Details

sample497.0ms

Algorithm: halfpoints

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	2419
3	423
2	97
1	35
0	19

prune96.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize824.0ms

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)))
0.8b	(/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

rewrite125.0ms

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:

15.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
16.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
77.0ms	(/.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)))
13.0ms	(/.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)))

simplify1.1s

Counts

169 → 169

Iterations

Iter	Nodes
done	5001
2	771
1	111
0	55

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize426.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.2b	(.p16 (/.p16 (/.p16 (+.p16 alpha beta) (real->posit16 1.0)) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 2.0))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha (*.p16 i (real->posit16 2))) beta)))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha (*.p16 i (real->posit16 2))) beta))
0.6b	(/.p16 (/.p16 (+.p16 alpha beta) (real->posit16 1.0)) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

555×	`p16-times-frac`
438×	`p16-lft-identity-expand` `p16--un-lft-identity`
276×	`*p16-rgt-identity-expand`
160×	`associate-l`
108×	`p16-distribute-lft-out` `distribute-lft-out`
34×	`/p16-rgt-identity-expand`
29×	`associate-/r/`
27×	`distribute-rgt-out`
16×	`associate-/l*`
15×	`associate-/r*`
13×	`associate-r`
7×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
6×	`introduce-quire` `-p16-rgt-identity-expand`
3×	`associate-/l/`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
1×	`+-commutative` `associate-+l+` `associate-+r-` `insert-quire-add` `associate-l/` `associate-r/` `p16-flip--` `*-commutative` `insert-quire-fdp-add` `associate-+l-`

Counts

4 → 421

Calls

4 calls:

13.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
38.0ms	(.p16 (/.p16 (/.p16 (+.p16 alpha beta) (real->posit16 1.0)) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 2.0))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha (*.p16 i (real->posit16 2))) beta)))
12.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha (*.p16 i (real->posit16 2))) beta))
68.0ms	(/.p16 (/.p16 (+.p16 alpha beta) (real->posit16 1.0)) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.0ms	(.p16 (/.p16 (/.p16 (+.p16 alpha beta) (real->posit16 1.0)) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 2.0))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha (*.p16 i (real->posit16 2))) beta)))
0.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha (*.p16 i (real->posit16 2))) beta))
0.0ms	(/.p16 (/.p16 (+.p16 alpha beta) (real->posit16 1.0)) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))

simplify1.9s

Counts

425 → 425

Iterations

Iter	Nodes
done	5002
2	1711
1	161
0	66

prune2.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize587.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i)))
0.2b	(/.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (.p16 (real->posit16 2) i)))) (+.p16 (+.p16 (real->posit16 2.0) beta) (+.p16 alpha (.p16 (real->posit16 2) i))))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i))))
0.7b	(.p16 (/.p16 (/.p16 (+.p16 alpha beta) (real->posit16 1.0)) (real->posit16 1.0)) (/.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (.p16 (real->posit16 2) i)))) (+.p16 (+.p16 (real->posit16 2.0) beta) (+.p16 alpha (*.p16 (real->posit16 2) i)))))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

612×	`p16-times-frac`
466×	`p16-lft-identity-expand` `p16--un-lft-identity`
304×	`*p16-rgt-identity-expand`
160×	`associate-r`
108×	`p16-distribute-lft-out` `distribute-lft-out`
43×	`associate-l`
37×	`/p16-rgt-identity-expand`
32×	`associate-/r/`
27×	`distribute-rgt-out`
16×	`associate-/l*`
15×	`associate-/r*`
6×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
4×	`introduce-quire`
3×	`associate-+r-` `associate-/l/`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`+-commutative` `associate-+r+` `associate-l/` `associate-r/` `p16-flip--` `*-commutative`

Counts

4 → 447

Calls

4 calls:

8.0ms	(+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i)))
63.0ms	(/.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (.p16 (real->posit16 2) i)))) (+.p16 (+.p16 (real->posit16 2.0) beta) (+.p16 alpha (.p16 (real->posit16 2) i))))
13.0ms	(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i))))
38.0ms	(.p16 (/.p16 (/.p16 (+.p16 alpha beta) (real->posit16 1.0)) (real->posit16 1.0)) (/.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (.p16 (real->posit16 2) i)))) (+.p16 (+.p16 (real->posit16 2.0) beta) (+.p16 alpha (*.p16 (real->posit16 2) i)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i)))
0.0ms	(/.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (.p16 (real->posit16 2) i)))) (+.p16 (+.p16 (real->posit16 2.0) beta) (+.p16 alpha (.p16 (real->posit16 2) i))))
0.0ms	(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i))))
0.0ms	(.p16 (/.p16 (/.p16 (+.p16 alpha beta) (real->posit16 1.0)) (real->posit16 1.0)) (/.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (.p16 (real->posit16 2) i)))) (+.p16 (+.p16 (real->posit16 2.0) beta) (+.p16 alpha (*.p16 (real->posit16 2) i)))))

