Details

Time bar (total: 18.7s)

sample35.0ms

Algorithm
intervals
Results
16.0ms270×body80valid

simplify15.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01115
11713
22113
done2113

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y.re y.re (* y.im y.im))
0.5b
(fma x.re y.re (* x.im y.im))
24.7b
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-exp-log add-cbrt-cube
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×fma-udef
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 49
Calls
3 calls:
0.0ms
(fma y.re y.re (* y.im y.im))
0.0ms
(fma x.re y.re (* x.im y.im))
5.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

series212.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(fma y.re y.re (* y.im y.im))
42.0ms
(fma x.re y.re (* x.im y.im))
131.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

simplify2.4s

Counts
58 → 58
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
074833
1114819
2287707
3782707
42290707
done5000707

prune247.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)))
0.5b
(fma x.re y.re (* x.im y.im))
14.7b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

rewrite36.0ms

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:
25.0ms
(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)))
0.0ms
(fma x.re y.re (* x.im y.im))
5.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

series477.0ms

Counts
3 → 9
Calls
3 calls:
255.0ms
(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)))
52.0ms
(fma x.re y.re (* x.im y.im))
171.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

simplify3.5s

Counts
106 → 106
Iterations

Useful iterations: done (3.5s)

IterNodesCost
01401895
13281763
210681527
339791527
done50001494

prune424.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.5b
(fma x.re y.re (* x.im y.im))
14.7b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

rewrite44.0ms

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:
26.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
1.0ms
(fma x.re y.re (* x.im y.im))
9.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

series424.0ms

Counts
3 → 9
Calls
3 calls:
199.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
49.0ms
(fma x.re y.re (* x.im y.im))
176.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

simplify2.2s

Counts
120 → 120
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01612484
13222423
27032246
320302192
done50002130

prune497.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im))))
0.3b
(* (/ 1 (hypot y.im y.re)) (/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))))
0.5b
(fma x.re y.re (* x.im y.im))
14.8b
(/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
187×times-frac
143×add-sqr-sqrt
107×*-un-lft-identity
100×add-exp-log
96×add-cube-cbrt
50×div-exp
44×associate-*r*
32×add-cbrt-cube
28×prod-exp
17×rec-exp 1-exp
16×associate-/r*
15×unswap-sqr
13×cbrt-undiv associate-*l*
11×div-inv
9×pow1
6×cbrt-unprod associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-flip pow-prod-down inv-pow
2×frac-2neg clear-num associate-/r/
1×frac-times associate-*r/ associate-*l/ un-div-inv *-commutative fma-udef
Counts
4 → 240
Calls
4 calls:
24.0ms
(/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im))))
84.0ms
(* (/ 1 (hypot y.im y.re)) (/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))))
1.0ms
(fma x.re y.re (* x.im y.im))
18.0ms
(/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))

series724.0ms

Counts
4 → 12
Calls
4 calls:
258.0ms
(/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im))))
289.0ms
(* (/ 1 (hypot y.im y.re)) (/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))))
50.0ms
(fma x.re y.re (* x.im y.im))
127.0ms
(/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))

simplify4.7s

Counts
252 → 252
Iterations

Useful iterations: done (4.7s)

IterNodesCost
02925363
17224687
215354048
343114030
done50013953

prune818.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.2b

regimes321.0ms

Accuracy

22.8% (11.1b remaining)

Error of 13.4b against oracle of 2.3b and baseline of 16.6b

bsearch103.0ms

Steps
ItersRangePoint
9
1.7909339157589686e+111
2.7605556854190684e+118
2.61942369601016e+118
7
-5.543583609067316e+248
-2.6626358598662032e+247
-2.686314195490964e+247

simplify7.0ms

Iterations

Useful iterations: 3 (6.0ms)

IterNodesCost
02343
13139
23535
33934
done3934

end0.0ms

sample1.3s

Algorithm
intervals
Results
811.0ms8495×body80valid