Details

Time bar (total: 6.7s)

sample419.0ms

Algorithm
intervals
Results
43.0ms58×body640valid
33.0ms59×body1280valid
20.0ms254×body80valid
4.0ms16×body320valid
2.0ms10×body160valid

simplify37.0ms

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: 33.8b

localize27.0ms

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)))

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)))
26.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
164.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify73.0ms

Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0191422
1501385
21134381
32496381
45001381
done5001381

prune322.0ms

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)))

rewrite53.0ms

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:
21.0ms
(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)
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series257.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
95.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify56.0ms

Counts
81 → 81
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0280545
1825486
22118481
35001481
done5001481

prune292.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.5b

localize15.0ms

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)))

rewrite59.0ms

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:
6.0ms
(exp (* (atan2 x.im x.re) y.im))
34.0ms
(/ (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)))

series209.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(exp (* (atan2 x.im x.re) y.im))
126.0ms
(/ (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) y.re) (exp (* (atan2 x.im x.re) y.im)))
18.0ms
(* (atan2 x.im x.re) y.im)
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify41.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03671194
112991130
250011129
done50011129

prune373.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.5b

localize10.0ms

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)

rewrite28.0ms

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:
14.0ms
(/ (pow x.im y.re) (exp (* (atan2 x.im x.re) y.im)))
4.0ms
(exp (* (atan2 x.im x.re) y.im))
7.0ms
(* (atan2 x.im x.re) y.im)

series125.0ms

Counts
3 → 9
Calls
3 calls:
84.0ms
(/ (pow x.im y.re) (exp (* (atan2 x.im x.re) y.im)))
23.0ms
(exp (* (atan2 x.im x.re) y.im))
18.0ms
(* (atan2 x.im x.re) y.im)

simplify35.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0262595
1986561
25002560
done5002560

prune224.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.5b

regimes245.0ms

Accuracy

61.3% (6.2b remaining)

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

bsearch358.0ms

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

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05647
16847
26847
done6847

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.1s2003×body1280valid
640.0ms8000×body80valid
557.0ms1489×body640valid
159.0ms628×body320valid
54.0ms301×body160valid