Details

Time bar (total: 21.2s)

sample310.0ms

Algorithm
intervals
Results
116.0ms45×body1280valid
47.0ms252×body80valid
27.0ms34×body640valid
11.0ms18×body320valid
3.0ms8×body160valid

simplify1.6s

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.2b

localize39.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.re)
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite56.0ms

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:
6.0ms
(* (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)))
34.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series329.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (atan2 x.im x.re) y.re)
50.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
52.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
193.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts
68 → 68
Iterations
IterNodes
done5001
32591
2545
1195
094

prune654.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.1b

localize50.0ms

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))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.1b
(* (atan2 x.im x.re) y.im)
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite58.0ms

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))
18.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
147.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
34.0ms
(* (atan2 x.im x.re) y.im)
52.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify749.0ms

Counts
78 → 78
Iterations
IterNodes
done5000
21066
1303
0131

prune619.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.5b

localize68.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.re)
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b
(cos (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

rewrite44.0ms

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:
10.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms
(cos (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

series343.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.re)
54.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
62.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
207.0ms
(cos (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

simplify1.5s

Counts
68 → 68
Iterations
IterNodes
done5001
32586
2545
1195
094

prune641.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.4b

localize72.0ms

Local error

Found 4 expressions with local error:

28.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.0b
(cos (+ (* (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
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log add-log-exp
3×cos-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)))
20.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
13.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
14.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series684.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
192.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
212.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
241.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify955.0ms

Counts
51 → 51
Iterations
IterNodes
done5000
41878
3652
2289
1139
068

prune729.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.4b

regimes719.0ms

Accuracy

82.6% (5.1b remaining)

Error of 8.7b against oracle of 3.6b and baseline of 33.1b

bsearch190.0ms

Steps
ItersRangePoint
11
-4.548712206828868e-306
1.3944372280248121e-288
-2.75041588701475e-310

simplify5.0ms

Iterations
IterNodes
done38
238
133
023

end0.0ms

sample8.8s

Algorithm
intervals
Results
3.3s1974×body1280valid
2.2s7983×body80valid
1.3s1409×body640valid
691.0ms308×body160valid
482.0ms695×body320valid