Details

Time bar (total: 23.4s)

sample313.0ms

Algorithm
intervals
Results
111.0ms47×body1280valid
51.0ms252×body80valid
29.0ms35×body640valid
9.0ms16×body320valid
3.0ms7×body160valid

simplify1.5s

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.2b

localize78.0ms

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)))

rewrite70.0ms

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:
10.0ms
(* (atan2 x.im x.re) y.re)
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.re)
44.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
66.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
293.0ms
(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

prune646.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.3b

localize98.0ms

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))))

rewrite41.0ms

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:
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)))
21.0ms
(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))))

series447.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (atan2 x.im x.re) y.im)
46.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
70.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
299.0ms
(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))))

simplify2.1s

Counts
68 → 68
Iterations
IterNodes
done5002
33071
2590
1213
0103

prune834.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 20.3b

localize96.0ms

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)))))

rewrite74.0ms

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)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
55.0ms
(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)))))

series430.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(cbrt (* (atan2 x.im x.re) y.re))
67.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
47.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
240.0ms
(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)))))

simplify1.5s

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

prune722.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 20.3b

localize95.0ms

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)))))))

rewrite85.0ms

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)))
23.0ms
(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
27.0ms
(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
28.0ms
(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

series691.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
190.0ms
(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
211.0ms
(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))
232.0ms
(sin (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

simplify926.0ms

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

prune591.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 20.3b

regimes674.0ms

Accuracy

66.5% (4.6b remaining)

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

bsearch432.0ms

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

simplify9.0ms

Iterations
IterNodes
done56
156
040

end0.0ms

sample9.0s

Algorithm
intervals
Results
3.9s2173×body1280valid
2.2s7959×body80valid
1.4s1386×body640valid
365.0ms583×body320valid
151.0ms45×body2560valid
83.0ms223×body160valid