Details

Time bar (total: 12.7s)

sample30.0ms

Algorithm
intervals
Results
13.0ms274×body80valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01115
11713
22113
done2113

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.2b
(+ (* x.re y.re) (* x.im y.im))
24.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite72.0ms

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
4×flip3-+ flip-+
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×+-commutative fma-def sum-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 61
Calls
3 calls:
10.0ms
(+ (* y.re y.re) (* y.im y.im))
10.0ms
(+ (* x.re y.re) (* x.im y.im))
50.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series209.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(+ (* y.re y.re) (* y.im y.im))
58.0ms
(+ (* x.re y.re) (* x.im y.im))
109.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts
70 → 70
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01051154
1307970
21602869
done5001867

prune323.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.5b

localize21.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
0.3b
(fma x.re y.re (* x.im y.im))
15.2b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
34×times-frac
27×add-exp-log *-un-lft-identity
25×add-cube-cbrt
17×add-cbrt-cube
13×associate-*r* associate-*l*
9×div-exp
8×prod-exp
6×unswap-sqr
5×pow1 cbrt-undiv
4×cbrt-unprod
3×expm1-log1p-u associate-/r* log1p-expm1-u div-inv associate-/l* add-log-exp
2×rec-exp 1-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative fma-udef
Counts
3 → 97
Calls
3 calls:
41.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
0.0ms
(fma x.re y.re (* x.im y.im))
6.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series582.0ms

Counts
3 → 9
Calls
3 calls:
298.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
76.0ms
(fma x.re y.re (* x.im y.im))
207.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify2.9s

Counts
106 → 106
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01401895
13721783
229171541
done50011527

prune401.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.2b

localize28.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.3b
(fma x.re y.re (* x.im y.im))
15.2b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite25.0ms

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:
13.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.0ms
(fma x.re y.re (* x.im y.im))
6.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series457.0ms

Counts
3 → 9
Calls
3 calls:
176.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
74.0ms
(fma x.re y.re (* x.im y.im))
207.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify1.1s

Counts
120 → 120
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01612484
13502423
217362254
done50002212

prune593.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
0.3b
(fma x.re y.re (* x.im y.im))
0.5b
(/ 1 (/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))))
15.2b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
60×associate-/r*
32×add-exp-log
23×div-inv
20×add-cbrt-cube
19×div-exp
10×cbrt-undiv
9×associate-/l*
6×associate-/r/
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp frac-2neg 1-exp clear-num
1×pow-flip fma-udef inv-pow
Counts
4 → 317
Calls
4 calls:
11.0ms
(/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
0.0ms
(fma x.re y.re (* x.im y.im))
29.0ms
(/ 1 (/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))))
11.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series605.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
53.0ms
(fma x.re y.re (* x.im y.im))
258.0ms
(/ 1 (/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))))
188.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify869.0ms

Counts
329 → 329
Iterations

Useful iterations: done (847.0ms)

IterNodesCost
04399092
112158346
done50017966

prune1.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.1b

regimes267.0ms

Accuracy

32.2% (7.7b remaining)

Error of 13.3b against oracle of 5.6b and baseline of 16.9b

bsearch89.0ms

Steps
ItersRangePoint
8
3.909580657839742e+222
1.7405675075945448e+227
5.396385525097289e+222
6
-8.945616726736062e+128
-9.921620365554097e+127
-1.9122070425426486e+128

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01833
12033
done2033

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s8393×body80valid