Details

Time bar (total: 33.8s)

sample347.0ms

Algorithm
intervals
Results
88.0ms45×body640valid
71.0ms75×body1280valid
41.0ms257×body80valid
8.0ms18×body320valid
3.0ms9×body160valid

simplify3.3s

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: 30.6b

localize82.0ms

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)))
29.6b
(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:
11.0ms
(* (atan2 x.im x.re) y.im)
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series346.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (atan2 x.im x.re) y.im)
45.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
45.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
234.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts
68 → 68
Iterations
IterNodes
done5001
33046
2577
1204
099

prune690.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.1b

localize116.0ms

Local error

Found 4 expressions with local error:

5.5b
(cbrt (* (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)))
29.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite61.0ms

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:
6.0ms
(cbrt (* (atan2 x.im x.re) y.im))
14.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(cbrt (* (atan2 x.im x.re) y.im))
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
42.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
246.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify6.4s

Counts
59 → 59
Iterations
IterNodes
done5000
43170
3953
2401
1197
0100

prune670.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.1b

localize198.0ms

Local error

Found 4 expressions with local error:

5.5b
(cbrt (* (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)))
29.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite42.0ms

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.im))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
25.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(cbrt (* (atan2 x.im x.re) y.im))
55.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
69.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
188.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify6.0s

Counts
59 → 59
Iterations
IterNodes
done5000
43170
3953
2401
1197
0100

prune871.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.1b

localize162.0ms

Local error

Found 4 expressions with local error:

26.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
29.6b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite66.0ms

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:
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
23.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series702.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
195.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
228.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
224.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.3s

Counts
51 → 51
Iterations
IterNodes
done5001
41892
3654
2294
1144
071

prune623.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.1b

regimes631.0ms

Accuracy

77.7% (3.1b remaining)

Error of 22.0b against oracle of 18.9b and baseline of 32.7b

bsearch273.0ms

Steps
ItersRangePoint
10
-8.38583807968836e-299
6.218782843424262e-302
-4.3999011435792e-310

simplify26.0ms

Iterations
IterNodes
done53
353
251
149
038

end0.0ms

sample7.9s

Algorithm
intervals
Results
3.2s2239×body1280valid
2.0s1448×body640valid
1.6s7959×body80valid
419.0ms580×body320valid
94.0ms40×body2560valid
73.0ms219×body160valid