Details

Time bar (total: 12.6s)

sample56.0ms

Algorithm
halfpoints

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done13
213
112
07

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize88.0ms

Local error

Found 2 expressions with local error:

0.1b
(sqrt.p16 (+.p16 x (real->posit16 1)))
0.7b
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
7×*p16-lft-identity-expand p16-*-un-lft-identity
6×introduce-quire
5×*p16-rgt-identity-expand
4×+p16-lft-identity-expand -p16-rgt-identity-expand +p16-rgt-identity-expand distribute-lft-out--
3×insert-quire-fdp-sub
2×associate--l+ /p16-rgt-identity-expand associate--r+
1×associate--l- insert-quire-sub sub-neg distribute-rgt-out-- p16-flip-- associate--r-
Counts
2 → 33
Calls
2 calls:
0.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))
3.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

series0.0ms

Counts
2 → 2
Calls
2 calls:
0.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))
0.0ms
(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

simplify1.2s

Counts
35 → 35
Iterations
IterNodes
done5001
3790
2132
137
023

prune320.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.7b

localize255.0ms

Local error

Found 4 expressions with local error:

0.1b
(+.p16 (sqrt.p16 x) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.1b
(/.p16 (*.p16 (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 x) (sqrt.p16 (+.p16 (real->posit16 1) x)))) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.2b
(*.p16 (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 x) (sqrt.p16 (+.p16 (real->posit16 1) x))))
0.7b
(-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
50×*p16-lft-identity-expand p16-*-un-lft-identity
22×*p16-rgt-identity-expand
16×p16-distribute-lft-out distribute-lft-out
12×associate-/r* introduce-quire p16-times-frac associate-*r*
10×/p16-rgt-identity-expand
8×+p16-lft-identity-expand associate-*l* -p16-rgt-identity-expand +p16-rgt-identity-expand distribute-lft-out--
4×distribute-rgt-out associate-*l/ associate-/l/
3×p16-flip-- insert-quire-fdp-add insert-quire-fdp-sub
2×associate-+l+ associate-+r+ distribute-rgt-out-- associate--l+ associate-*r/ associate--r+
1×associate--l- distribute-rgt-in +-commutative insert-quire-sub associate-+r- sub-neg insert-quire-add distribute-lft-in associate-/r/ *-commutative associate-+l- associate-/l* associate--r-
Counts
4 → 125
Calls
4 calls:
7.0ms
(+.p16 (sqrt.p16 x) (sqrt.p16 (+.p16 (real->posit16 1) x)))
13.0ms
(/.p16 (*.p16 (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 x) (sqrt.p16 (+.p16 (real->posit16 1) x)))) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
9.0ms
(*.p16 (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 x) (sqrt.p16 (+.p16 (real->posit16 1) x))))
6.0ms
(-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(+.p16 (sqrt.p16 x) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.0ms
(/.p16 (*.p16 (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 x) (sqrt.p16 (+.p16 (real->posit16 1) x)))) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.0ms
(*.p16 (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 x) (sqrt.p16 (+.p16 (real->posit16 1) x))))
0.0ms
(-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))

simplify1.6s

Counts
129 → 129
Iterations
IterNodes
done5000
2666
1102
050

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize263.0ms

Local error

Found 4 expressions with local error:

