Details

sample281.0ms

Algorithm: halfpoints

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5006
4	3067
3	490
2	109
1	39
0	18

prune55.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize323.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
0.3b	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.3b	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.7b	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

rewrite293.0ms

Algorithm

rewrite-expression-head

Rules

468×	`p16-times-frac`
372×	`p16-lft-identity-expand` `p16--un-lft-identity`
338×	`*p16-rgt-identity-expand`
102×	`p16-distribute-lft-out` `distribute-lft-out`
80×	`associate-/l*`
51×	`distribute-rgt-out`
18×	`introduce-quire`
17×	`distribute-lft1-in`
14×	`insert-quire-fdp-add`
11×	`/p16-rgt-identity-expand`
10×	`-p16-rgt-identity-expand`
8×	`insert-quire-add`
6×	`associate-/r*` `+p16-lft-identity-expand` `associate-/r/` `+p16-rgt-identity-expand`
5×	`associate-+l-`
4×	`associate-+r+`
3×	`associate-+r-`
2×	`+-commutative` `associate-+l+` `associate-/l/`

Counts

4 → 406

Calls

4 calls:

48.0ms	(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
111.0ms	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
18.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
106.0ms	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 beta alpha)) (real->posit16 1.0))
0.0ms	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) (real->posit16 1))))
0.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.0ms	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

simplify4.5s

Counts

410 → 410

Iterations

Iter	Nodes
done	5001
3	4067
2	517
1	116
0	55

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize437.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
0.3b	(.p16 (/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (.p16 (real->posit16 1) (real->posit16 2))) alpha)))
0.3b	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.7b	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

783×	`p16-times-frac`
535×	`p16-lft-identity-expand` `p16--un-lft-identity`
493×	`*p16-rgt-identity-expand`
187×	`associate-l`
126×	`p16-distribute-lft-out` `distribute-lft-out`
64×	`associate-/l*`
63×	`distribute-rgt-out`
21×	`distribute-lft1-in`
16×	`/p16-rgt-identity-expand`
13×	`associate-r`
11×	`associate-/r/`
7×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
6×	`associate-/r*` `introduce-quire` `-p16-rgt-identity-expand`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `associate-/l/`
1×	`+-commutative` `associate-+l+` `associate-+r-` `insert-quire-add` `associate-l/` `associate-r/` `*-commutative` `insert-quire-fdp-add` `associate-+l-`

Counts

4 → 513

Calls

4 calls:

12.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
95.0ms	(.p16 (/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (.p16 (real->posit16 1) (real->posit16 2))) alpha)))
9.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
77.0ms	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
0.0ms	(.p16 (/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (.p16 (real->posit16 1) (real->posit16 2))) alpha)))
0.0ms	(+.p16 (+.p16 alpha beta) (*.p16 beta alpha))
0.0ms	(/.p16 (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 beta alpha)) (real->posit16 1.0)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) (real->posit16 1))))

simplify3.3s

Counts

517 → 517

Iterations

Iter	Nodes
done	5007
3	1972
2	593
1	146
0	58

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize613.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
0.3b	(.p16 (quire16->posit16 (posit16->quire16 (/.p16 (+.p16 (+.p16 (real->posit16 1.0) (+.p16 beta (.p16 beta alpha))) alpha) (+.p16 (+.p16 (.p16 (real->posit16 2) (real->posit16 1)) beta) alpha)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (.p16 (real->posit16 1) (real->posit16 2))) alpha)))
0.3b	(+.p16 (+.p16 (real->posit16 1.0) (+.p16 beta (*.p16 beta alpha))) alpha)
0.7b	(/.p16 (+.p16 (+.p16 (real->posit16 1.0) (+.p16 beta (.p16 beta alpha))) alpha) (+.p16 (+.p16 (.p16 (real->posit16 2) (real->posit16 1)) beta) alpha))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

29×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
27×	`p16-times-frac`
13×	`associate-r`
10×	`/p16-rgt-identity-expand`
9×	`introduce-quire`
8×	`-p16-rgt-identity-expand`
6×	`associate-/r` `insert-quire-add` `+p16-lft-identity-expand` `+p16-rgt-identity-expand` `associate-/l`
5×	`associate-+l-`
3×	`associate-+r-` `associate-l` `associate-/r/` `insert-quire-fdp-add`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-/l/`
1×	`+-commutative` `associate-+l+` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 100

Calls

4 calls:

