Details

Time bar (total: 22.0s)

sample116.0ms

Algorithm
halfpoints

simplify15.0ms

Counts
1 → 1
Iterations
IterNodes
done15
215
114
09

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize173.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt.p16 (+.p16 x (real->posit16 1)))
0.1b
(/.p16 (real->posit16 1) (sqrt.p16 x))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.4b
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
77×p16-times-frac
71×*p16-lft-identity-expand p16-*-un-lft-identity
51×*p16-rgt-identity-expand
24×distribute-lft-out--
18×introduce-quire
13×/p16-rgt-identity-expand insert-quire-fdp-sub
9×distribute-rgt-out--
7×associate-/r/
6×associate-/r* +p16-lft-identity-expand -p16-rgt-identity-expand +p16-rgt-identity-expand associate-/l*
2×associate--l+ associate--r+ associate-/l/
1×associate--l- insert-quire-sub sub-neg p16-flip-- associate--r-
Counts
4 → 121
Calls
4 calls:
0.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))
3.0ms
(/.p16 (real->posit16 1) (sqrt.p16 x))
3.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
26.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

series0.0ms

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

simplify1.6s

Counts
125 → 125
Iterations
IterNodes
done5027
31366
2269
168
042

prune828.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize327.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
726×p16-times-frac
518×*p16-lft-identity-expand p16-*-un-lft-identity
258×*p16-rgt-identity-expand
120×p16-distribute-lft-out distribute-lft-out
62×difference-of-squares
60×associate-/r*
45×distribute-rgt-out
30×/p16-rgt-identity-expand
26×associate-*r* associate-*l*
25×associate-/r/
14×+p16-lft-identity-expand +p16-rgt-identity-expand
8×distribute-rgt-in distribute-lft-in
6×introduce-quire -p16-rgt-identity-expand associate--l+ associate--r+
4×associate-/l*
2×associate-*l/ associate-*r/ p16-flip-- *-commutative associate-/l/
1×associate--l- insert-quire-sub sub-neg insert-quire-fdp-sub associate--r-
Counts
4 → 424
Calls
4 calls:
5.0ms
(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))
65.0ms
(/.p16 (-.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
4.0ms
(-.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
5.0ms
(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

series0.0ms

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

simplify5.0s

Counts
428 → 428
Iterations
IterNodes
done5004
34197
21005
1204
084

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize235.0ms

Local error

Found 4 expressions with local error:

0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.2b
(/.p16 (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))))
0.4b
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))))

rewrite496.0ms

Algorithm
rewrite-expression-head
Rules
8617×p16-times-frac
5961×*p16-lft-identity-expand p16-*-un-lft-identity
2797×*p16-rgt-identity-expand
1488×distribute-lft-out--
888×p16-distribute-lft-out distribute-lft-out
558×distribute-rgt-out--
407×/p16-rgt-identity-expand
400×associate-/r/
333×distribute-rgt-out
66×associate-/r*
42×associate-/l*
18×introduce-quire
13×insert-quire-fdp-sub
6×+p16-lft-identity-expand -p16-rgt-identity-expand +p16-rgt-identity-expand
4×associate-/l/
2×associate--l+ p16-flip-- associate--r+
1×associate--l- insert-quire-sub sub-neg associate--r-
Counts
4 → 2380
Calls
4 calls:
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))
131.0ms
(/.p16 (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x)))))
17.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 (real->posit16 1) x))))

series0.0ms

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

simplify3.7s

Counts
2384 → 2384
Iterations
IterNodes
done5017
33035
2483
1118
066

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize345.0ms

Local error

Found 4 expressions with local error:

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

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
564×p16-times-frac
423×*p16-lft-identity-expand p16-*-un-lft-identity
215×*p16-rgt-identity-expand
96×p16-distribute-lft-out distribute-lft-out
63×associate-/r*
36×distribute-rgt-out
28×/p16-rgt-identity-expand
21×associate-/r/
13×associate-*r* associate-*l*
12×introduce-quire
10×+p16-lft-identity-expand +p16-rgt-identity-expand
7×insert-quire-fdp-sub
6×-p16-rgt-identity-expand associate--l+
5×associate-/l/
4×distribute-rgt-in distribute-lft-in associate-/l*
2×associate-*l/ associate-*r/ p16-flip-- associate--r+
1×associate--l- insert-quire-sub sub-neg *-commutative associate--r-
Counts
4 → 342
Calls
4 calls:
10.0ms
(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))
88.0ms
(/.p16 (-.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (/.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
5.0ms
(/.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1))))
14.0ms
(-.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (/.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (real->posit16 1)) (sqrt.p16 (+.p16 x (real->posit16 1)))))

series0.0ms

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

simplify2.4s

Counts
346 → 346
Iterations
IterNodes
done5002
2831
1155
071

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

regimes222.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done14
114
012

end0.0ms

sample2.5s

Algorithm
halfpoints