Details

Time bar (total: 21.0s)

sample76.0ms

Algorithm
halfpoints

simplify10.0ms

Counts
1 → 1
Iterations
IterNodes
done13
213
112
07

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize137.0ms

Local error

Found 2 expressions with local error:

0.2b
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.6b
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
15×*p16-lft-identity-expand p16-*-un-lft-identity
14×*p16-rgt-identity-expand
9×p16-times-frac
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×associate-/r* insert-quire-fdp-sub associate-/l*
2×distribute-rgt-out-- associate--l+ associate-/r/ associate--r+
1×associate--l- insert-quire-sub sub-neg p16-flip-- associate--r- associate-/l/
Counts
2 → 51
Calls
2 calls:
8.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
28.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))

series0.0ms

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

simplify1.4s

Counts
53 → 53
Iterations
IterNodes
done5008
31281
2237
152
029

prune389.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize250.0ms

Local error

Found 4 expressions with local error:

0.3b
(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
0.3b
(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
0.6b
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))
0.8b
(/.p16 (*.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
57×*p16-lft-identity-expand p16-*-un-lft-identity
36×introduce-quire *p16-rgt-identity-expand
31×p16-times-frac
26×insert-quire-fdp-add
16×p16-distribute-lft-out distribute-lft-out
15×/p16-rgt-identity-expand
13×associate-/r*
10×+p16-lft-identity-expand -p16-rgt-identity-expand +p16-rgt-identity-expand
8×distribute-rgt-out associate-/r/
4×associate-+l+ associate-+r+ distribute-lft-out-- associate-/l/
3×insert-quire-fdp-sub
2×+-commutative associate-+r- insert-quire-add distribute-rgt-out-- associate-*l/ associate--l+ p16-flip-- associate-+l- associate--r+
1×associate--l- insert-quire-sub sub-neg associate-*r/ associate-/l* associate--r-
Counts
4 → 144
Calls
4 calls:
26.0ms
(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
39.0ms
(+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))
33.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))
66.0ms
(/.p16 (*.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))))

series0.0ms

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

simplify1.7s

Counts
148 → 148
Iterations
IterNodes
done5000
2635
192
048

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize372.0ms

Local error

Found 4 expressions with local error:

0.3b
(+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))
0.5b
(-.p16 (*.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (*.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) x)))
0.8b
(/.p16 (*.p16 (/.p16 (-.p16 (*.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (*.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) x))) (+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))))
0.8b
(/.p16 (-.p16 (*.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (*.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) x))) (+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
90×*p16-lft-identity-expand p16-*-un-lft-identity
65×p16-times-frac
50×*p16-rgt-identity-expand
32×p16-distribute-lft-out distribute-lft-out
26×associate-/r*
17×/p16-rgt-identity-expand
16×distribute-rgt-out
15×difference-of-squares
12×+p16-lft-identity-expand +p16-rgt-identity-expand
10×introduce-quire associate-/r/
8×-p16-rgt-identity-expand
6×associate--l+ associate--r+
5×associate-/l* associate-/l/
4×distribute-rgt-in distribute-lft-in
3×insert-quire-fdp-add
2×associate-+l+ associate-+r+ p16-flip--
1×associate--l- +-commutative insert-quire-sub associate-+r- sub-neg insert-quire-add associate-*l/ associate-*r/ associate-+l- insert-quire-fdp-sub associate--r-
Counts
4 → 175
Calls
4 calls:
36.0ms
(+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))
7.0ms
(-.p16 (*.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (*.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) x)))
66.0ms
(/.p16 (*.p16 (/.p16 (-.p16 (*.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (*.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) x))) (+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x))) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))))
69.0ms
(/.p16 (-.p16 (*.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))) (*.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) x))) (+.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))

series0.0ms

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

simplify2.0s

Counts
179 → 179
Iterations
IterNodes
done5000
2862
1151
066

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

localize470.0ms

Local error

Found 4 expressions with local error:

0.3b
(+.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x))
0.6b
(-.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x))
0.8b
(*.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x)) (-.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x))) (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x))))
0.8b
(/.p16 (*.p16 (*.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x)) (-.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x))) (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x)))) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
77×*p16-lft-identity-expand p16-*-un-lft-identity
52×p16-times-frac
46×*p16-rgt-identity-expand
43×associate-*r*
24×p16-distribute-lft-out distribute-lft-out
22×/p16-rgt-identity-expand
16×associate-*l/
13×associate-/r*
12×distribute-rgt-out introduce-quire
10×+p16-lft-identity-expand +p16-rgt-identity-expand
9×associate-/r/
8×-p16-rgt-identity-expand associate-/l/
7×associate-*r/
4×distribute-lft-out--
3×p16-flip-- insert-quire-fdp-add insert-quire-fdp-sub
2×distribute-rgt-in associate-+l+ associate-+r+ distribute-lft-in distribute-rgt-out-- associate--l+ associate--r+
1×associate--l- +-commutative insert-quire-sub associate-+r- sub-neg insert-quire-add associate-*l* *-commutative associate-+l- associate-/l* associate--r-
Counts
4 → 161
Calls
4 calls:
49.0ms
(+.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x))
28.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x))
42.0ms
(*.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x)) (-.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x))) (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x))))
65.0ms
(/.p16 (*.p16 (*.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x)) (-.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x))) (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x)))) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(+.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x))
0.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x))
0.0ms
(*.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x)) (-.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x))) (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x))))
0.0ms
(/.p16 (*.p16 (*.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x)) (-.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x))) (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) (+.p16 (real->posit16 1) x)) (/.p16 (real->posit16 1) x)))) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) x) (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))))

simplify8.1s

Counts
165 → 165
Iterations
IterNodes
done5000
2653
1130
053

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.4b

regimes184.0ms

Accuracy

0% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done9
19
07

end0.0ms

sample2.1s

Algorithm
halfpoints