Details

sample658.0ms

Algorithm: halfpoints

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5025
4	2074
3	418
2	93
1	35
0	19

prune56.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize427.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

24×	`/p16-rgt-identity-expand`
21×	`p16-lft-identity-expand` `p16--un-lft-identity`
19×	`*p16-rgt-identity-expand`
15×	`associate-/r/`
12×	`distribute-rgt-out`
10×	`-p16-rgt-identity-expand`
8×	`introduce-quire` `associate-*l/`
7×	`associate-+r-` `associate-*r/`
6×	`p16-distribute-lft-out` `+p16-lft-identity-expand` `+p16-rgt-identity-expand` `distribute-lft-out`
4×	`distribute-lft1-in` `associate-/l/`
3×	`associate-+r+` `associate-r` `associate-l` `insert-quire-fdp-add` `associate-+l-`
2×	`+-commutative` `associate-+l+`
1×	`distribute-rgt-in` `associate-/r` `insert-quire-add` `distribute-lft-in` `p16-times-frac` `p16-flip--` `-commutative` `associate-/l*`

Counts

4 → 98

Calls

4 calls:

40.0ms	(.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))
15.0ms	(+.p16 (/.p16 (.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 alpha (+.p16 (.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))) (real->posit16 1.0))
15.0ms	(+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))
13.0ms	(/.p16 (.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 alpha (+.p16 (.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify3.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
3	3976
2	511
1	118
0	46

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize430.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (.p16 (/.p16 (-.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 beta alpha) (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))) (real->posit16 1.0))
0.2b	(+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))
0.5b	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))
0.6b	(/.p16 (+.p16 beta alpha) (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

11.0ms	(+.p16 (.p16 (/.p16 (-.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 beta alpha) (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))) (real->posit16 1.0))
32.0ms	(+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))
26.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))
47.0ms	(/.p16 (+.p16 beta alpha) (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify3.5s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
3	1484
2	320
1	96
0	52

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize372.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (real->posit16 2.0))) (-.p16 (real->posit16 0.0) beta))
0.2b	(+.p16 (.p16 (/.p16 (-.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 beta alpha) (-.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (real->posit16 2.0))) (-.p16 (real->posit16 0.0) beta)))) (real->posit16 1.0))
0.5b	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))
0.6b	(/.p16 (+.p16 beta alpha) (-.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (real->posit16 2.0))) (-.p16 (real->posit16 0.0) beta)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

47×	`p16-lft-identity-expand` `p16--un-lft-identity`
37×	`*p16-rgt-identity-expand`
33×	`p16-times-frac`
20×	`distribute-lft-out--`
12×	`introduce-quire`
11×	`associate-/r*`
10×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
8×	`/p16-rgt-identity-expand`
6×	`associate-+l+` `associate-/l*`
5×	`associate-+r-` `distribute-rgt-out--` `associate--r+`
4×	`associate--l-`
3×	`associate--l+` `p16-flip--` `associate-/r/` `insert-quire-fdp-add` `insert-quire-fdp-sub` `associate-/l/`
2×	`distribute-rgt-in` `associate-+r+` `sub-neg` `distribute-lft-in` `associate-+l-`
1×	`+-commutative` `insert-quire-sub` `insert-quire-add` `associate--r-`

Counts

4 → 125

Calls

4 calls:

19.0ms	(-.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (real->posit16 2.0))) (-.p16 (real->posit16 0.0) beta))
7.0ms	(+.p16 (.p16 (/.p16 (-.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 beta alpha) (-.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (real->posit16 2.0))) (-.p16 (real->posit16 0.0) beta)))) (real->posit16 1.0))
23.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))
54.0ms	(/.p16 (+.p16 beta alpha) (-.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (real->posit16 2.0))) (-.p16 (real->posit16 0.0) beta)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify4.7s

Counts

129 → 129

Iterations

Iter	Nodes
done	5000
2	706
1	143
0	64

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize458.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (.p16 (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (-.p16 beta alpha))) (/.p16 (+.p16 beta alpha) (-.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (real->posit16 2.0))) (-.p16 (real->posit16 0.0) beta)))) (real->posit16 1.0))
0.3b	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (-.p16 beta alpha)))
0.5b	(/.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (-.p16 beta alpha))
0.6b	(/.p16 (+.p16 beta alpha) (-.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (real->posit16 2.0))) (-.p16 (real->posit16 0.0) beta)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

111×	`p16-times-frac`
85×	`p16-lft-identity-expand` `p16--un-lft-identity`
77×	`*p16-rgt-identity-expand`
25×	`associate-/r*`
16×	`distribute-lft-out--`
13×	`associate-/r/` `/p16-rgt-identity-expand`
9×	`associate-/l*`
8×	`+p16-lft-identity-expand` `introduce-quire` `+p16-rgt-identity-expand`
6×	`associate-+l+` `-p16-rgt-identity-expand` `p16-flip--`
4×	`distribute-rgt-out--`
3×	`insert-quire-fdp-add` `associate-/l/`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `associate-+l-`

Counts

4 → 164

Calls

4 calls:

12.0ms	(+.p16 (.p16 (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (-.p16 beta alpha))) (/.p16 (+.p16 beta alpha) (-.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (real->posit16 2.0))) (-.p16 (real->posit16 0.0) beta)))) (real->posit16 1.0))
35.0ms	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (-.p16 beta alpha)))
28.0ms	(/.p16 (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)) (-.p16 beta alpha))
51.0ms	(/.p16 (+.p16 beta alpha) (-.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (real->posit16 2.0))) (-.p16 (real->posit16 0.0) beta)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.5s

Counts

168 → 168

Iterations

Iter	Nodes
done	5014
3	2489
2	451
1	135
0	66

prune1.6s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.2b

regimes1.4s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	29
0	29

end0.0ms

sample15.0s

Algorithm: halfpoints