Details

Time bar (total: 23.9s)

sample236.0ms

Algorithm
intervals
Results
69.0ms69×body1280valid
55.0ms32×body640valid
34.0ms258×body80valid
9.0ms22×body320valid
4.0ms13×body160valid

simplify2.8s

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize89.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.re)
29.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite39.0ms

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×cos-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.re)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (atan2 x.im x.re) y.re)
46.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
59.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
227.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.9s

Counts
68 → 68
Iterations
IterNodes
done5001
32591
2545
1195
094

prune745.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.1b
(* (atan2 x.im x.re) y.im)
29.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×*-un-lft-identity associate-*l* add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×associate-*r* add-log-exp
3×log-pow sqrt-prod
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sub-neg flip3-+ flip3-- diff-log flip-+ flip--
Counts
4 → 66
Calls
4 calls:
9.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
9.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
10.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series384.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
128.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
34.0ms
(* (atan2 x.im x.re) y.im)
57.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.2s

Counts
78 → 78
Iterations
IterNodes
done5000
21066
1303
0131

prune652.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.9b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
0.1b
(* (log (- x.re)) y.re)
1.1b
(* (atan2 x.im x.re) y.im)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×pow1
7×*-un-lft-identity add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r*
5×add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg flip3-- diff-log log-pow flip--
Counts
3 → 49
Calls
3 calls:
11.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
6.0ms
(* (log (- x.re)) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)

series373.0ms

Counts
3 → 9
Calls
3 calls:
205.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
135.0ms
(* (log (- x.re)) y.re)
33.0ms
(* (atan2 x.im x.re) y.im)

simplify1.2s

Counts
58 → 58
Iterations
IterNodes
done5001
2870
1234
0104

prune413.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
1.1b
(* (atan2 x.im x.re) y.im)
3.8b
(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
29.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×pow1
8×add-cbrt-cube add-exp-log log-pow
7×associate-*l*
6×exp-prod associate-*r* sqrt-prod
4×add-log-exp
3×log-prod
2×sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 rem-log-exp flip-+
Counts
4 → 70
Calls
4 calls:
11.0ms
(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
5.0ms
(* (atan2 x.im x.re) y.im)
13.0ms
(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series315.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
36.0ms
(* (atan2 x.im x.re) y.im)
72.0ms
(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
68.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.4s

Counts
82 → 82
Iterations
IterNodes
done5000
34281
2777
1267
0131

prune674.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.9b

regimes588.0ms

Accuracy

83.5% (5.3b remaining)

Error of 9.1b against oracle of 3.8b and baseline of 35.8b

bsearch191.0ms

Steps
ItersRangePoint
8
-1.9669057843849594e-307
1.7581278845975106e-307
3.1386120183459e-310

simplify8.0ms

Iterations
IterNodes
done30
230
128
021

end0.0ms

sample8.0s

Algorithm
intervals
Results
2.4s1955×body1280valid
2.2s7929×body80valid
1.7s1507×body640valid
920.0ms636×body320valid
101.0ms309×body160valid