Details

Time bar (total: 29.3s)

sample377.0ms

Algorithm
intervals
Results
106.0ms257×body80valid
77.0ms69×body1280valid
29.0ms45×body640valid
9.0ms19×body320valid
4.0ms14×body160valid

simplify3.0s

Counts
1 → 1
Iterations
IterNodes
done5001
5808
4197
382
253
131
019

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize58.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.im)
26.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log sqrt-prod
4×sqrt-div add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
5.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series369.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (atan2 x.im x.re) y.im)
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
59.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
245.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.8s

Counts
68 → 68
Iterations
IterNodes
done5001
42098
3914
2415
1199
096

prune655.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.5b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.2b
(* (atan2 x.im x.re) y.im)
26.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1
10×*-un-lft-identity add-cube-cbrt
9×associate-*l*
8×add-cbrt-cube add-exp-log
7×add-log-exp
6×associate-*r*
3×exp-prod log-pow sqrt-prod
2×sqrt-pow1 pow1/2 sqrt-div exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
1×rem-sqrt-square sub-neg flip3-+ exp-diff diff-log flip-+
Counts
4 → 69
Calls
4 calls:
26.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
14.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
5.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
144.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
25.0ms
(* (atan2 x.im x.re) y.im)
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.1s

Counts
81 → 81
Iterations
IterNodes
done5001
44960
31755
2699
1293
0133

prune699.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.0b

localize127.0ms

Local error

Found 4 expressions with local error:

3.3b
(cbrt (atan2 x.im x.re))
26.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b
(cos (+ (* (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
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×pow1 sqrt-prod
4×add-cbrt-cube sqrt-div add-exp-log add-log-exp
3×cbrt-prod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow1/3
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt (atan2 x.im x.re))
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(cbrt (atan2 x.im x.re))
46.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
264.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.3s

Counts
61 → 61
Iterations
IterNodes
done5012
54423
41502
3641
2314
1161
082

prune587.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.0b

localize155.0ms

Local error

Found 4 expressions with local error:

26.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log add-log-exp
3×cos-sum sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 39
Calls
4 calls:
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
25.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
25.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series673.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
170.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
239.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
208.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.3s

Counts
51 → 51
Iterations
IterNodes
done5001
53717
41186
3531
2263
1139
068

prune698.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.0b

regimes734.0ms

Accuracy

80.1% (5.8b remaining)

Error of 9.3b against oracle of 3.5b and baseline of 32.7b

bsearch336.0ms

Steps
ItersRangePoint
10
-8.38583807968836e-299
6.218782843424262e-302
-4.3999011435792e-310
2
-5.403457229871107e-30
-4.784620847803006e-30
-5.3261026821125945e-30
7
-78527178.93455619
-2719823.3768185643
-2759744.904025152

simplify14.0ms

Iterations
IterNodes
done48
148
039

end0.0ms

sample8.2s

Algorithm
intervals
Results
2.8s2050×body1280valid
1.7s1496×body640valid
1.7s7984×body80valid
958.0ms660×body320valid
128.0ms295×body160valid