Details

Time bar (total: 23.2s)

sample355.0ms

Algorithm
intervals
Results
106.0ms252×body80valid
93.0ms47×body1280valid
31.0ms35×body640valid
10.0ms16×body320valid
3.0ms7×body160valid

simplify1.6s

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

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.2b

localize51.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.re)
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite84.0ms

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×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
11.0ms
(* (atan2 x.im x.re) y.re)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series439.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (atan2 x.im x.re) y.re)
67.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
70.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
271.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts
68 → 68
Iterations
IterNodes
done5000
32557
2543
1200
097

prune666.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.3b

localize92.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (atan2 x.im x.re) y.im)
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt y.re) (* (atan2 x.im x.re) (cbrt y.re))) (cbrt y.re))))

rewrite68.0ms

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×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
6.0ms
(* (atan2 x.im x.re) y.im)
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt y.re) (* (atan2 x.im x.re) (cbrt y.re))) (cbrt y.re))))

series457.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (atan2 x.im x.re) y.im)
68.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
297.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt y.re) (* (atan2 x.im x.re) (cbrt y.re))) (cbrt y.re))))

simplify2.2s

Counts
68 → 68
Iterations
IterNodes
done5002
33071
2590
1213
0103

prune742.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 20.3b

localize109.0ms

Local error

Found 4 expressions with local error:

8.2b
(cbrt (* (atan2 x.im x.re) y.re))
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.8b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×add-cbrt-cube sqrt-div add-exp-log add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cbrt-prod sin-sum pow1/3
Counts
4 → 47
Calls
4 calls:
3.0ms
(cbrt (* (atan2 x.im x.re) y.re))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

series458.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(cbrt (* (atan2 x.im x.re) y.re))
45.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
284.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

simplify1.2s

Counts
59 → 59
Iterations
IterNodes
done5000
43158
3970
2401
1195
099

prune708.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 20.3b

localize71.0ms

Local error

Found 4 expressions with local error:

28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b
(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
31.3b
(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
31.3b
(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

rewrite65.0ms

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×sin-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)))
21.0ms
(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
22.0ms
(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
14.0ms
(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

series789.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
261.0ms
(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
256.0ms
(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
202.0ms
(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

simplify963.0ms

Counts
51 → 51
Iterations
IterNodes
done5001
41883
3654
2294
1144
071

prune703.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 20.3b

regimes685.0ms

Accuracy

66.5% (4.6b remaining)

Error of 24.1b against oracle of 19.5b and baseline of 33.2b

bsearch480.0ms

Steps
ItersRangePoint
9
1.5036552484345302e-250
1.418559766594171e-245
1.13533427586206e-248
10
-205.8624528279525
-1.2620558025192223e-10
-4.946097345847493e-09

simplify11.0ms

Iterations
IterNodes
done56
156
040

end0.0ms

sample8.7s

Algorithm
intervals
Results
3.3s2173×body1280valid
2.1s7959×body80valid
1.3s1386×body640valid
548.0ms223×body160valid
452.0ms583×body320valid
157.0ms45×body2560valid