24.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
15.0ms	(.p16 (quire16->posit16 (posit16->quire16 (/.p16 (+.p16 (+.p16 (real->posit16 1.0) (+.p16 beta (.p16 beta alpha))) alpha) (+.p16 (+.p16 (.p16 (real->posit16 2) (real->posit16 1)) beta) alpha)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (.p16 (real->posit16 1) (real->posit16 2))) alpha)))
47.0ms	(+.p16 (+.p16 (real->posit16 1.0) (+.p16 beta (*.p16 beta alpha))) alpha)
80.0ms	(/.p16 (+.p16 (+.p16 (real->posit16 1.0) (+.p16 beta (.p16 beta alpha))) alpha) (+.p16 (+.p16 (.p16 (real->posit16 2) (real->posit16 1)) beta) alpha))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 1) (real->posit16 2))) alpha))
0.0ms	(.p16 (quire16->posit16 (posit16->quire16 (/.p16 (+.p16 (+.p16 (real->posit16 1.0) (+.p16 beta (.p16 beta alpha))) alpha) (+.p16 (+.p16 (.p16 (real->posit16 2) (real->posit16 1)) beta) alpha)))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 beta (.p16 (real->posit16 1) (real->posit16 2))) alpha)))
0.0ms	(+.p16 (+.p16 (real->posit16 1.0) (+.p16 beta (*.p16 beta alpha))) alpha)
0.0ms	(/.p16 (+.p16 (+.p16 (real->posit16 1.0) (+.p16 beta (.p16 beta alpha))) alpha) (+.p16 (+.p16 (.p16 (real->posit16 2) (real->posit16 1)) beta) alpha))

simplify2.1s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
4	1366
3	466
2	236
1	106
0	57

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize485.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 beta (+.p16 alpha (*.p16 (real->posit16 1) (real->posit16 2))))
0.3b	(*.p16 (+.p16 (real->posit16 1.0) beta) (+.p16 (real->posit16 1.0) alpha))
0.3b	(/.p16 (quire16->posit16 (posit16->quire16 (/.p16 (.p16 (+.p16 (real->posit16 1.0) beta) (+.p16 (real->posit16 1.0) alpha)) (+.p16 beta (+.p16 alpha (.p16 (real->posit16 1) (real->posit16 2))))))) (+.p16 beta (+.p16 alpha (*.p16 (real->posit16 1) (real->posit16 2)))))
0.7b	(/.p16 (.p16 (+.p16 (real->posit16 1.0) beta) (+.p16 (real->posit16 1.0) alpha)) (+.p16 beta (+.p16 alpha (.p16 (real->posit16 1) (real->posit16 2)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

16×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
12×	`p16-times-frac` `/p16-rgt-identity-expand`
6×	`associate-/r*` `-p16-rgt-identity-expand`
4×	`+p16-lft-identity-expand` `introduce-quire` `+p16-rgt-identity-expand` `associate-/l*` `associate-/l/`
3×	`associate-+r-` `associate-r` `associate-l`
2×	`associate-l/` `associate-r/` `associate-/r/`
1×	`distribute-rgt-in` `+-commutative` `associate-+r+` `distribute-lft-in` `*-commutative`

Counts

4 → 75

Calls

4 calls:

4.0ms	(+.p16 beta (+.p16 alpha (*.p16 (real->posit16 1) (real->posit16 2))))
6.0ms	(*.p16 (+.p16 (real->posit16 1.0) beta) (+.p16 (real->posit16 1.0) alpha))
6.0ms	(/.p16 (quire16->posit16 (posit16->quire16 (/.p16 (.p16 (+.p16 (real->posit16 1.0) beta) (+.p16 (real->posit16 1.0) alpha)) (+.p16 beta (+.p16 alpha (.p16 (real->posit16 1) (real->posit16 2))))))) (+.p16 beta (+.p16 alpha (*.p16 (real->posit16 1) (real->posit16 2)))))
14.0ms	(/.p16 (.p16 (+.p16 (real->posit16 1.0) beta) (+.p16 (real->posit16 1.0) alpha)) (+.p16 beta (+.p16 alpha (.p16 (real->posit16 1) (real->posit16 2)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 beta (+.p16 alpha (*.p16 (real->posit16 1) (real->posit16 2))))
0.0ms	(*.p16 (+.p16 (real->posit16 1.0) beta) (+.p16 (real->posit16 1.0) alpha))
0.0ms	(/.p16 (quire16->posit16 (posit16->quire16 (/.p16 (.p16 (+.p16 (real->posit16 1.0) beta) (+.p16 (real->posit16 1.0) alpha)) (+.p16 beta (+.p16 alpha (.p16 (real->posit16 1) (real->posit16 2))))))) (+.p16 beta (+.p16 alpha (*.p16 (real->posit16 1) (real->posit16 2)))))
0.0ms	(/.p16 (.p16 (+.p16 (real->posit16 1.0) beta) (+.p16 (real->posit16 1.0) alpha)) (+.p16 beta (+.p16 alpha (.p16 (real->posit16 1) (real->posit16 2)))))

simplify4.2s

Counts

79 → 79

Iterations

Iter	Nodes
done	5009
4	3993
3	1188
2	355
1	92
0	47

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes468.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	27
1	27
0	25

end0.0ms

sample6.5s

Algorithm: halfpoints