Details

Time bar (total: 7.9s)

sample439.0ms

Algorithm
intervals
Results
46.0ms76×body1280valid
45.0ms255×body80valid
15.0ms36×body640valid
5.0msbody2560valid
4.0ms16×body320valid
2.0msbody160valid

simplify36.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120
done500120

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.3b

localize24.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (atan2 x.im x.re) y.im)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
pow1 add-cube-cbrt *-un-lft-identity
add-exp-log sqrt-prod add-cbrt-cube
sqrt-div add-log-exp
associate-*r* associate-*l*
rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
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)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series264.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
170.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify74.0ms

Counts
68 → 68
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0196427
1506390
21139386
32509386
45001386
done5001386

prune336.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.1b

localize30.0ms

Local error

Found 4 expressions with local error:

30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
32.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
pow1 add-cube-cbrt *-un-lft-identity
add-exp-log add-cbrt-cube add-log-exp
sin-sum sqrt-prod
sqrt-div
rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 39
Calls
4 calls:
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series500.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
152.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
154.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
154.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify158.0ms

Counts
51 → 51
Iterations

Useful iterations: 4 (51.0ms)

IterNodesCost
0142553
1288487
2611487
31523487
44766486
55002486
done5002486

prune352.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.1b

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (atan2 x.im x.re) y.im)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
pow1 add-cube-cbrt *-un-lft-identity
add-exp-log sqrt-prod add-cbrt-cube
sqrt-div add-log-exp
associate-*r* associate-*l*
rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
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)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (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)))
156.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify73.0ms

Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0196425
1506388
21139386
32509386
45001386
done5001386

prune328.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 19.1b

localize26.0ms

Local error

Found 4 expressions with local error:

12.4b
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
11×add-sqr-sqrt
add-cube-cbrt *-un-lft-identity
pow1 sqrt-prod
add-exp-log sqrt-div add-cbrt-cube add-log-exp
unpow-prod-down cube-prod
rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
cube-mult sin-sum pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 59
Calls
4 calls:
12.0ms
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(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)))

series381.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(cbrt (pow (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))) 3))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
155.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify142.0ms

Counts
71 → 71
Iterations

Useful iterations: 4 (135.0ms)

IterNodesCost
0191729
1493719
21274719
34723719
45001649
done5001649

prune328.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 19.1b

regimes321.0ms

Accuracy

77.2% (3.3b remaining)

Error of 22.6b against oracle of 19.3b and baseline of 33.6b

bsearch125.0ms

Steps
ItersRangePoint
9
-1.2772633849980886e-303
5.690367183293641e-307
-5.101377825655846e-309

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04236
14236
done4236

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s2307×body1280valid
681.0ms7933×body80valid
579.0ms1431×body640valid
158.0ms562×body320valid
77.0ms50×body2560valid
45.0ms247×body160valid