Details

Time bar (total: 21.8s)

sample357.0ms

Algorithm
intervals
Results
148.0ms85×body1280valid
46.0ms255×body80valid
40.0ms50×body640valid
19.0ms31×body320valid
4.0ms10×body160valid

simplify1.6s

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize60.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) y.re)
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0b
(cos (+ (* (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×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)))
26.0ms
(cos (+ (* (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:
20.0ms
(* (atan2 x.im x.re) y.re)
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
56.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
241.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts
68 → 68
Iterations
IterNodes
done5001
32591
2545
1195
094

prune687.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.2b

localize51.0ms

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)
1.3b
(* (atan2 x.im x.re) y.im)
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite56.0ms

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))
18.0ms
(* (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)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
144.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
32.0ms
(* (atan2 x.im x.re) y.im)
74.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify730.0ms

Counts
78 → 78
Iterations
IterNodes
done5000
21066
1303
0131

prune623.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.2b

localize72.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) y.re)
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.2b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0b
(cos (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

rewrite61.0ms

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:
8.0ms
(* (atan2 x.im x.re) y.re)
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms
(cos (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

series371.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (atan2 x.im x.re) y.re)
71.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
218.0ms
(cos (+ (* (atan2 x.im x.re) y.re) (* y.im (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))))

simplify1.4s

Counts
68 → 68
Iterations
IterNodes
done5001
32586
2545
1195
094

prune758.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (- y.re) (log (/ -1 x.re))) (* (atan2 x.im x.re) y.im)))
0.0b
(- (* (- y.re) (log (/ -1 x.re))) (* (atan2 x.im x.re) y.im))
0.1b
(* (- y.re) (log (/ -1 x.re)))
1.3b
(* (atan2 x.im x.re) y.im)

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
78×log-prod
57×add-sqr-sqrt
54×times-frac
53×*-un-lft-identity add-cube-cbrt
52×associate--l+
39×distribute-rgt-in distribute-lft-in
28×exp-sum
13×associate-*l*
9×pow1 add-log-exp
8×add-cbrt-cube add-exp-log
7×associate-*r*
6×div-inv
3×distribute-lft-neg-in exp-prod distribute-rgt-neg-in
2×sub-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
1×distribute-lft-neg-out neg-mul-1 flip3-- exp-diff log-pow flip--
Counts
4 → 150
Calls
4 calls:
28.0ms
(exp (- (* (- y.re) (log (/ -1 x.re))) (* (atan2 x.im x.re) y.im)))
15.0ms
(- (* (- y.re) (log (/ -1 x.re))) (* (atan2 x.im x.re) y.im))
25.0ms
(* (- y.re) (log (/ -1 x.re)))
10.0ms
(* (atan2 x.im x.re) y.im)

series317.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(exp (- (* (- y.re) (log (/ -1 x.re))) (* (atan2 x.im x.re) y.im)))
141.0ms
(- (* (- y.re) (log (/ -1 x.re))) (* (atan2 x.im x.re) y.im))
62.0ms
(* (- y.re) (log (/ -1 x.re)))
20.0ms
(* (atan2 x.im x.re) y.im)

simplify1.7s

Counts
162 → 162
Iterations
IterNodes
done5001
23379
1753
0290

prune824.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.1b

regimes666.0ms

Accuracy

81.8% (5.5b remaining)

Error of 9.1b against oracle of 3.6b and baseline of 33.6b

bsearch214.0ms

Steps
ItersRangePoint
10
-2.631585147976807e-302
4.078675660601341e-299
2.1393293584853e-311

simplify430.0ms

Iterations
IterNodes
done36
236
134
026

end0.0ms

sample8.3s

Algorithm
intervals
Results
3.3s2058×body1280valid
1.8s1493×body640valid
1.7s7977×body80valid
506.0ms653×body320valid
157.0ms301×body160valid