Details

Time bar (total: 7.7s)

sample438.0ms

Algorithm
intervals
Results
64.0ms68×body1280valid
23.0ms256×body80valid
14.0ms35×body640valid
5.0ms15×body320valid
3.0ms2×body2560valid
1.0ms7×body160valid

simplify43.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120
done500120

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.7b

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (atan2 x.im x.re) y.im)
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b
(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
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)))
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)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
176.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify79.0ms

Counts
68 → 68
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0196425
1506388
21139386
32509386
45001386
done5001386

prune327.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.5b

localize27.0ms

Local error

Found 4 expressions with local error:

5.2b
(cbrt (atan2 x.im x.re))
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube add-log-exp
3×cbrt-prod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sin-sum pow1/3
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt (atan2 x.im x.re))
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)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(cbrt (atan2 x.im x.re))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
157.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify67.0ms

Counts
61 → 61
Iterations

Useful iterations: 4 (62.0ms)

IterNodesCost
0160405
1334373
2731371
31992371
45002369
done5002369

prune344.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.5b

localize33.0ms

Local error

Found 4 expressions with local error:

5.2b
(cbrt (atan2 x.im x.re))
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube add-log-exp
3×cbrt-prod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sin-sum pow1/3
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt (atan2 x.im x.re))
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(cbrt (atan2 x.im x.re))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
157.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Counts
61 → 61
Iterations

Useful iterations: 4 (60.0ms)

IterNodesCost
0160405
1334373
2731371
31992371
45002369
done5002369

prune388.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.5b

localize33.0ms

Local error

Found 4 expressions with local error:

29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.4b
(cbrt (+ (* x.re x.re) (* x.im x.im)))
30.4b
(cbrt (+ (* x.re x.re) (* x.im x.im)))
30.6b
(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log cbrt-div add-cbrt-cube add-log-exp
3×flip3-+ sqrt-prod flip-+
2×pow1/3 sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2 sin-sum
Counts
4 → 49
Calls
4 calls:
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms
(cbrt (+ (* x.re x.re) (* x.im x.im)))
5.0ms
(cbrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms
(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

series511.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
93.0ms
(cbrt (+ (* x.re x.re) (* x.im x.im)))
93.0ms
(cbrt (+ (* x.re x.re) (* x.im x.im)))
286.0ms
(sin (+ (* (log (* (fabs (cbrt (+ (* x.re x.re) (* x.im x.im)))) (sqrt (cbrt (+ (* x.re x.re) (* x.im x.im)))))) y.im) (* (atan2 x.im x.re) y.re)))

simplify63.0ms

Counts
61 → 61
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
0226600
1690543
22010539
35002538
done5002538

prune386.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.4b

regimes337.0ms

Accuracy

77.4% (3.1b remaining)

Error of 23.3b against oracle of 20.2b and baseline of 33.9b

bsearch85.0ms

Steps
ItersRangePoint
5
-3.438365405825084e-301
-1.1703177744694063e-301
-1.1934760330154431e-301

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04765
14765
done4765

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s2191×body1280valid
703.0ms7935×body80valid
588.0ms1428×body640valid
158.0ms557×body320valid
95.0ms62×body2560valid
43.0ms231×body160valid