Details

sample632.0ms

Algorithm: halfpoints

simplify995.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2003
4	2003
3	418
2	93
1	35
0	19

prune51.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize260.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.2b	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.5b	(/.p16 (/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
0.7b	(/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

126×	`p16-times-frac`
104×	`p16-lft-identity-expand` `p16--un-lft-identity`
56×	`*p16-rgt-identity-expand`
32×	`p16-distribute-lft-out` `distribute-lft-out`
22×	`/p16-rgt-identity-expand`
15×	`associate-/r*` `associate-/r/`
8×	`distribute-rgt-out` `introduce-quire` `-p16-rgt-identity-expand` `associate-/l*`
6×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
5×	`associate-/l/`
4×	`associate-+r+`
2×	`+-commutative` `associate-+l+` `associate-+r-` `insert-quire-add` `associate-*r/` `insert-quire-fdp-add` `associate-+l-`
1×	`associate-*l/` `p16-flip--`

Counts

4 → 165

Calls

4 calls:

9.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
9.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
74.0ms	(/.p16 (/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
14.0ms	(/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.0ms	(/.p16 (/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
0.0ms	(/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

simplify663.0ms

Counts

169 → 169

Iterations

Iter	Nodes
done	2001
3	2001
2	426
1	110
0	55

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize264.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2)))
0.2b	(.p16 (/.p16 (+.p16 beta alpha) (+.p16 (real->posit16 2.0) (+.p16 (+.p16 beta alpha) (.p16 i (real->posit16 2))))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2)))))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2))))
0.6b	(/.p16 (+.p16 beta alpha) (+.p16 (real->posit16 2.0) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2)))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

108×	`p16-lft-identity-expand` `p16--un-lft-identity`
90×	`p16-times-frac`
66×	`*p16-rgt-identity-expand`
40×	`associate-l`
28×	`p16-distribute-lft-out` `distribute-lft-out`
15×	`associate-/r*`
13×	`associate-r`
10×	`/p16-rgt-identity-expand`
9×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
7×	`distribute-rgt-out`
6×	`associate-+r+` `introduce-quire` `-p16-rgt-identity-expand` `associate-/l*`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`
3×	`associate-/l/`
1×	`+-commutative` `associate-+l+` `associate-+r-` `insert-quire-add` `associate-l/` `associate-r/` `p16-flip--` `*-commutative` `insert-quire-fdp-add` `associate-+l-`

Counts

4 → 175

Calls

4 calls:

9.0ms	(+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2)))
38.0ms	(.p16 (/.p16 (+.p16 beta alpha) (+.p16 (real->posit16 2.0) (+.p16 (+.p16 beta alpha) (.p16 i (real->posit16 2))))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2)))))
14.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2))))
66.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (real->posit16 2.0) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2)))
0.0ms	(.p16 (/.p16 (+.p16 beta alpha) (+.p16 (real->posit16 2.0) (+.p16 (+.p16 beta alpha) (.p16 i (real->posit16 2))))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2)))))
0.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2))))
0.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (real->posit16 2.0) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2)))))

simplify1.7s

Counts

179 → 179

Iterations

Iter	Nodes
done	2001
4	2001
3	1804
2	606
1	135
0	62

prune2.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize316.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 2.0)) (+.p16 alpha beta))
0.2b	(.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 (.p16 i (real->posit16 2)) (real->posit16 2.0)) (+.p16 alpha beta))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2)))))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2))))
0.6b	(/.p16 (+.p16 alpha beta) (+.p16 (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 2.0)) (+.p16 alpha beta)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

125×	`p16-lft-identity-expand` `p16--un-lft-identity`
90×	`p16-times-frac`
77×	`*p16-rgt-identity-expand`
40×	`associate-l`
32×	`p16-distribute-lft-out` `distribute-lft-out`
27×	`insert-quire-fdp-add`
24×	`introduce-quire`
15×	`associate-/r*`
13×	`associate-r`
10×	`/p16-rgt-identity-expand`
9×	`insert-quire-add`
8×	`distribute-rgt-out` `-p16-rgt-identity-expand`
6×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand` `associate-/l*`
4×	`associate-/r/` `associate-+l-`
3×	`associate-/l/`
2×	`distribute-rgt-in` `associate-+r-` `distribute-lft-in`
1×	`+-commutative` `associate-+l+` `associate-+r+` `associate-l/` `associate-r/` `p16-flip--` `*-commutative`

Counts

4 → 199

Calls

4 calls:

19.0ms	(+.p16 (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 2.0)) (+.p16 alpha beta))
20.0ms	(.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 (.p16 i (real->posit16 2)) (real->posit16 2.0)) (+.p16 alpha beta))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2)))))
28.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2))))
27.0ms	(/.p16 (+.p16 alpha beta) (+.p16 (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 2.0)) (+.p16 alpha beta)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 2.0)) (+.p16 alpha beta))
0.0ms	(.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 (.p16 i (real->posit16 2)) (real->posit16 2.0)) (+.p16 alpha beta))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2)))))
0.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2))))
0.0ms	(/.p16 (+.p16 alpha beta) (+.p16 (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 2.0)) (+.p16 alpha beta)))

simplify1.3s

Counts

203 → 203

Iterations

Iter	Nodes
done	2003
3	2003
2	498
1	148
0	67

prune1.6s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

localize309.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 2.0)) alpha) beta)
0.2b	(.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 (+.p16 (.p16 i (real->posit16 2)) (real->posit16 2.0)) alpha) beta)) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2)))))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2))))
0.6b	(/.p16 (+.p16 alpha beta) (+.p16 (+.p16 (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 2.0)) alpha) beta))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

36×	`p16-times-frac`
35×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
13×	`associate-r` `associate-l`
12×	`insert-quire-add`
10×	`introduce-quire` `/p16-rgt-identity-expand`
8×	`-p16-rgt-identity-expand` `associate-+l-`
6×	`associate-/r` `+p16-lft-identity-expand` `+p16-rgt-identity-expand` `associate-/l`
4×	`associate-/r/`
3×	`insert-quire-fdp-add` `associate-/l/`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`+-commutative` `associate-+l+` `associate-+r-` `associate-l/` `associate-r/` `p16-flip--` `*-commutative`

Counts

4 → 112

Calls

4 calls:

31.0ms	(+.p16 (+.p16 (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 2.0)) alpha) beta)
41.0ms	(.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 (+.p16 (.p16 i (real->posit16 2)) (real->posit16 2.0)) alpha) beta)) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2)))))
15.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2))))
62.0ms	(/.p16 (+.p16 alpha beta) (+.p16 (+.p16 (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 2.0)) alpha) beta))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (+.p16 (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 2.0)) alpha) beta)
0.0ms	(.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 (+.p16 (.p16 i (real->posit16 2)) (real->posit16 2.0)) alpha) beta)) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2)))))
0.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 beta alpha) (*.p16 i (real->posit16 2))))
0.0ms	(/.p16 (+.p16 alpha beta) (+.p16 (+.p16 (+.p16 (*.p16 i (real->posit16 2)) (real->posit16 2.0)) alpha) beta))

simplify812.0ms

Counts

116 → 116

Iterations

Iter	Nodes
done	2004
3	2004
2	543
1	150
0	69

prune1.7s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

regimes927.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	22
0	22

end0.0ms

sample14.4s

Algorithm: halfpoints