Details

Time bar (total: 12.5s)

sample22.0ms

Algorithm
intervals
Results
9.0ms275×body80valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01115
11713
22113
done2113

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y.re y.re (* y.im y.im))
0.8b
(fma x.re y.re (* x.im y.im))
26.9b
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

rewrite6.0ms

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)))

series169.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(fma y.re y.re (* y.im y.im))
40.0ms
(fma x.re y.re (* x.im y.im))
92.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

simplify1.8s

Counts
58 → 58
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
074833
1114819
2287707
3782707
42290707
done5000707

prune153.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)))
0.8b
(fma x.re y.re (* x.im y.im))
17.2b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

rewrite32.0ms

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:
24.0ms
(* (/ 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))

series327.0ms

Counts
3 → 9
Calls
3 calls:
172.0ms
(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)))
41.0ms
(fma x.re y.re (* x.im y.im))
114.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

simplify2.6s

Counts
106 → 106
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01401895
13281763
210681527
339791527
done50001494

prune253.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize12.0ms

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))
0.8b
(fma x.re y.re (* x.im y.im))
17.2b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

rewrite22.0ms

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.im y.re)) (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))

series275.0ms

Counts
3 → 9
Calls
3 calls:
120.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
39.0ms
(fma x.re y.re (* x.im y.im))
116.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

simplify1.5s

Counts
120 → 120
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01612484
13222423
27032246
320302192
done50002130

prune385.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.5b

localize14.0ms

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))))
0.2b
(* (/ 1 (hypot y.im y.re)) (/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))))
0.8b
(fma x.re y.re (* x.im y.im))
17.2b
(/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))

rewrite72.0ms

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:
12.0ms
(/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im))))
43.0ms
(* (/ 1 (hypot y.im y.re)) (/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))))
0.0ms
(fma x.re y.re (* x.im y.im))
5.0ms
(/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im))))
184.0ms
(* (/ 1 (hypot y.im y.re)) (/ 1 (/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))))
39.0ms
(fma x.re y.re (* x.im y.im))
97.0ms
(/ (hypot y.im y.re) (fma x.re y.re (* x.im y.im)))

simplify2.9s

Counts
252 → 252
Iterations

Useful iterations: done (2.9s)

IterNodesCost
02925363
17224687
215354048
343114030
done50013953

prune482.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.6b

regimes197.0ms

Accuracy

27.5% (10.4b remaining)

Error of 12.6b against oracle of 2.2b and baseline of 16.6b

bsearch69.0ms

Steps
ItersRangePoint
9
2.4623341819280814e+110
1.7160855860025047e+115
8.470980326725045e+114
6
-7.685632808780201e+93
-7.158098543380477e+92
-7.572549191493679e+93

simplify9.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02557
13251
23351
33651
44051
done4051

end0.0ms

sample579.0ms

Algorithm
intervals
Results
272.0ms8491×body80valid