0.1b
(*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.2b
(-.p16 (*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
0.3b
(*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.3b
(/.p16 (*.p16 (-.p16 (*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (sqrt.p16 x) (sqrt.p16 x))) (+.p16 (sqrt.p16 x) (sqrt.p16 (+.p16 (real->posit16 1) x)))) (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
24×*p16-lft-identity-expand p16-*-un-lft-identity
15×associate-*r* associate-*l*
14×/p16-rgt-identity-expand
12×+p16-lft-identity-expand *p16-rgt-identity-expand +p16-rgt-identity-expand
8×p16-distribute-lft-out distribute-lft-out
7×distribute-rgt-in distribute-lft-in
6×introduce-quire -p16-rgt-identity-expand associate--l+ associate--r+
5×associate-*l/
4×associate-*r/ associate-/l/
3×associate-/r/
2×distribute-rgt-out p16-flip-- *-commutative
1×associate--l- insert-quire-sub associate-/r* sub-neg p16-times-frac sqrt-sqrd.p16 insert-quire-fdp-sub associate-/l* associate--r- difference-of-squares
Counts
4 → 104
Calls
4 calls:
11.0ms
(*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
7.0ms
(-.p16 (*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
5.0ms
(*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x)))
5.0ms
(/.p16 (*.p16 (-.p16 (*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (sqrt.p16 x) (sqrt.p16 x))) (+.p16 (sqrt.p16 x) (sqrt.p16 (+.p16 (real->posit16 1) x)))) (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.0ms
(-.p16 (*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
0.0ms
(*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.0ms
(/.p16 (*.p16 (-.p16 (*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (*.p16 (sqrt.p16 x) (sqrt.p16 x))) (+.p16 (sqrt.p16 x) (sqrt.p16 (+.p16 (real->posit16 1) x)))) (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))))

simplify1.9s

Counts
108 → 108
Iterations
IterNodes
done5001
2683
1135
055

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize246.0ms

Local error

Found 4 expressions with local error:

0.1b
(*.p16 (sqrt.p16 x) (sqrt.p16 x))
0.1b
(*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.2b
(-.p16 (+.p16 (real->posit16 1) x) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
0.3b
(/.p16 (*.p16 (-.p16 (+.p16 (real->posit16 1) x) (*.p16 (sqrt.p16 x) (sqrt.p16 x))) (+.p16 (sqrt.p16 x) (sqrt.p16 (+.p16 (real->posit16 1) x)))) (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
24×*p16-lft-identity-expand p16-*-un-lft-identity
15×associate-*r* associate-*l*
14×/p16-rgt-identity-expand
12×*p16-rgt-identity-expand
9×+p16-lft-identity-expand +p16-rgt-identity-expand
8×p16-distribute-lft-out introduce-quire distribute-lft-out
7×-p16-rgt-identity-expand
6×associate--r+
5×distribute-rgt-in distribute-lft-in associate-*l/
4×associate-*r/ associate-/l/
3×associate-/r/
2×associate--l- insert-quire-sub insert-quire-add distribute-rgt-out p16-flip-- *-commutative insert-quire-fdp-sub
1×associate-/r* sub-neg p16-times-frac associate--l+ associate-+l- sqrt-sqrd.p16 associate-/l* associate--r-
Counts
4 → 101
Calls
4 calls:
2.0ms
(*.p16 (sqrt.p16 x) (sqrt.p16 x))
6.0ms
(*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
10.0ms
(-.p16 (+.p16 (real->posit16 1) x) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
4.0ms
(/.p16 (*.p16 (-.p16 (+.p16 (real->posit16 1) x) (*.p16 (sqrt.p16 x) (sqrt.p16 x))) (+.p16 (sqrt.p16 x) (sqrt.p16 (+.p16 (real->posit16 1) x)))) (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(*.p16 (sqrt.p16 x) (sqrt.p16 x))
0.0ms
(*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.0ms
(-.p16 (+.p16 (real->posit16 1) x) (*.p16 (sqrt.p16 x) (sqrt.p16 x)))
0.0ms
(/.p16 (*.p16 (-.p16 (+.p16 (real->posit16 1) x) (*.p16 (sqrt.p16 x) (sqrt.p16 x))) (+.p16 (sqrt.p16 x) (sqrt.p16 (+.p16 (real->posit16 1) x)))) (*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))))

simplify1.2s

Counts
105 → 105
Iterations
IterNodes
done5002
2829
1139
056

prune994.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

regimes128.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done20
120
018

end0.0ms

sample2.1s

Algorithm
halfpoints