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum
Counts
4 → 53
Calls
4 calls:
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
63.0ms
(cos (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
163.0ms
(cos (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify67.0ms

Counts
65 → 65

prune385.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

localize41.0ms

Local error

Found 4 expressions with local error:

28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.5b
(cos (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum
Counts
4 → 53
Calls
4 calls:
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
63.0ms
(cos (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series285.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
159.0ms
(cos (+ (* (log (* (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify67.0ms

Counts
65 → 65

prune403.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.3b

regimes243.0ms

Accuracy

66.1% (5.5b remaining)

Error of 8.9b against oracle of 3.3b and baseline of 19.6b

bsearch458.0ms

Steps
ItersRangePoint
6
2.2524128374152173e-253
9.621112749143273e-253
2.2749190715002034e-253
9
-4.4155048382497566e-247
-1.2679007535439676e-253
-2.4650652845751404e-250
8
-6.891939961880446e-81
-1.0333275260154136e-84
-2.988405257106978e-83
7
-0.00044970739729878565
-6.972010091685586e-06
-1.366350780039598e-05

simplify2.0ms

end0.0ms

sample5.8s

Algorithm
intervals
Results
1.8s1949×body1280valid
1.8s8002×body80valid
1.2s1416×body640valid
223.0ms657×body320valid
110.0ms288×body160valid