Details

sample1.3s

Algorithm: halfpoints

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5014
3	1591
2	264
1	60
0	19

prune62.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize359.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.2b	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))
1.4b	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
3.6b	(/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))

rewrite27.4s

Algorithm

rewrite-expression-head

Rules

213267×	`p16-lft-identity-expand` `p16--un-lft-identity`
201708×	`associate-l`
190020×	`p16-times-frac`
108979×	`associate-r`
89295×	`*p16-rgt-identity-expand`
77172×	`p16-distribute-lft-out` `distribute-lft-out`
74151×	`distribute-lft-out--`
15186×	`distribute-rgt-out`
14228×	`*-commutative`
7062×	`distribute-rgt-out--` `difference-of-squares`
2354×	`difference-of-sqr-1`
1228×	`associate-/l*`
260×	`/p16-rgt-identity-expand`
248×	`associate-/r/`
170×	`associate-/r*`
86×	`associate-l/` `associate-r/`
85×	`associate-/l/`
22×	`introduce-quire`
20×	`associate-+r+`
16×	`insert-quire-fdp-add`
14×	`associate-+l+`
12×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
8×	`distribute-rgt-in` `distribute-lft-in` `-p16-rgt-identity-expand`
7×	`+-commutative`
2×	`associate-+r-` `insert-quire-add` `associate-+l-`
1×	`p16-flip--`

Counts

4 → 96772

Calls

4 calls:

19.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
46.0ms	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))
4.1s	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
207.0ms	(/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))

series1.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.3m

Counts

96776 → 96776

Iterations

Iter	Nodes
done	5001
1	847
0	333

prune8.2s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 0.5b

localize360.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.6b	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
1.5b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.5b	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

rewrite10.5s

Algorithm

rewrite-expression-head

Rules

110553×	`p16-lft-identity-expand` `p16--un-lft-identity`
84656×	`p16-times-frac`
58617×	`p16-distribute-lft-out` `distribute-lft-out`
41263×	`*p16-rgt-identity-expand`
33664×	`associate-l`
9927×	`distribute-rgt-out`
9405×	`distribute-lft-out--`
6368×	`associate-r`
1302×	`*-commutative`
495×	`distribute-rgt-out--`
470×	`associate-/l*`
265×	`distribute-lft1-in`
264×	`associate-/r*`
202×	`/p16-rgt-identity-expand`
191×	`associate-/r/`
74×	`associate-/l/`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
2×	`associate-*r/`
1×	`p16-flip--`

Counts

4 → 43477

Calls

4 calls:

1.4s	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
525.0ms	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
178.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
80.0ms	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

series1.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify29.5s

Counts

43481 → 43481

Iterations

Iter	Nodes
done	5004
2	1812
1	239
0	99

prune3.3s

Pruning

32 alts after pruning (31 fresh and 1 done)

Merged error: 0.4b

localize547.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.7b	(/.p16 i (+.p16 (-.p16 (*.p16 i (real->posit16 2)) (real->posit16 1.0)) (+.p16 alpha beta)))
1.1b	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
1.5b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite7.6s

Algorithm

rewrite-expression-head

Rules

87200×	`p16-lft-identity-expand` `p16--un-lft-identity`
63933×	`p16-times-frac`
50509×	`p16-distribute-lft-out` `distribute-lft-out`
32130×	`*p16-rgt-identity-expand`
25528×	`associate-l`
8911×	`distribute-rgt-out`
2474×	`associate-r`
293×	`associate-/l*`
265×	`distribute-lft1-in`
224×	`associate-/r*`
134×	`/p16-rgt-identity-expand`
126×	`associate-/r/`
39×	`associate-/l/`
24×	`distribute-rgt-out--` `distribute-lft-out--`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`

Counts

4 → 32771

Calls

4 calls:

1.2s	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
45.0ms	(/.p16 i (+.p16 (-.p16 (*.p16 i (real->posit16 2)) (real->posit16 1.0)) (+.p16 alpha beta)))
21.0ms	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
118.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

series1.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify25.2s

Counts

32775 → 32775

Iterations

Iter	Nodes
done	5007
3	3260
2	617
1	139
0	62

prune2.4s

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 0.4b

localize679.0ms

Local error

Found 4 expressions with local error:

0.7b	(/.p16 i (+.p16 (-.p16 (*.p16 i (real->posit16 2)) (real->posit16 1.0)) (+.p16 alpha beta)))
0.8b	(.p16 (/.p16 (real->posit16 1.0) (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 1.0)))) (/.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 i (+.p16 beta alpha)))) (+.p16 (+.p16 beta (*.p16 i (real->posit16 2))) alpha)))
1.1b	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
1.5b	(/.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 i (+.p16 beta alpha)))) (+.p16 (+.p16 beta (*.p16 i (real->posit16 2))) alpha))

rewrite587.0ms

Algorithm

rewrite-expression-head

Rules

583×	`p16-lft-identity-expand` `p16--un-lft-identity`
365×	`*p16-rgt-identity-expand`
312×	`p16-times-frac`
292×	`p16-distribute-lft-out` `distribute-lft-out`
229×	`associate-l`
144×	`associate-/r*`
81×	`distribute-rgt-out` `associate-*l/`
71×	`associate-r`
32×	`associate-/l*`
24×	`distribute-rgt-out--` `distribute-lft-out--`
19×	`associate-*r/`
15×	`/p16-rgt-identity-expand`
8×	`distribute-lft1-in`
6×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
5×	`associate-/r/`
4×	`introduce-quire` `-p16-rgt-identity-expand` `associate-/l/`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`*-commutative`

Counts

4 → 544

Calls

4 calls:

46.0ms	(/.p16 i (+.p16 (-.p16 (*.p16 i (real->posit16 2)) (real->posit16 1.0)) (+.p16 alpha beta)))
384.0ms	(.p16 (/.p16 (real->posit16 1.0) (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 1.0)))) (/.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 i (+.p16 beta alpha)))) (+.p16 (+.p16 beta (*.p16 i (real->posit16 2))) alpha)))
42.0ms	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
82.0ms	(/.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 i (+.p16 beta alpha)))) (+.p16 (+.p16 beta (*.p16 i (real->posit16 2))) alpha))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.1s

Counts

548 → 548

Iterations

Iter	Nodes
done	5129
3	2141
2	501
1	149
0	58

prune2.0s

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 0.4b

regimes2.6s

Accuracy

0% (1.0b remaining)

Error of 1.4b against oracle of 0.4b and baseline of 1.4b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	30
0	30

end0.0ms

sample30.2s

Algorithm: halfpoints