Details

Time bar (total: 19.4s)

sample115.0ms

Algorithm
halfpoints

simplify11.0ms

Counts
1 → 1
Iterations
IterNodes
done15
215
114
09

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize253.0ms

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)))))

rewrite20.0ms

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)))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 x))
3.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
11.0ms
(-.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)))))

simplify1.8s

Counts
125 → 125
Iterations
IterNodes
done5008
31245
2275
168
042

prune940.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize250.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
317×p16-times-frac
241×*p16-lft-identity-expand p16-*-un-lft-identity
117×*p16-rgt-identity-expand
66×associate-/r*
48×p16-distribute-lft-out distribute-lft-out
25×/p16-rgt-identity-expand
24×distribute-lft-out--
18×distribute-rgt-out introduce-quire
16×associate-/r/
13×insert-quire-fdp-sub
9×distribute-rgt-out--
7×associate-/l*
6×+p16-lft-identity-expand -p16-rgt-identity-expand +p16-rgt-identity-expand associate-/l/
2×associate--l+ associate-*r/ p16-flip-- associate--r+
1×associate--l- insert-quire-sub sub-neg associate-*l/ associate--r-
Counts
4 → 247
Calls
4 calls:
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
1.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
23.0ms
(/.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.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)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))
11.0ms
(-.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
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(/.p16 (*.p16 (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.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)))))) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.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)))))

simplify3.1s

Counts
251 → 251
Iterations
IterNodes
done5036
33129
2508
1104
055

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize294.0ms

Local error

Found 4 expressions with local error:

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

rewrite189.0ms

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 x (real->posit16 1))))
1.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
22.0ms
(/.p16 (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.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))))))
6.0ms
(-.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
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(/.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 (+.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 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

simplify3.1s

Counts
2384 → 2384
Iterations
IterNodes
done5040
32680
2492
1118
066

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize292.0ms

Local error

Found 4 expressions with local error:

0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.2b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.2b
(*.p16 (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.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))))))
0.4b
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
577×p16-times-frac
432×*p16-lft-identity-expand p16-*-un-lft-identity
236×*p16-rgt-identity-expand
184×associate-*l*
72×p16-distribute-lft-out distribute-lft-out
48×distribute-lft-out--
36×associate-*r*
31×/p16-rgt-identity-expand
27×distribute-rgt-out
24×associate-/r/
18×distribute-rgt-out-- introduce-quire
13×insert-quire-fdp-sub
10×+p16-lft-identity-expand +p16-rgt-identity-expand
8×-p16-rgt-identity-expand
6×distribute-rgt-in associate-/r* distribute-lft-in associate--l+ associate-/l*
3×sub-neg associate--r-
2×associate-*r/ p16-flip-- associate--r+ associate-/l/
1×associate--l- insert-quire-sub associate-*l/ *-commutative
Counts
4 → 357
Calls
4 calls:
1.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
1.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
20.0ms
(*.p16 (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.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))))))
11.0ms
(-.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
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.0ms
(*.p16 (/.p16 (real->posit16 1.0) (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.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 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

simplify3.2s

Counts
361 → 361
Iterations
IterNodes
done5000
33133
2590
1145
060

prune928.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

regimes110.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done17
117
015

end0.0ms

sample2.4s

Algorithm
halfpoints