Details

Time bar (total: 17.9s)

sample386.0ms

Algorithm
intervals
Results
45.0ms69×body1280valid
26.0ms263×body80valid
23.0ms55×body640valid
5.0ms17×body320valid
2.0ms11×body160valid
1.0ms1×body2560valid

simplify673.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
01937
13137
25336
38436
420136
585136
done500036

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (atan2 x.im x.re) y.im)
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b
(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)))

rewrite20.0ms

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:
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
168.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.5s

Counts
68 → 68
Iterations

Useful iterations: 3 (153.0ms)

IterNodesCost
098845
1198787
2439699
3871686
41747686
54898686
done5000686

prune342.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.1b

localize30.0ms

Local error

Found 4 expressions with local error:

29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b
(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)))

rewrite78.0ms

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:
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
67.0ms
(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)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
150.0ms
(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)))

simplify2.6s

Counts
65 → 65
Iterations

Useful iterations: 3 (94.0ms)

IterNodesCost
0731155
11501073
2293767
3587718
41459718
54820718
done5000718

prune371.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.1b

localize28.0ms

Local error

Found 4 expressions with local error:

29.2b
(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)))

rewrite22.0ms

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:
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
146.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
150.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
147.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts
51 → 51
Iterations

Useful iterations: 3 (86.0ms)

IterNodesCost
0711005
1144975
2278851
3561842
41234842
53231842
done5000842

prune351.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 17.1b

localize26.0ms

Local error

Found 4 expressions with local error:

9.8b
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
29.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.2b
(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)))

rewrite19.0ms

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:
5.0ms
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
149.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts
71 → 71
Iterations

Useful iterations: 3 (159.0ms)

IterNodesCost
0961505
11921290
24351146
310301132
432241132
done50001132

prune317.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 17.1b

regimes254.0ms

Accuracy

77.9% (3.1b remaining)

Error of 22.3b against oracle of 19.2b and baseline of 33.3b

bsearch166.0ms

Steps
ItersRangePoint
11
-1.0078999971950184e-293
6.598713796727423e-304
-5.36935851968977e-309

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03066
13966
done3966

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.4s2157×body1280valid
721.0ms8048×body80valid
569.0ms1370×body640valid
153.0ms530×body320valid
70.0ms45×body2560valid
43.0ms231×body160valid