Details

Time bar (total: 30.8s)

sample449.0ms

Algorithm
intervals
Results
197.0ms255×body80valid
63.0ms54×body1280valid
39.0ms49×body640valid
38.0ms14×body320valid
8.0ms3×body2560valid
4.0ms10×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
01937
13137
25336
38236
420136
582936
done500036

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize50.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (atan2 x.im x.re) y.re)
26.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite58.0ms

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:
14.0ms
(* (atan2 x.im x.re) y.re)
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(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)))

series407.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (atan2 x.im x.re) y.re)
68.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
54.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
254.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.2s

Counts
68 → 68
Iterations

Useful iterations: 3 (394.0ms)

IterNodesCost
097845
1196787
2437699
3824686
41659686
54095686
done5001686

prune522.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.1b

localize61.0ms

Local error

Found 4 expressions with local error:

26.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b
(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite257.0ms

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×sin-sum
Counts
4 → 53
Calls
4 calls:
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
225.0ms
(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
252.0ms
(sin (+ (* (log (* (* (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im))))) (cbrt (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts
65 → 65
Iterations

Useful iterations: 3 (188.0ms)

IterNodesCost
0731155
11501073
2293767
3578718
41509718
done5000718

prune742.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.1b

localize81.0ms

Local error

Found 4 expressions with local error:

26.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.7b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.7b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite112.0ms

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)))
21.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
23.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
50.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series738.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(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)))
226.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
218.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.7s

Counts
51 → 51
Iterations

Useful iterations: 3 (188.0ms)

IterNodesCost
0711005
1144975
2279851
3547842
41284842
53417842
done5000842

prune592.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 16.1b

localize40.0ms

Local error

Found 4 expressions with local error:

10.0b
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
26.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.7b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube add-log-exp
3×unpow-prod-down cube-prod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cube-mult sin-sum pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 59
Calls
4 calls:
13.0ms
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
18.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series628.0ms

Counts
4 → 12
Calls
4 calls:
270.0ms
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
75.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
47.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
235.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.4s

Counts
71 → 71
Iterations

Useful iterations: done (3.4s)

IterNodesCost
0961505
11921290
24071146
39301132
431441132
done50001125

prune613.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 16.1b

regimes778.0ms

Accuracy

77.6% (3.1b remaining)

Error of 22.7b against oracle of 19.6b and baseline of 33.5b

bsearch179.0ms

Steps
ItersRangePoint
8
-1.7207244416510206e-306
1.6239292071936692e-306
-5.121219671519224e-309

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03066
13966
done3966

end0.0ms

sample9.2s

Algorithm
intervals
Results
4.1s2272×body1280valid
1.9s7965×body80valid
1.8s1408×body640valid
361.0ms586×body320valid
143.0ms250×body160valid
91.0ms40×body2560valid