Details

Time bar (total: 30.3s)

sample493.0ms

Algorithm
intervals
Results
201.0ms255×body80valid
81.0ms40×body640valid
81.0ms54×body1280valid
10.0ms14×body320valid
4.0ms8×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
01937
13137
25336
38236
420136
582936
done500036

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize77.0ms

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)))

rewrite75.0ms

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:
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (atan2 x.im x.re) y.im)
43.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
50.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
238.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.1s

Counts
68 → 68
Iterations

Useful iterations: 3 (363.0ms)

IterNodesCost
098845
1198787
2442699
3831686
41663686
54083686
done5001686

prune570.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.5b

localize53.0ms

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)))

rewrite117.0ms

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:
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
37.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series787.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
281.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
227.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
213.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.6s

Counts
51 → 51
Iterations

Useful iterations: 3 (188.0ms)

IterNodesCost
0711005
1144975
2279851
3547842
41284842
53417842
done5000842

prune557.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.5b

localize109.0ms

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)))

rewrite89.0ms

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:
23.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
18.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
18.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series1.0s

Counts
4 → 12
Calls
4 calls:
248.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
303.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
257.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
219.0ms
(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 (83.0ms)

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

prune537.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.5b

localize53.0ms

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))

rewrite70.0ms

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:
14.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
22.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
11.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series371.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
233.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
43.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify1.7s

Counts
79 → 79
Iterations

Useful iterations: 3 (371.0ms)

IterNodesCost
01101332
12421008
2480942
31496923
done5001923

prune672.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 18.5b

regimes589.0ms

Accuracy

78.1% (3.1b remaining)

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

bsearch326.0ms

Steps
ItersRangePoint
11
-1.8064072260362412e-290
5.147296625674691e-303
-8.7495601278646e-311

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02965
13965
done3965

end0.0ms

sample9.1s

Algorithm
intervals
Results
3.0s2113×body1280valid
2.4s7966×body80valid
1.7s1370×body640valid
924.0ms587×body320valid
85.0ms237×body160valid
79.0ms30×body2560valid