Details

Time bar (total: 23.2s)

sample397.0ms

Algorithm
intervals
Results
110.0ms256×body80valid
76.0ms56×body1280valid
36.0ms41×body640valid
12.0ms20×body320valid
1.0ms4×body160valid

simplify2.7s

Counts
1 → 1
Iterations
IterNodes
done5000
51115
4236
385
253
131
019

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize92.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (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)))
34.5b
(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)
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
20.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series325.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
52.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
208.0ms
(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
32779
2562
1199
096

prune623.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.4b
(* (atan2 x.im x.re) y.im)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite60.0ms

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:
15.0ms
(exp (- (* (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)
18.0ms
(* (atan2 x.im x.re) y.im)
10.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
139.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
32.0ms
(* (atan2 x.im x.re) y.im)
50.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.1s

Counts
81 → 81
Iterations
IterNodes
done5000
2953
1293
0133

prune789.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize109.0ms

Local error

Found 4 expressions with local error:

5.5b
(cbrt (atan2 x.im x.re))
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.5b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite54.0ms

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))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(cbrt (atan2 x.im x.re))
51.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
44.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
216.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.7s

Counts
61 → 61
Iterations
IterNodes
done5002
42626
3851
2356
1161
082

prune636.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize146.0ms

Local error

Found 4 expressions with local error:

5.5b
(cbrt (atan2 x.im x.re))
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.5b
(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))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms
(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)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(cbrt (atan2 x.im x.re))
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
217.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts
61 → 61
Iterations
IterNodes
done5002
42626
3851
2356
1161
082

prune721.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.9b

regimes639.0ms

Accuracy

81.6% (5.4b remaining)

Error of 9.0b against oracle of 3.6b and baseline of 33.2b

bsearch215.0ms

Steps
ItersRangePoint
9
-8.047445764076778e-305
9.039519750896997e-304
2.00937700819994e-310

simplify8.0ms

Iterations
IterNodes
done30
230
128
021

end0.0ms

sample8.0s

Algorithm
intervals
Results
3.2s2015×body1280valid
1.6s8005×body80valid
1.4s1389×body640valid
871.0ms648×body320valid
144.0ms319×body160valid