Details

sample380.0ms

Algorithm: halfpoints

simplify58.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	16
2	16
1	14
0	10

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.9b

localize134.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.p16 (.p16 b_2 b_2) (.p16 c a))
0.3b	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
0.4b	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
1.2b	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

4.0ms	(-.p16 (.p16 b_2 b_2) (.p16 c a))
3.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
0.0ms	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
4.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

series1.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(-.p16 (.p16 b_2 b_2) (.p16 c a))
0.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
0.0ms	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
0.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

simplify10.6s

Counts

57 → 57

Iterations

Iter	Nodes
4	9276
3	1003
2	203
1	72
0	39

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.5b

localize199.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a))) b_2) a)
0.4b	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a)))
1.2b	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a))) b_2)
5.0b	(quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a)

rewrite13.0ms

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:

7.0ms	(/.p16 (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a))) b_2) a)
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a)))
5.0ms	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a))) b_2)
1.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a))) b_2) a)
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a)))
0.0ms	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a))) b_2)
0.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 b_2 b_2)) c a)

simplify1.1m

Counts

39 → 39

Iterations

Iter	Nodes
6	5937
5	1681
4	332
3	114
2	53
1	41
0	28

prune1.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.5b

localize176.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.p16 (real->posit16 1.0) (/.p16 a (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)))
0.3b	(/.p16 a (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2))
0.4b	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
1.2b	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

2.0ms	(/.p16 (real->posit16 1.0) (/.p16 a (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)))
2.0ms	(/.p16 a (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2))
0.0ms	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
2.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (real->posit16 1.0) (/.p16 a (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)))
0.0ms	(/.p16 a (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2))
0.0ms	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
0.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

simplify1.2s

Counts

72 → 72

Iterations

Iter	Nodes
4	3038
3	428
2	130
1	51
0	33

prune2.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 1.4b

localize241.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.p16 (.p16 b_2 b_2) (.p16 c a))
0.4b	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
0.4b	(.p16 (/.p16 (real->posit16 1.0) a) (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (*.p16 c a))) b_2))
1.2b	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

6.0ms	(-.p16 (.p16 b_2 b_2) (.p16 c a))
0.0ms	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
8.0ms	(.p16 (/.p16 (real->posit16 1.0) a) (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (*.p16 c a))) b_2))
5.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(-.p16 (.p16 b_2 b_2) (.p16 c a))
0.0ms	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
0.0ms	(.p16 (/.p16 (real->posit16 1.0) a) (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (*.p16 c a))) b_2))
0.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

simplify8.6m

Iterations

Iter	Nodes
3	1583
2	381
1	109
0	48