Details

Time bar (total: 6.5s)

sample426.0ms

Algorithm
intervals
Results
42.0ms76×body1280valid
41.0ms254×body80valid
13.0ms34×body640valid
5.0ms21×body320valid
2.0ms8×body160valid

simplify41.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117
done500117

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.2b

localize24.0ms

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)))

rewrite52.0ms

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)))

series253.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
162.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify82.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0207456
1556415
21286411
32863411
45002411
done5002411

prune373.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.0b

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)
1.4b
(* (atan2 x.im x.re) y.im)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite52.0ms

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)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series252.0ms

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)))
94.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify64.0ms

Counts
91 → 91
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
0308585
1921522
22504484
35002467
done5002467

prune332.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.3b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
7×associate-*l* add-log-exp
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u
3×exp-prod exp-sum
2×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×sub-neg hypot-udef exp-diff diff-log prod-diff log-pow
Counts
4 → 69
Calls
4 calls:
20.0ms
(exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
0.0ms
(hypot x.re x.im)
8.0ms
(* (log (hypot x.re x.im)) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)

series278.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
48.0ms
(hypot x.re x.im)
102.0ms
(* (log (hypot x.re x.im)) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)

simplify50.0ms

Counts
81 → 81
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0232382
1692340
21887332
35001332
done5001332

prune265.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.3b

localize12.0ms

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)

series200.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(hypot x.re x.im)
133.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
21.0ms
(* (atan2 x.im x.re) y.im)

simplify88.0ms

Counts
86 → 86
Iterations

Useful iterations: 3 (81.0ms)

IterNodesCost
0265659
1870621
23804619
35001618
done5001618

prune269.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.3b

regimes144.0ms

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
0187
1207
2207
done207

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.2s2143×body1280valid
655.0ms7948×body80valid
544.0ms1451×body640valid
171.0ms669×body320valid
57.0ms319×body160valid