Details

Time bar (total: 22.4s)

sample684.0ms

Algorithm
intervals
Results
183.0ms59×body1280valid
165.0ms254×body80valid
38.0ms58×body640valid
7.0ms16×body320valid
3.0ms10×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
01937
13137
25336
38236
420136
582936
done500036

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.8b

localize24.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.im)
31.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.2b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite82.0ms

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)
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
45.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (atan2 x.im x.re) y.im)
52.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
46.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
195.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.7s

Counts
68 → 68
Iterations

Useful iterations: 3 (308.0ms)

IterNodesCost
095836
1193778
2437690
3816677
41651677
54087677
done5001677

prune502.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.9b

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)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.8b
(* (atan2 x.im x.re) y.im)
31.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite76.0ms

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:
27.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
19.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
14.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
130.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.7s

Counts
81 → 81
Iterations

Useful iterations: 4 (2.1s)

IterNodesCost
01321042
1282985
2691871
31455860
44042859
done5000859

prune465.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (* (atan2 x.im x.re) y.im))
0.3b
(/ (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (exp (* (atan2 x.im x.re) y.im)))
1.8b
(* (atan2 x.im x.re) y.im)
31.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
30×add-cube-cbrt *-un-lft-identity times-frac
24×unpow-prod-down
15×sqrt-prod
10×associate-/l*
8×add-exp-log add-cbrt-cube
7×pow1
6×add-log-exp
4×sqr-pow
3×div-exp associate-*r* associate-*l* associate-/r*
2×sqrt-div
1×cbrt-undiv pow-to-exp rem-sqrt-square exp-prod exp-to-pow frac-2neg sqrt-pow1 flip3-+ pow1/2 pow-prod-down pow-exp prod-exp clear-num *-commutative cbrt-unprod flip-+ div-inv rem-exp-log unswap-sqr
Counts
4 → 100
Calls
4 calls:
8.0ms
(exp (* (atan2 x.im x.re) y.im))
43.0ms
(/ (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (exp (* (atan2 x.im x.re) y.im)))
7.0ms
(* (atan2 x.im x.re) y.im)
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series355.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(exp (* (atan2 x.im x.re) y.im))
231.0ms
(/ (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (exp (* (atan2 x.im x.re) y.im)))
33.0ms
(* (atan2 x.im x.re) y.im)
66.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.0s

Counts
112 → 112
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01832243
13642125
29192024
328222013
done50002012

prune588.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.5b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (pow x.im y.re) (exp (* (atan2 x.im x.re) y.im)))
0.0b
(exp (* (atan2 x.im x.re) y.im))
1.8b
(* (atan2 x.im x.re) y.im)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity times-frac
12×unpow-prod-down
7×add-exp-log add-cbrt-cube associate-/l*
5×pow1 add-log-exp
4×sqr-pow
3×div-exp associate-*r* associate-*l* associate-/r*
1×cbrt-undiv pow-to-exp exp-prod exp-to-pow frac-2neg pow-prod-down pow-exp prod-exp clear-num *-commutative cbrt-unprod div-inv rem-exp-log unswap-sqr
Counts
3 → 73
Calls
3 calls:
27.0ms
(/ (pow x.im y.re) (exp (* (atan2 x.im x.re) y.im)))
8.0ms
(exp (* (atan2 x.im x.re) y.im))
14.0ms
(* (atan2 x.im x.re) y.im)

series156.0ms

Counts
3 → 9
Calls
3 calls:
106.0ms
(/ (pow x.im y.re) (exp (* (atan2 x.im x.re) y.im)))
25.0ms
(exp (* (atan2 x.im x.re) y.im))
25.0ms
(* (atan2 x.im x.re) y.im)

simplify1.8s

Counts
82 → 82
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01411140
12581099
26701035
322641026
done50011024

prune357.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.5b

regimes338.0ms

Accuracy

61.3% (6.2b remaining)

Error of 9.8b against oracle of 3.6b and baseline of 19.7b

bsearch528.0ms

Steps
ItersRangePoint
6
6.476954101584147e-43
6.332450095449654e-42
1.5324100439937538e-42
9
-9.973106733526674e-202
-2.0474186848388073e-207
-4.3965240455902896e-206
9
-3.5576549797351977e-149
-1.0403165532282834e-154
-7.64882803387166e-153
8
-2.098883984402802e+33
-4.9514695543205084e+29
-5.026083376449556e+29

simplify10.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
041101
15591
25791
done5791

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.7s2003×body1280valid
966.0ms8000×body80valid
835.0ms1489×body640valid
255.0ms628×body320valid
79.0ms301×body160valid