simplify2.5s

Counts

451 → 451

Iterations

Iter	Nodes
done	5000
2	1826
1	198
0	70

prune2.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.2b

localize466.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i)))
0.2b	(/.p16 (/.p16 (-.p16 beta alpha) (quire16->posit16 (posit16->quire16 (+.p16 alpha (+.p16 beta (.p16 (real->posit16 2) i)))))) (+.p16 (+.p16 (real->posit16 2.0) beta) (+.p16 alpha (.p16 (real->posit16 2) i))))
0.6b	(/.p16 (-.p16 beta alpha) (quire16->posit16 (posit16->quire16 (+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i))))))
0.7b	(.p16 (/.p16 (/.p16 (+.p16 alpha beta) (real->posit16 1.0)) (real->posit16 1.0)) (/.p16 (/.p16 (-.p16 beta alpha) (quire16->posit16 (posit16->quire16 (+.p16 alpha (+.p16 beta (.p16 (real->posit16 2) i)))))) (+.p16 (+.p16 (real->posit16 2.0) beta) (+.p16 alpha (*.p16 (real->posit16 2) i)))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

612×	`p16-times-frac`
466×	`p16-lft-identity-expand` `p16--un-lft-identity`
304×	`*p16-rgt-identity-expand`
160×	`associate-r`
108×	`p16-distribute-lft-out` `distribute-lft-out`
43×	`associate-l`
37×	`/p16-rgt-identity-expand`
32×	`associate-/r/`
27×	`distribute-rgt-out`
16×	`associate-/l*`
15×	`associate-/r*`
6×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
4×	`introduce-quire`
3×	`associate-+r-` `associate-/l/`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`+-commutative` `associate-+r+` `associate-l/` `associate-r/` `p16-flip--` `*-commutative`

Counts

4 → 447

Calls

4 calls:

5.0ms	(+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i)))
43.0ms	(/.p16 (/.p16 (-.p16 beta alpha) (quire16->posit16 (posit16->quire16 (+.p16 alpha (+.p16 beta (.p16 (real->posit16 2) i)))))) (+.p16 (+.p16 (real->posit16 2.0) beta) (+.p16 alpha (.p16 (real->posit16 2) i))))
3.0ms	(/.p16 (-.p16 beta alpha) (quire16->posit16 (posit16->quire16 (+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i))))))
25.0ms	(.p16 (/.p16 (/.p16 (+.p16 alpha beta) (real->posit16 1.0)) (real->posit16 1.0)) (/.p16 (/.p16 (-.p16 beta alpha) (quire16->posit16 (posit16->quire16 (+.p16 alpha (+.p16 beta (.p16 (real->posit16 2) i)))))) (+.p16 (+.p16 (real->posit16 2.0) beta) (+.p16 alpha (*.p16 (real->posit16 2) i)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i)))
0.0ms	(/.p16 (/.p16 (-.p16 beta alpha) (quire16->posit16 (posit16->quire16 (+.p16 alpha (+.p16 beta (.p16 (real->posit16 2) i)))))) (+.p16 (+.p16 (real->posit16 2.0) beta) (+.p16 alpha (.p16 (real->posit16 2) i))))
0.0ms	(/.p16 (-.p16 beta alpha) (quire16->posit16 (posit16->quire16 (+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i))))))
0.0ms	(.p16 (/.p16 (/.p16 (+.p16 alpha beta) (real->posit16 1.0)) (real->posit16 1.0)) (/.p16 (/.p16 (-.p16 beta alpha) (quire16->posit16 (posit16->quire16 (+.p16 alpha (+.p16 beta (.p16 (real->posit16 2) i)))))) (+.p16 (+.p16 (real->posit16 2.0) beta) (+.p16 alpha (*.p16 (real->posit16 2) i)))))

simplify2.6s

Counts

451 → 451

Iterations

Iter	Nodes
done	5000
2	1562
1	192
0	69

prune2.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

regimes1.5s

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	23
0	23

end0.0ms

sample14.5s

Algorithm: halfpoints