Details

Time bar (total: 6.3s)

sample417.0ms

Algorithm
intervals
Results
55.0ms63×body1280valid
22.0ms256×body80valid
14.0ms37×body640valid
4.0ms17×body320valid
2.0ms10×body160valid

simplify38.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120
done500120

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.5b

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (atan2 x.im x.re) y.im)
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log sqrt-prod add-cbrt-cube
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:
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series257.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
160.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Counts
68 → 68
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0191420
1501383
21134381
32496381
45001381
done5001381

prune324.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (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)
1.4b
(* (atan2 x.im x.re) y.im)
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
8×add-exp-log add-cbrt-cube
7×add-log-exp
6×associate-*r*
3×exp-prod sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×sub-neg rem-sqrt-square flip3-+ exp-diff diff-log flip-+
Counts
4 → 69
Calls
4 calls:
20.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
14.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
90.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify60.0ms

Counts
81 → 81
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0280545
1825486
22118481
35001481
done5001481

prune300.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.7b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (- (* (atan2 x.im x.re) y.im)))
1.4b
(* (atan2 x.im x.re) y.im)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×exp-prod
5×add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
2×rem-exp-log
1×neg-sub0 distribute-lft-neg-in exp-neg neg-mul-1 distribute-rgt-neg-in exp-diff pow-prod-down neg-log prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
2 → 35
Calls
2 calls:
5.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
7.0ms
(* (atan2 x.im x.re) y.im)

series45.0ms

Counts
2 → 6
Calls
2 calls:
26.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
18.0ms
(* (atan2 x.im x.re) y.im)

simplify58.0ms

Counts
41 → 41
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0119163
1468147
22163147
35001146
done5001146

prune142.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (atan2 x.im x.re) y.im)))
0.0b
(exp (- (* (atan2 x.im x.re) y.im)))
1.4b
(* (atan2 x.im x.re) y.im)
1.4b
(* (atan2 x.im x.re) y.im)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×exp-prod
10×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube add-log-exp
6×associate-*r* associate-*l*
4×rem-exp-log
2×neg-sub0 distribute-lft-neg-in exp-neg neg-mul-1 distribute-rgt-neg-in exp-diff pow-prod-down neg-log prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 70
Calls
4 calls:
5.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
5.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
7.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(* (atan2 x.im x.re) y.im)

series90.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
27.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
18.0ms
(* (atan2 x.im x.re) y.im)
18.0ms
(* (atan2 x.im x.re) y.im)

simplify57.0ms

Counts
82 → 82
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0119326
1468294
22163294
35001292
done5001292

prune290.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.7b

regimes314.0ms

Accuracy

68.5% (5.3b remaining)

Error of 9.1b against oracle of 3.8b and baseline of 20.7b

bsearch279.0ms

Steps
ItersRangePoint
8
-6.337876436014474e-306
4.475267169186454e-307
1.94572259503746e-310
9
-1.681704872267351e-189
-1.622727529386889e-195
-2.9973447128076877e-193
7
-4.618867104902589e-22
-2.1609630462704366e-24
-1.3400450056721967e-23

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04934
15534
25534
done5534

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s2048×body1280valid
656.0ms7966×body80valid
541.0ms1440×body640valid
166.0ms648×body320valid
52.0ms302×body160valid