Details

Time bar (total: 27.3s)

sample268.0ms

Algorithm
intervals
Results
72.0ms257×body80valid
59.0ms75×body1280valid
25.0ms45×body640valid
6.0ms18×body320valid
2.0ms9×body160valid

simplify2.9s

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize94.0ms

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)))

rewrite55.0ms

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)
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (atan2 x.im x.re) y.im)
66.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
51.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
239.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts
68 → 68
Iterations
IterNodes
done5001
42165
3915
2424
1204
099

prune727.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.1b

localize106.0ms

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)))

rewrite36.0ms

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:
5.0ms
(cbrt (* (atan2 x.im x.re) y.im))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
14.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series789.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(cbrt (* (atan2 x.im x.re) y.im))
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
60.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
567.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.7s

Counts
59 → 59
Iterations
IterNodes
done5000
41683
3726
2363
1197
0100

prune641.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.1b

localize126.0ms

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)))

rewrite30.0ms

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)))
15.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(cbrt (* (atan2 x.im x.re) y.im))
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
43.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
164.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts
59 → 59
Iterations
IterNodes
done5000
41683
3726
2363
1197
0100

prune753.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.1b

localize183.0ms

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)))

rewrite75.0ms

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:
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
14.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
19.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series713.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(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)))
219.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
192.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.0s

Counts
51 → 51
Iterations
IterNodes
done5000
53680
41190
3540
2268
1144
071

prune696.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.1b

regimes693.0ms

Accuracy

77.7% (3.1b remaining)

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

bsearch328.0ms

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

simplify20.0ms

Iterations
IterNodes
done49
149
037

end0.0ms

sample8.5s

Algorithm
intervals
Results
3.0s2239×body1280valid
2.5s7959×body80valid
1.4s1448×body640valid
542.0ms40×body2560valid
366.0ms580×body320valid
72.0ms219×body160valid