Details

Time bar (total: 6.7s)

sample448.0ms

Algorithm
intervals
Results
46.0ms254×body80valid
44.0ms76×body1280valid
13.0ms34×body640valid
6.0ms21×body320valid
2.0ms8×body160valid

simplify39.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117
done500117

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.2b

localize27.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (atan2 x.im x.re) y.im)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.9b
(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×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
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)))
27.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
166.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify78.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0207456
1556415
21286411
32863411
45002411
done5002411

prune370.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.0b

localize17.0ms

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)
1.4b
(* (atan2 x.im x.re) y.im)
30.5b
(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*
4×expm1-log1p-u log1p-expm1-u
3×exp-prod exp-sum sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×sub-neg rem-sqrt-square flip3-+ exp-diff diff-log prod-diff flip-+ hypot-def
Counts
4 → 79
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)))

series253.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(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)
22.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify65.0ms

Counts
91 → 91
Iterations

Useful iterations: 3 (56.0ms)

IterNodesCost
0308585
1921522
22504484
35002467
done5002467

prune324.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot x.re x.im)
0.3b
(* (log (exp (log (hypot x.re x.im)))) y.re)
1.4b
(* (atan2 x.im x.re) y.im)
5.8b
(exp (log (hypot x.re x.im)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1 add-cube-cbrt *-un-lft-identity associate-*l*
8×add-exp-log exp-prod add-cbrt-cube
7×log-pow
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×log-prod exp-sum
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×hypot-udef rem-exp-log
Counts
4 → 72
Calls
4 calls:
0.0ms
(hypot x.re x.im)
15.0ms
(* (log (exp (log (hypot x.re x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(exp (log (hypot x.re x.im)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot x.re x.im)
104.0ms
(* (log (exp (log (hypot x.re x.im)))) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
53.0ms
(exp (log (hypot x.re x.im)))

simplify70.0ms

Counts
84 → 84
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
0206312
1528270
21355264
32600258
45002258
done5002258

prune312.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x.re x.im)
0.3b
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
1.4b
(* (atan2 x.im x.re) y.im)

rewrite21.0ms

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
4×sqr-pow
3×expm1-log1p-u div-exp associate-*r* associate-*l* associate-/r* log1p-expm1-u add-log-exp
1×cbrt-undiv pow-to-exp hypot-udef frac-2neg pow-prod-down pow-exp prod-exp clear-num *-commutative cbrt-unprod div-inv unswap-sqr
Counts
3 → 77
Calls
3 calls:
0.0ms
(hypot x.re x.im)
11.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
7.0ms
(* (atan2 x.im x.re) y.im)

series205.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(hypot x.re x.im)
136.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
22.0ms
(* (atan2 x.im x.re) y.im)

simplify91.0ms

Counts
86 → 86
Iterations

Useful iterations: 3 (80.0ms)

IterNodesCost
0265659
1870621
23804619
35001618
done5001618

prune282.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.3b

regimes149.0ms

Accuracy

0% (0.5b remaining)

Error of 4.1b against oracle of 3.6b and baseline of 4.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0209
1229
2229
done229

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.3s2143×body1280valid
668.0ms7948×body80valid
577.0ms1451×body640valid
181.0ms669×body320valid
58.0ms319×body160valid