Details

Time bar (total: 11.8s)

sample21.0ms

Algorithm
intervals
Results
10.0ms274×body80valid

simplify51.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01115
12114
24014
35614
47614
58814
69214
done9214

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
1.0b
(- (* x.im y.re) (* x.re y.im))
27.9b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num sum-log div-inv
Counts
3 → 64
Calls
3 calls:
3.0ms
(+ (* y.re y.re) (* y.im y.im))
3.0ms
(- (* x.im y.re) (* x.re y.im))
10.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series148.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* y.re y.re) (* y.im y.im))
36.0ms
(- (* x.im y.re) (* x.re y.im))
85.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts
73 → 73
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01121202
13121070
21116961
34256961
done5000959

prune228.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot y.re y.im))
0.2b
(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
0.3b
(fma x.im y.re (- (* y.im x.re)))
16.1b
(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
43×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
32×add-exp-log
20×add-cbrt-cube
13×associate-*r* associate-*l*
11×div-exp
8×prod-exp
7×pow1
6×cbrt-undiv associate-/r* associate-/l* unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×rec-exp 1-exp
2×frac-2neg clear-num
1×frac-times pow-flip associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef inv-pow
Counts
4 → 130
Calls
4 calls:
2.0ms
(/ 1 (hypot y.re y.im))
16.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
0.0ms
(fma x.im y.re (- (* y.im x.re)))
2.0ms
(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

series430.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ 1 (hypot y.re y.im))
192.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
47.0ms
(fma x.im y.re (- (* y.im x.re)))
135.0ms
(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

simplify3.6s

Counts
142 → 142
Iterations

Useful iterations: done (3.6s)

IterNodesCost
01552322
13792162
211901874
346971874
done50011873

prune369.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
0.3b
(fma x.im y.re (- (* y.im x.re)))
16.1b
(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×fma-udef associate-/l/
Counts
3 → 111
Calls
3 calls:
6.0ms
(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
0.0ms
(fma x.im y.re (- (* y.im x.re)))
2.0ms
(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

series323.0ms

Counts
3 → 9
Calls
3 calls:
138.0ms
(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
45.0ms
(fma x.im y.re (- (* y.im x.re)))
139.0ms
(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

simplify1.8s

Counts
120 → 120
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01622652
13352592
28252403
327182349
done50002347

prune358.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* y.im x.re) (* x.im y.re)) (- (hypot y.re y.im))) (hypot y.re y.im))
0.8b
(- (* y.im x.re) (* x.im y.re))
16.1b
(/ (- (* y.im x.re) (* x.im y.re)) (- (hypot y.re y.im)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
141×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
48×distribute-lft-neg-in distribute-rgt-neg-in
37×associate-/l*
16×neg-mul-1
13×associate-/r*
10×add-exp-log add-cbrt-cube
6×div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg fma-neg diff-log prod-diff
Counts
3 → 233
Calls
3 calls:
15.0ms
(/ (/ (- (* y.im x.re) (* x.im y.re)) (- (hypot y.re y.im))) (hypot y.re y.im))
5.0ms
(- (* y.im x.re) (* x.im y.re))
9.0ms
(/ (- (* y.im x.re) (* x.im y.re)) (- (hypot y.re y.im)))

series253.0ms

Counts
3 → 9
Calls
3 calls:
112.0ms
(/ (/ (- (* y.im x.re) (* x.im y.re)) (- (hypot y.re y.im))) (hypot y.re y.im))
41.0ms
(- (* y.im x.re) (* x.im y.re))
100.0ms
(/ (- (* y.im x.re) (* x.im y.re)) (- (hypot y.re y.im)))

simplify1.0s

Counts
242 → 242
Iterations

Useful iterations: 2 (508.0ms)

IterNodesCost
03456324
18486154
226155931
done50005931

prune630.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.1b

regimes154.0ms

Accuracy

34.5% (5.2b remaining)

Error of 6.4b against oracle of 1.2b and baseline of 9.2b

bsearch70.0ms

Steps
ItersRangePoint
6
1.64509935319664e+151
2.4117396496446514e+152
2.0302445674537431e+152
8
-1.592064737660755e+235
-1.0585057548241573e+231
-1.9542110853942293e+231

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02140
12440
done2440

end0.0ms

sample553.0ms

Algorithm
intervals
Results
321.0ms8491×body80valid