Details

Time bar (total: 9.4s)

sample115.0ms

Algorithm
halfpoints
Results

simplify243.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
243.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize174.0ms

Local error

Found 4 expressions with local error:

0.8b
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
0.4b
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
0.2b
(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
0.2b
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
2×sub-neg p16-flip--
1×+-commutative associate-+l+ associate-/r/ associate-+l-
Counts
4 → 6
Calls
4 calls:
Slowest
17.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
5.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
3.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
3.0ms
(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) 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 2) x))
0.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
0.0ms
(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))

simplify1.0s

Counts
7 → 10
Calls
7 calls:
Slowest
299.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
269.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
251.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
190.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
10.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))

prune395.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize305.0ms

Local error

Found 4 expressions with local error:

0.8b
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (/.p16 (real->posit16 2) x) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))))
0.4b
(-.p16 (/.p16 (real->posit16 2) x) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
0.2b
(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
0.2b
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
3×sub-neg p16-flip--
1×associate-/r/ associate--r+ associate--r-
Counts
4 → 7
Calls
4 calls:
Slowest
12.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
5.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (/.p16 (real->posit16 2) x) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))))
4.0ms
(-.p16 (/.p16 (real->posit16 2) x) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
3.0ms
(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (/.p16 (real->posit16 2) x) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))))
0.0ms
(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
0.0ms
(-.p16 (/.p16 (real->posit16 2) x) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
0.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))

simplify177.0ms

Counts
7 → 11
Calls
7 calls:
Slowest
97.0ms
(neg.p16 (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1))))
26.0ms
(/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))
13.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
11.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
11.0ms
(/.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))

prune534.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.8b

localize386.0ms

Local error

Found 4 expressions with local error:

0.8b
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (+.p16 x (real->posit16 1))))
0.6b
(*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (+.p16 x (real->posit16 1)))
0.4b
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
0.2b
(/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
3×p16-flip--
2×distribute-rgt-in associate-+r+ sub-neg distribute-lft-in associate-/r/
1×+-commutative associate-+l+ associate-/r* associate-*l* associate-*l/ *-commutative associate-+l- difference-of-squares
Counts
4 → 14
Calls
4 calls:
Slowest
12.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (+.p16 x (real->posit16 1))))
8.0ms
(/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1))))
3.0ms
(*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (+.p16 x (real->posit16 1)))
3.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (+.p16 x (real->posit16 1))))
0.0ms
(*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (+.p16 x (real->posit16 1)))
0.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
0.0ms
(/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1))))

simplify1.5s

Counts
14 → 18
Calls
14 calls:
Slowest
371.0ms
(/.p16 (real->posit16 1) (-.p16 (*.p16 (*.p16 x x) (*.p16 x x)) (*.p16 (*.p16 (real->posit16 1) (real->posit16 1)) (*.p16 (real->posit16 1) (real->posit16 1)))))
315.0ms
(*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))))
303.0ms
(*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (real->posit16 1))
220.0ms
(*.p16 (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))) (real->posit16 1))
203.0ms
(*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))))

prune715.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.7b

localize396.0ms

Local error

Found 4 expressions with local error:

0.8b
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (*.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))))
0.6b
(/.p16 (*.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1))))
0.4b
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
0.2b
(-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
3×sub-neg p16-flip-- difference-of-squares
1×+-commutative associate-+l+ associate-/r* p16-times-frac associate-/r/ associate-+l- associate-/l*
Counts
4 → 12
Calls
4 calls:
Slowest
27.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (*.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))))
7.0ms
(/.p16 (*.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1))))
5.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))
5.0ms
(-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
0.0ms
(+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (*.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))))
0.0ms
(/.p16 (*.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1))))
0.0ms
(-.p16 (*.p16 x x) (*.p16 (real->posit16 1) (real->posit16 1)))
0.0ms
(-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x))

simplify179.0ms

Counts
13 → 16
Calls
13 calls:
Slowest
29.0ms
(/.p16 (+.p16 x (real->posit16 1)) (-.p16 x (real->posit16 1)))
18.0ms
(*.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
17.0ms
(*.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
16.0ms
(*.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))
16.0ms
(*.p16 (real->posit16 1) (+.p16 x (real->posit16 1)))

prune471.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.7b

regimes197.0ms

Accuracy

-∞% (-63.0b remaining)

Error of 1.0b against oracle of 64.0b and baseline of 64.0b

bsearch3.0ms

end0.0ms

sample2.4s

Algorithm
halfpoints
Results