Details

Time bar (total: 24.5s)

sample798.0ms

Algorithm
intervals
Results
554.0ms69×body1280valid
51.0ms258×body80valid
33.0ms32×body640valid
14.0ms22×body320valid
6.0ms13×body160valid

simplify2.8s

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize106.0ms

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)))

rewrite54.0ms

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)))
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (atan2 x.im x.re) y.re)
61.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
59.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
206.0ms
(cos (+ (* (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
done5000
42008
3859
2408
1195
094

prune681.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.3b

localize42.0ms

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)))

rewrite46.0ms

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:
12.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
20.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
5.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
212.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
160.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
61.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.2s

Counts
78 → 78
Iterations
IterNodes
done5002
32099
2745
1303
0131

prune671.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.9b

localize36.0ms

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)

rewrite34.0ms

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:
6.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
16.0ms
(* (log (- x.re)) y.re)
11.0ms
(* (atan2 x.im x.re) y.im)

series260.0ms

Counts
3 → 9
Calls
3 calls:
156.0ms
(- (* (log (- x.re)) y.re) (* (atan2 x.im x.re) y.im))
85.0ms
(* (log (- x.re)) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)

simplify1.9s

Counts
58 → 58
Iterations
IterNodes
done5001
31717
2593
1234
0104

prune432.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.9b

localize50.0ms

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)))

rewrite42.0ms

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:
6.0ms
(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
5.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
33.0ms
(* (atan2 x.im x.re) y.im)
55.0ms
(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.1s

Counts
82 → 82
Iterations
IterNodes
done5004
42220
31119
2561
1266
0131

prune671.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.9b

regimes573.0ms

Accuracy

83.5% (5.3b remaining)

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

bsearch201.0ms

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

simplify7.0ms

Iterations
IterNodes
done28
128
021

end0.0ms

sample7.7s

Algorithm
intervals
Results
2.5s1955×body1280valid
2.2s7929×body80valid
1.8s1507×body640valid
362.0ms636×body320valid
145.0ms309×body160valid