Details

Time bar (total: 29.9s)

sample321.0ms

Algorithm
intervals
Results
114.0ms255×body80valid
72.0ms54×body1280valid
40.0ms40×body640valid
9.0ms14×body320valid
3.0ms8×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
01937
13137
25336
38236
420136
582936
done500036

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize75.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (atan2 x.im x.re) y.im)
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite68.0ms

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×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
10.0ms
(* (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)))
36.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (atan2 x.im x.re) y.im)
45.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
296.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.3s

Counts
68 → 68
Iterations

Useful iterations: 3 (401.0ms)

IterNodesCost
098845
1198787
2442699
3831686
41663686
54083686
done5001686

prune530.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.5b

localize95.0ms

Local error

Found 4 expressions with local error:

29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×sin-sum sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 39
Calls
4 calls:
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
42.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
39.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series771.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
228.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
240.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
239.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.3s

Counts
51 → 51
Iterations

Useful iterations: 3 (166.0ms)

IterNodesCost
0711005
1144975
2279851
3547842
41284842
53417842
done5000842

prune613.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.5b

localize136.0ms

Local error

Found 4 expressions with local error:

31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity sin-sum add-cbrt-cube add-log-exp
Counts
4 → 32
Calls
4 calls:
21.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
20.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series983.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
267.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
285.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
228.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.2s

Counts
44 → 44
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0421056
1651052
286908
3121904
4191904
5268904
6372904
7527904
8857904
92277904
done5001904

prune557.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.5b

localize61.0ms

Local error

Found 4 expressions with local error:

29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
39.3b
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
13×add-sqr-sqrt
12×sqrt-prod
11×add-cube-cbrt *-un-lft-identity
6×pow1 unpow-prod-down sqrt-div cube-prod
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ flip-+
2×cube-div rem-sqrt-square cbrt-div sqrt-pow1 pow1/2
1×cube-mult sin-sum pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 67
Calls
4 calls:
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series412.0ms

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)))
264.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
65.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify1.8s

Counts
79 → 79
Iterations

Useful iterations: 3 (342.0ms)

IterNodesCost
01101332
12421008
2480942
31496923
done5001923

prune651.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 18.5b

regimes459.0ms

Accuracy

78.1% (3.1b remaining)

Error of 22.8b against oracle of 19.7b and baseline of 33.9b

bsearch339.0ms

Steps
ItersRangePoint
11
-1.8064072260362412e-290
5.147296625674691e-303
-5.248617845655335e-309

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03066
13966
done3966

end0.0ms

sample9.1s

Algorithm
intervals
Results
3.0s2113×body1280valid
2.2s1370×body640valid
2.0s7966×body80valid
885.0ms587×body320valid
85.0ms237×body160valid
74.0ms30×body2560valid