Details

Time bar (total: 16.7s)

sample122.0ms

Algorithm
halfpoints
Results

simplify974.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
974.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize196.0ms

Local error

Found 4 expressions with local error:

0.5b
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.3b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.1b
(/.p16 (real->posit16 1) (sqrt.p16 x))
0.1b
(sqrt.p16 (+.p16 x (real->posit16 1)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
1×sub-neg p16-flip--
Counts
4 → 2
Calls
4 calls:
Slowest
6.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 x))
0.0ms
(sqrt.p16 (+.p16 x (real->posit16 1)))

series0.0ms

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

simplify4.3s

Counts
7 → 6
Calls
7 calls:
Slowest
999.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
987.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
963.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
953.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
392.0ms
(-.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))))))

prune114.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize275.0ms

Local error

Found 4 expressions with local error:

0.4b
(-.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)))))
0.3b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.3b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
1×sub-neg associate-*l/ associate-*r/ p16-flip-- *-commutative difference-of-squares
Counts
4 → 6
Calls
4 calls:
Slowest
5.0ms
(-.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)))))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
Slowest
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)))))
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))))

simplify3.6s

Counts
15 → 10
Calls
15 calls:
Slowest
1.1s
(-.p16 (*.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (*.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)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))))
842.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
440.0ms
(-.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))))))
426.0ms
(-.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))))))
378.0ms
(-.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))))))

prune464.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize369.0ms

Local error

Found 4 expressions with local error:

0.4b
(-.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (/.p16 (*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1)))))
0.3b
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))
0.3b
(/.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 x))) (/.p16 (*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (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))))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
2×p16-flip--
1×sub-neg associate-/l/
Counts
4 → 3
Calls
4 calls:
Slowest
8.0ms
(/.p16 (-.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (/.p16 (*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (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) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1)))))
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))))

series0.0ms

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

simplify329.0ms

Counts
8 → 7
Calls
8 calls:
Slowest
151.0ms
(*.p16 (+.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (+.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (/.p16 (*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1))))))
99.0ms
(-.p16 (*.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x)))) (*.p16 (/.p16 (*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1)))) (/.p16 (*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1))))))
30.0ms
(+.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 x))) (/.p16 (*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1)))))
16.0ms
(neg.p16 (/.p16 (*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))) (sqrt.p16 (+.p16 x (real->posit16 1)))))
8.0ms
(*.p16 (real->posit16 1) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))

prune169.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

localize197.0ms

Local error

Found 4 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
1×sub-neg p16-flip--
Counts
4 → 2
Calls
4 calls:
Slowest
3.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
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))))
1.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))

series0.0ms

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

simplify3.3s

Counts
11 → 6
Calls
11 calls:
Slowest
846.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
807.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
688.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
603.0ms
(-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1)))))
262.0ms
(-.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))))))

prune99.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.5b

regimes103.0ms

Accuracy

-∞% (-63.4b remaining)

Error of 0.6b against oracle of 64.0b and baseline of 64.0b

bsearch2.0ms

end0.0ms

sample2.0s

Algorithm
halfpoints
Results