Details

Time bar (total: 30.7s)

sample1.2s

Algorithm
intervals
Results
751.0ms256×body80valid
138.0ms63×body1280valid
45.0ms45×body640valid
12.0ms21×body320valid
5.0ms11×body160valid

simplify3.3s

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize112.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.im)
27.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.7b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite56.0ms

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:
9.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (atan2 x.im x.re) y.im)
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms
(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)))

simplify2.0s

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

prune639.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.7b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (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)
1.3b
(* (atan2 x.im x.re) y.im)
27.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×*-un-lft-identity associate-*l* add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×associate-*r* add-log-exp
3×log-pow sqrt-prod
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sub-neg flip3-+ flip3-- diff-log flip-+ flip--
Counts
4 → 66
Calls
4 calls:
7.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
15.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
10.0ms
(* (atan2 x.im x.re) y.im)
20.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series355.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
96.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
26.0ms
(* (atan2 x.im x.re) y.im)
52.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.2s

Counts
78 → 78
Iterations
IterNodes
done5002
32099
2745
1303
0131

prune798.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.9b

localize175.0ms

Local error

Found 4 expressions with local error:

27.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.7b
(cos (+ (* (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)))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div
4×add-cbrt-cube add-exp-log add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum
Counts
4 → 53
Calls
4 calls:
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
165.0ms
(cos (+ (* (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)))

series348.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
218.0ms
(cos (+ (* (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)))

simplify3.3s

Counts
65 → 65
Iterations
IterNodes
done5001
54541
41441
3599
2278
1145
070

prune826.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.9b

localize304.0ms

Local error

Found 4 expressions with local error:

27.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.7b
(cos (+ (* (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)))
30.7b
(cos (+ (* (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)))
30.7b
(cos (+ (* (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)))

rewrite452.0ms

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)))
155.0ms
(cos (+ (* (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)))
135.0ms
(cos (+ (* (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)))
153.0ms
(cos (+ (* (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)))

series733.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
213.0ms
(cos (+ (* (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)))
216.0ms
(cos (+ (* (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)))
236.0ms
(cos (+ (* (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)))

simplify3.4s

Counts
51 → 51
Iterations
IterNodes
done5001
54541
41441
3599
2278
1145
070

prune800.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.9b

regimes666.0ms

Accuracy

65.9% (5.6b remaining)

Error of 9.2b against oracle of 3.7b and baseline of 20.0b

bsearch528.0ms

Steps
ItersRangePoint
10
-4.717474720489223e-303
6.137578524759544e-299
-3.3897962259337e-311
5
-1.2241197495985362e-221
-4.639363407720588e-222
-1.1035715812514838e-221
8
-2.4352478824823101e-91
-3.647363321328955e-95
-1.3029490041766688e-91

simplify9.0ms

Iterations
IterNodes
done46
146
037

end0.0ms

sample7.9s

Algorithm
intervals
Results
3.3s1987×body1280valid
2.3s7979×body80valid
1.1s1444×body640valid
517.0ms703×body320valid
144.0ms291×body160valid