Details

sample398.0ms

Algorithm: halfpoints

simplify93.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	37
3	37
2	35
1	27
0	16

prune60.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

localize422.0ms

Local error

Found 4 expressions with local error:

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	(-.p16 (.p16 b b) (.p16 (real->posit16 4) (*.p16 a c)))
0.4b	(.p16 (real->posit16 4) (.p16 a c))
0.9b	(-.p16 (neg.p16 b) (sqrt.p16 (-.p16 (.p16 b b) (.p16 (real->posit16 4) (*.p16 a c)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

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

series1.0ms

Counts

4 → 4

Calls

4 calls:

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	(-.p16 (.p16 b b) (.p16 (real->posit16 4) (*.p16 a c)))
0.0ms	(.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)))))

simplify1.9s

Counts

99 → 99

Iterations

Iter	Nodes
3	3691
2	541
1	123
0	62

prune6.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.9b

localize331.0ms

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))))
0.3b	(/.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))
0.9b	(-.p16 (neg.p16 b) (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))))
12.1b	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))

rewrite15.0ms

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:

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

simplify32.9s

Counts

66 → 66

Iterations

Iter	Nodes
4	21150
3	1978
2	302
1	71
0	43

prune5.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.9b

localize337.0ms

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))))
0.3b	(.p16 (/.p16 (-.p16 (real->posit16 0.0) (+.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (*.p16 a c)))) b)) (real->posit16 2)) (/.p16 (real->posit16 1.0) a))
0.9b	(+.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))) b)
12.1b	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))
13.0ms	(.p16 (/.p16 (-.p16 (real->posit16 0.0) (+.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (*.p16 a c)))) b)) (real->posit16 2)) (/.p16 (real->posit16 1.0) a))
19.0ms	(+.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))) b)
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 (real->posit16 0.0) (+.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (*.p16 a c)))) b)) (real->posit16 2)) (/.p16 (real->posit16 1.0) a))
0.0ms	(+.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))) b)
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))

simplify1.0m

Counts

71 → 71

Iterations

Iter	Nodes
4	5776
3	539
2	215
1	86
0	40

prune5.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.9b

localize323.0ms

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))))
0.3b	(.p16 (/.p16 (-.p16 (real->posit16 0.0) (+.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))) b)) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (.p16 a (real->posit16 2))))
0.9b	(+.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))) b)
12.1b	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

29×	`p16-lft-identity-expand` `p16--un-lft-identity`
28×	`associate-l`
27×	`p16-times-frac`
23×	`*p16-rgt-identity-expand`
12×	`distribute-lft-out--`
8×	`associate-r`
6×	`+p16-lft-identity-expand` `/p16-rgt-identity-expand` `+p16-rgt-identity-expand`
4×	`introduce-quire` `-p16-rgt-identity-expand`
3×	`distribute-rgt-out--` `associate-/r/`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-*r/`
1×	`+-commutative` `insert-quire-add` `associate-l/` `-commutative` `associate-+l-`

Counts

4 → 72

Calls

4 calls:

0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))
7.0ms	(.p16 (/.p16 (-.p16 (real->posit16 0.0) (+.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))) b)) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (.p16 a (real->posit16 2))))
3.0ms	(+.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))) b)
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	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))))
0.0ms	(.p16 (/.p16 (-.p16 (real->posit16 0.0) (+.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))) b)) (real->posit16 1.0)) (/.p16 (real->posit16 1.0) (.p16 a (real->posit16 2))))
0.0ms	(+.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c)))) b)
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (real->posit16 4) (.p16 a c))

simplify4.8s

Counts

76 → 76

Iterations

Iter	Nodes
4	2123
3	465
2	187
1	82
0	39

prune5.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.9b

regimes1.2s

Accuracy

0% (0.5b remaining)

Error of 1.6b against oracle of 1.1b and baseline of 1.6b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
1	23
0	23

end0.0ms

sample3.8s

Algorithm: halfpoints