Details

sample243.0ms

Algorithm: halfpoints

simplify30.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	35
3	35
2	34
1	26
0	16

prune109.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.6b

localize286.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4))))
0.3b	(-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))
0.4b	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (.p16 c a) (real->posit16 4)))) b) (.p16 (real->posit16 2) a))
1.1b	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))) b)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

9×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
7×	`introduce-quire` `-p16-rgt-identity-expand` `/p16-rgt-identity-expand`
6×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `associate--r+` `p16-*-un-lft-identity`
4×	`associate--l+`
3×	`p16-times-frac` `p16-flip--` `associate-/l*`
2×	`associate--l-` `distribute-rgt-in` `insert-quire-sub` `sub-neg` `distribute-lft-in` `associate-/r/` `associate-/l/`
1×	`associate-/r` `associate-l/` `insert-quire-fdp-sub` `associate--r-`

Counts

4 → 63

Calls

4 calls:

0.0ms	(sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4))))
5.0ms	(-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))
4.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (.p16 c a) (real->posit16 4)))) b) (.p16 (real->posit16 2) a))
4.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))) b)

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify3.4s

Counts

67 → 67

Iterations

Iter	Nodes
3	3433
2	413
1	112
0	55

prune4.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize323.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4))))
0.4b	(/.p16 (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4)))) b) (*.p16 (real->posit16 2) a))
1.1b	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4)))) b)
10.6b	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

6×	`/p16-rgt-identity-expand`
5×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
3×	`p16-times-frac` `associate-/l*`
2×	`associate--l+` `p16-flip--` `associate-/r/` `associate-/l/`
1×	`associate--l-` `insert-quire-sub` `associate-/r` `sub-neg` `associate-l/`

Counts

4 → 41

Calls

4 calls:

0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4))))
7.0ms	(/.p16 (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4)))) b) (*.p16 (real->posit16 2) a))
4.0ms	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4)))) b)
1.0ms	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.4s

Counts

45 → 45

Iterations

Iter	Nodes
4	3261
3	574
2	166
1	61
0	38

prune2.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.2b

localize391.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4))))
0.3b	(/.p16 (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4)))) b) a)
1.1b	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4)))) b)
10.6b	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

4×	`p16-lft-identity-expand` `+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `/p16-rgt-identity-expand` `p16-rgt-identity-expand` `+p16-rgt-identity-expand` `p16-*-un-lft-identity`
3×	`associate-/l*`
2×	`associate--l+` `p16-flip--` `associate-/l/`
1×	`associate--l-` `insert-quire-sub` `sub-neg`

Counts

4 → 35

Calls

4 calls:

0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4))))
7.0ms	(/.p16 (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4)))) b) a)
5.0ms	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4)))) b)
1.0ms	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify48.7s

Counts

39 → 39

Iterations

Iter	Nodes
6	32619
5	1609
4	357
3	122
2	60
1	48
0	34

prune2.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.2b

localize771.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4))))
0.3b	(.p16 (/.p16 (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (*.p16 c a) (real->posit16 4)))) b) (real->posit16 2)) (/.p16 (real->posit16 1.0) a))
1.1b	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4)))) b)
10.6b	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`associate-l`
11×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
9×	`p16-times-frac`
6×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
4×	`introduce-quire` `-p16-rgt-identity-expand` `/p16-rgt-identity-expand`
3×	`associate-r`
2×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `associate-l/` `associate-r/` `p16-flip--` `associate-/r/` `*-commutative`

Counts

4 → 53

Calls

4 calls:

0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4))))
7.0ms	(.p16 (/.p16 (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (*.p16 c a) (real->posit16 4)))) b) (real->posit16 2)) (/.p16 (real->posit16 1.0) a))
5.0ms	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4)))) b)
1.0ms	(quire16-mul-sub (posit16->quire16 (.p16 b b)) (.p16 c a) (real->posit16 4))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.1m

Counts

57 → 57

Iterations

Iter	Nodes
4	7290
3	706
2	257
1	88
0	43

prune3.8s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 1.2b

regimes1.1s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
1	16
0	16

end0.0ms

sample3.8s

Algorithm: halfpoints