Details

Time bar (total: 10.0m)

sample103.0ms

Algorithm
halfpoints

simplify4.4s

Counts
1 → 1
Iterations
IterNodes
done5001
84615
73127
61308
5586
4220
3107
249
120
011

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize290.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.p16 (+.p16 (*.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
0.2b
(*.p16 (-.p16 (*.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
0.3b
(-.p16 (*.p16 x.re x.re) (*.p16 x.im x.im))
0.3b
(+.p16 (*.p16 (-.p16 (*.p16 x.re x.re) (*.p16 x.im x.im)) x.im) (*.p16 (+.p16 (*.p16 x.re x.im) (*.p16 x.im x.re)) x.re))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
8×+p16-lft-identity-expand introduce-quire -p16-rgt-identity-expand +p16-rgt-identity-expand
7×associate-*l*
6×*p16-lft-identity-expand /p16-rgt-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
3×associate-*l/
2×associate-+l+ associate-+r+ associate--l+ p16-flip-- *-commutative associate--r+ difference-of-squares
1×associate--l- +-commutative insert-quire-sub associate-+r- sub-neg insert-quire-add insert-quire-fdp-add associate-+l- insert-quire-fdp-sub associate--r-
Counts
4 → 64
Calls
4 calls:
3.0ms
(*.p16 (+.p16 (*.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
4.0ms
(*.p16 (-.p16 (*.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
5.0ms
(-.p16 (*.p16 x.re x.re) (*.p16 x.im x.im))
7.0ms
(+.p16 (*.p16 (-.p16 (*.p16 x.re x.re) (*.p16 x.im x.im)) x.im) (*.p16 (+.p16 (*.p16 x.re x.im) (*.p16 x.im x.re)) x.re))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(*.p16 (+.p16 (*.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
0.0ms
(*.p16 (-.p16 (*.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
0.0ms
(-.p16 (*.p16 x.re x.re) (*.p16 x.im x.im))
0.0ms
(+.p16 (*.p16 (-.p16 (*.p16 x.re x.re) (*.p16 x.im x.im)) x.im) (*.p16 (+.p16 (*.p16 x.re x.im) (*.p16 x.im x.re)) x.re))

simplify2.0s

Counts
68 → 68
Iterations
IterNodes
done5008
31200
2258
179
041

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize393.0ms

Local error

Found 4 expressions with local error:

0.1b
(+.p16 (*.p16 x.re x.im) (*.p16 x.re x.im))
0.2b
(*.p16 (+.p16 x.im x.re) x.im)
0.2b
(*.p16 (-.p16 x.re x.im) (*.p16 (+.p16 x.im x.re) x.im))
8.4b
(quire16-mul-add (posit16->quire16 (*.p16 (-.p16 x.re x.im) (*.p16 (+.p16 x.im x.re) x.im))) (+.p16 (*.p16 x.re x.im) (*.p16 x.re x.im)) x.re)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
7×+p16-lft-identity-expand /p16-rgt-identity-expand +p16-rgt-identity-expand
6×associate-*l*
5×*p16-lft-identity-expand introduce-quire -p16-rgt-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
4×associate-*l/
2×distribute-rgt-in associate-+l+ associate-+r+ distribute-lft-in associate-*r/ *-commutative
1×+-commutative associate-+r- insert-quire-add p16-distribute-lft-out distribute-rgt-out associate-*r* p16-flip-- insert-quire-fdp-add associate-+l- distribute-lft-out
Counts
4 → 54
Calls
4 calls:
7.0ms
(+.p16 (*.p16 x.re x.im) (*.p16 x.re x.im))
7.0ms
(*.p16 (+.p16 x.im x.re) x.im)
11.0ms
(*.p16 (-.p16 x.re x.im) (*.p16 (+.p16 x.im x.re) x.im))
1.0ms
(quire16-mul-add (posit16->quire16 (*.p16 (-.p16 x.re x.im) (*.p16 (+.p16 x.im x.re) x.im))) (+.p16 (*.p16 x.re x.im) (*.p16 x.re x.im)) x.re)

