Details

sample299.0ms

Algorithm: halfpoints

simplify50.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	37
3	37
2	35
1	27
0	16

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize305.0ms

Local error

Found 4 expressions with local error:

0.3b	(-.p16 (.p16 b b) (.p16 (real->posit16 4) (*.p16 a c)))
0.3b	(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (.p16 b b) (.p16 (real->posit16 4) (.p16 a c))))) (.p16 (real->posit16 2) a))
0.3b	(sqrt.p16 (-.p16 (.p16 b b) (.p16 (real->posit16 4) (*.p16 a c))))
0.8b	(-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (.p16 b b) (.p16 (real->posit16 4) (*.p16 a c)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`p16-lft-identity-expand` `p16--un-lft-identity`
13×	`*p16-rgt-identity-expand`
12×	`distribute-lft-out--`
10×	`+p16-lft-identity-expand` `introduce-quire` `+p16-rgt-identity-expand`
8×	`p16-times-frac` `-p16-rgt-identity-expand` `associate-/l*` `associate--r+`
7×	`/p16-rgt-identity-expand`
4×	`associate--l+` `insert-quire-fdp-sub`
3×	`distribute-rgt-out--` `p16-flip--`
2×	`associate--l-` `distribute-rgt-in` `insert-quire-sub` `sub-neg` `distribute-lft-in` `associate-/r/` `associate--r-` `associate-/l/`
1×	`associate-/r` `associate-l/`

Counts

4 → 84

Calls

4 calls:

10.0ms	(-.p16 (.p16 b b) (.p16 (real->posit16 4) (*.p16 a c)))
8.0ms	(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (.p16 b b) (.p16 (real->posit16 4) (.p16 a c))))) (.p16 (real->posit16 2) a))
0.0ms	(sqrt.p16 (-.p16 (.p16 b b) (.p16 (real->posit16 4) (*.p16 a c))))
7.0ms	(-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (.p16 b b) (.p16 (real->posit16 4) (*.p16 a c)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(-.p16 (.p16 b b) (.p16 (real->posit16 4) (*.p16 a c)))
0.0ms	(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (.p16 b b) (.p16 (real->posit16 4) (.p16 a c))))) (.p16 (real->posit16 2) a))
0.0ms	(sqrt.p16 (-.p16 (.p16 b b) (.p16 (real->posit16 4) (*.p16 a c))))
0.0ms	(-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (.p16 b b) (.p16 (real->posit16 4) (*.p16 a c)))))

simplify1.0s

Counts

88 → 88

Iterations

Iter	Nodes
done	2004
3	2004
2	543
1	118
0	60

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize309.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))) (*.p16 (real->posit16 2) a))
0.3b	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))
0.8b	(-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))))
11.7b	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

18×	`p16-lft-identity-expand` `p16--un-lft-identity`
12×	`*p16-rgt-identity-expand` `distribute-lft-out--`
8×	`p16-times-frac` `associate-/l*`
7×	`introduce-quire`
6×	`/p16-rgt-identity-expand`
5×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
3×	`distribute-rgt-out--` `insert-quire-fdp-sub`
2×	`associate--l+` `p16-flip--` `associate-/r/` `associate--r+` `associate-/l/`
1×	`associate--l-` `insert-quire-sub` `associate-/r` `sub-neg` `associate-l/` `associate--r-`

Counts

4 → 62

Calls

4 calls:

5.0ms	(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))) (*.p16 (real->posit16 2) a))
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))
3.0ms	(-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))) (*.p16 (real->posit16 2) a))
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))
0.0ms	(-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))

simplify1.8s

Counts

66 → 66

Iterations

Iter	Nodes
done	2053
4	2053
3	1964
2	303
1	71
0	43

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.9b

localize295.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))) a)
0.3b	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))
0.8b	(-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))))
11.7b	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

13×	`p16-lft-identity-expand` `p16--un-lft-identity`
9×	`*p16-rgt-identity-expand`
8×	`associate-/l*` `distribute-lft-out--`
7×	`introduce-quire`
5×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
4×	`/p16-rgt-identity-expand`
3×	`insert-quire-fdp-sub`
2×	`distribute-rgt-out--` `associate--l+` `p16-flip--` `associate--r+` `associate-/l/`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `associate--r-`

Counts

4 → 51

Calls

4 calls:

4.0ms	(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))) a)
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))
3.0ms	(-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))) a)
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))
0.0ms	(-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))

simplify1.1s

Counts

55 → 55

Iterations

Iter	Nodes
done	2002
4	2002
3	1060
2	181
1	59
0	39

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.9b

localize387.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))
0.4b	(.p16 (/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (*.p16 a c))))) (real->posit16 2)) (/.p16 (real->posit16 1.0) a))
0.8b	(-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))))
11.7b	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

33×	`p16-lft-identity-expand` `p16--un-lft-identity`
28×	`associate-l`
25×	`*p16-rgt-identity-expand`
24×	`p16-times-frac`
16×	`distribute-lft-out--`
7×	`+p16-lft-identity-expand` `introduce-quire` `+p16-rgt-identity-expand`
5×	`-p16-rgt-identity-expand`
4×	`distribute-rgt-out--` `/p16-rgt-identity-expand`
3×	`associate-r` `insert-quire-fdp-sub`
2×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `associate--r+`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `associate-l/` `associate-r/` `p16-flip--` `associate-/r/` `*-commutative` `associate--r-`

Counts

4 → 79

Calls

4 calls:

0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))
8.0ms	(.p16 (/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (*.p16 a c))))) (real->posit16 2)) (/.p16 (real->posit16 1.0) a))
5.0ms	(-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))))
1.0ms	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))
0.0ms	(.p16 (/.p16 (-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (*.p16 a c))))) (real->posit16 2)) (/.p16 (real->posit16 1.0) a))
0.0ms	(-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))

simplify3.2s

Counts

83 → 83

Iterations

Iter	Nodes
done	2065
4	2065
3	1291
2	323
1	98
0	48

prune1.6s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.9b

regimes1.7s

Accuracy

0% (0.4b remaining)

Error of 1.5b against oracle of 1.1b and baseline of 1.5b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	20
0	20

end0.0ms

sample3.4s

Algorithm: halfpoints