Details

Time bar (total: 27.6s)

sample542.0ms

Algorithm
intervals
Results
138.0ms257×body80valid
92.0ms75×body1280valid
45.0ms45×body640valid
10.0ms18×body320valid
4.0ms9×body160valid

simplify2.9s

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize58.0ms

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)))

rewrite77.0ms

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:
9.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
42.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series364.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (atan2 x.im x.re) y.im)
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
61.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
221.0ms
(sin (+ (* (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
42165
3915
2424
1204
099

prune764.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.1b

localize115.0ms

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)))

rewrite31.0ms

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)))

series461.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(cbrt (* (atan2 x.im x.re) y.im))
66.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
244.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.8s

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

prune729.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.1b

localize157.0ms

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)))

rewrite41.0ms

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))
13.0ms
(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)))

series460.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(cbrt (* (atan2 x.im x.re) y.im))
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
68.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
229.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.8s

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

prune719.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.1b

localize176.0ms

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)))

rewrite84.0ms

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:
11.0ms
(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)))
26.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
17.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series668.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
208.0ms
(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)))
185.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.9s

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

prune664.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.1b

regimes641.0ms

Accuracy

77.7% (3.1b remaining)

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

bsearch262.0ms

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

simplify16.0ms

Iterations
IterNodes
done49
149
038

end0.0ms

sample9.2s

Algorithm
intervals
Results
3.2s2239×body1280valid
2.4s7959×body80valid
2.3s1448×body640valid
346.0ms580×body320valid
96.0ms40×body2560valid
78.0ms219×body160valid