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(+.p16 (*.p16 x.re x.im) (*.p16 x.re x.im))
0.0ms
(*.p16 (+.p16 x.im x.re) x.im)
0.0ms
(*.p16 (-.p16 x.re x.im) (*.p16 (+.p16 x.im x.re) x.im))
0.0ms
(quire16-mul-add (posit16->quire16 (*.p16 (-.p16 x.re x.im) (*.p16 (+.p16 x.im x.re) x.im))) (+.p16 (*.p16 x.re x.im) (*.p16 x.re x.im)) x.re)

simplify1.1s

Counts
58 → 58
Iterations
IterNodes
done5061
31244
2223
173
035

prune758.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize260.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.p16 (+.p16 (*.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
0.2b
(*.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)) x.im)
0.3b
(+.p16 (*.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)) x.im) (*.p16 (+.p16 (*.p16 x.re x.im) (*.p16 x.im x.re)) x.re))
7.1b
(quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
6×associate-*l*
5×*p16-lft-identity-expand +p16-lft-identity-expand introduce-quire -p16-rgt-identity-expand /p16-rgt-identity-expand *p16-rgt-identity-expand +p16-rgt-identity-expand p16-*-un-lft-identity
2×associate-+l+ associate-+r+ associate-*l/ *-commutative
1×+-commutative associate-+r- insert-quire-add insert-quire-fdp-add associate-+l-
Counts
4 → 43
Calls
4 calls:
3.0ms
(*.p16 (+.p16 (*.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
2.0ms
(*.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)) x.im)
4.0ms
(+.p16 (*.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)) x.im) (*.p16 (+.p16 (*.p16 x.re x.im) (*.p16 x.im x.re)) x.re))
0.0ms
(quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(*.p16 (+.p16 (*.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
0.0ms
(*.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)) x.im)
0.0ms
(+.p16 (*.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)) x.im) (*.p16 (+.p16 (*.p16 x.re x.im) (*.p16 x.im x.re)) x.re))
0.0ms
(quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)

simplify3.5s

Counts
47 → 47
Iterations
IterNodes
done5004
72348
61761
5873
4363
3187
273
139
026

prune990.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize402.0ms

Local error

Found 4 expressions with local error:

0.0b
(*.p16 x.im (+.p16 x.re x.re))
0.2b
(*.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)) x.im)
7.1b
(quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)
8.4b
(quire16-mul-add (posit16->quire16 (*.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)) x.im)) (*.p16 x.im (+.p16 x.re x.re)) x.re)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
4×*p16-lft-identity-expand /p16-rgt-identity-expand *p16-rgt-identity-expand p16-*-un-lft-identity
3×associate-*r* associate-*l*
2×+p16-lft-identity-expand introduce-quire -p16-rgt-identity-expand *-commutative +p16-rgt-identity-expand
1×distribute-rgt-in distribute-lft-in associate-*l/ associate-*r/
Counts
4 → 28
Calls
4 calls:
3.0ms
(*.p16 x.im (+.p16 x.re x.re))
2.0ms
(*.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)) x.im)
0.0ms
(quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)
0.0ms
(quire16-mul-add (posit16->quire16 (*.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)) x.im)) (*.p16 x.im (+.p16 x.re x.re)) x.re)

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(*.p16 x.im (+.p16 x.re x.re))
0.0ms
(*.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)) x.im)
0.0ms
(quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)
0.0ms
(quire16-mul-add (posit16->quire16 (*.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)) x.im)) (*.p16 x.im (+.p16 x.re x.re)) x.re)

simplify9.7m

Iterations
IterNodes
10084845
10074838
10064836
10054829
10044827
10034820
10024818
10014811
10004809
9994802
9984800
9974793
9964791
9954784
9944782
9934775
9924773
9914766
9904764
9894757
9884755
9874748
9864746
9854739
9844737
9834730
9824728
9814721
9804714
9794713
9784706
9774704
9764697
9754695
9744688
9734686
9724679
9714677
9704670
9694668
9684661
9674659
9664652
9654650
9644643
9634641
9624634
9614632
9604625
9594618
9584617
9574610
9564608
9554601
9544594
9534593
9524586
9514584
9504577
9494570
9484569
9474562
9464560
9454553
9444551
9434544
9424542
9414535
9404528
9394527
9384520
9374518
9364511
9354504
9344503
9334496
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9314487
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9294478
9284476
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9264462
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9244454
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9144410
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9114395
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9094386
9084379
9074377
9064370
9054368
9044361
9034359
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9014350
9004343
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8964326
8954319
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8934310
8924308
8914301
8904294
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8884286
8874284
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8854270
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8824260
8814253
8804246
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8714205
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8504102
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8404054
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8314013
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7623684
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112564
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109549
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101509
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86437
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84429
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81413
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71365
70358
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61317
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53278
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1594
1493
1386
1284
1177
1070
969
862
760
653
546
445
338
236
127
021