Details

Time bar (total: 33.8s)

sample402.0ms

Algorithm
halfpoints
Results

simplify385.0ms

Calls
1 calls:
Slowest
384.0ms
(*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (+.p16 (real->posit16 1) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand)))

prune48.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize342.0ms

Local error

Found 4 expressions with local error:

0.4b
(*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (+.p16 (real->posit16 1) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand)))
0.3b
(sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
0.3b
(*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
0.3b
(/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
3×distribute-rgt-in distribute-lft-in
2×+-commutative sub-neg p16-flip-- *-commutative
1×associate-*l/ associate-*r/
Calls
4 calls:
Slowest
8.0ms
(*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (+.p16 (real->posit16 1) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand)))
5.0ms
(*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
2.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))))
0.0ms
(sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))

series0.0ms

Calls
4 calls:
Slowest
0.0ms
(*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (+.p16 (real->posit16 1) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand)))
0.0ms
(sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
0.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))))
0.0ms
(*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))

simplify2.7s

Calls
12 calls:
Slowest
493.0ms
(*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (+.p16 (real->posit16 1) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand)))
467.0ms
(*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (+.p16 (real->posit16 1) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand)))
409.0ms
(*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (+.p16 (real->posit16 1) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand)))
386.0ms
(*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (+.p16 (real->posit16 1) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand)))
277.0ms
(*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand))

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize93.0ms

Local error

Found 4 expressions with local error:

0.6b
(*.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
0.4b
(+.p16 (*.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (*.p16 (real->posit16 1) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
0.3b
(sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
0.3b
(*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
8×sub-neg
7×*-commutative
4×distribute-rgt-in distribute-lft-in
2×associate-+l+ associate-+r+ associate-*l* associate-*l/ associate-*r/ p16-flip--
1×+-commutative p16-distribute-lft-out distribute-rgt-out distribute-lft-out
Calls
4 calls:
Slowest
38.0ms
(+.p16 (*.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (*.p16 (real->posit16 1) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
8.0ms
(*.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
5.0ms
(*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
0.0ms
(sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))

series0.0ms

Calls
4 calls:
Slowest
0.0ms
(*.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
0.0ms
(+.p16 (*.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (*.p16 (real->posit16 1) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
0.0ms
(sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
0.0ms
(*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))

simplify4.1s

Calls
22 calls:
Slowest
966.0ms
(/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))))
922.0ms
(*.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand) (neg.p16 (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
879.0ms
(*.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand) a)
179.0ms
(*.p16 a (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand))
161.0ms
(*.p16 (*.p16 (real->posit16 1) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize119.0ms

Local error

Found 4 expressions with local error:

0.6b
(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
0.4b
(+.p16 (*.p16 rand (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))) (*.p16 (real->posit16 1) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
0.3b
(sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
0.3b
(*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
10×sub-neg
7×distribute-rgt-in distribute-lft-in
4×associate-+l+
2×associate-+r+ associate-*r/ p16-flip-- *-commutative
1×+-commutative distribute-rgt-out associate-*r* associate-*l/
Calls
4 calls:
Slowest
30.0ms
(+.p16 (*.p16 rand (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))) (*.p16 (real->posit16 1) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
7.0ms
(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
5.0ms
(*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
0.0ms
(sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))

series0.0ms

Calls
4 calls:
Slowest
0.0ms
(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
0.0ms
(+.p16 (*.p16 rand (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))) (*.p16 (real->posit16 1) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
0.0ms
(*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
0.0ms
(sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))

simplify1.8s

Calls
15 calls:
Slowest
912.0ms
(*.p16 (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) a) rand)
143.0ms
(+.p16 (*.p16 rand (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))))) (real->posit16 1))
131.0ms
(*.p16 (neg.p16 (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))))
122.0ms
(*.p16 rand (*.p16 a (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))))))
122.0ms
(*.p16 rand (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) a))

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize183.0ms

Local error

Found 4 expressions with local error:

0.6b
(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (real->posit16 9)))) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
0.4b
(+.p16 (*.p16 rand (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (real->posit16 9)))) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))) (*.p16 (real->posit16 1) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
0.3b
(sqrt.p16 (*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (real->posit16 9)))
0.3b
(*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (real->posit16 9))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
8×sub-neg
6×distribute-rgt-in distribute-lft-in
4×associate-+l+
2×associate-+r+ associate-*l/ p16-flip-- *-commutative
1×+-commutative distribute-rgt-out associate-*r* associate-*r/
Calls
4 calls:
Slowest
21.0ms
(+.p16 (*.p16 rand (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (real->posit16 9)))) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))) (*.p16 (real->posit16 1) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
7.0ms
(*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (real->posit16 9))
5.0ms
(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (real->posit16 9)))) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
0.0ms
(sqrt.p16 (*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (real->posit16 9)))

series0.0ms

Calls
4 calls:
Slowest
0.0ms
(*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (real->posit16 9)))) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
0.0ms
(+.p16 (*.p16 rand (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (real->posit16 9)))) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))) (*.p16 (real->posit16 1) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
0.0ms
(*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (real->posit16 9))
0.0ms
(sqrt.p16 (*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (real->posit16 9)))

simplify4.1s

Calls
13 calls:
Slowest
1.5s
(+.p16 (*.p16 rand (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (real->posit16 9))))) (real->posit16 1))
903.0ms
(*.p16 rand (*.p16 a (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (real->posit16 9))))))
688.0ms
(*.p16 (-.p16 (*.p16 a a) (*.p16 (/.p16 (real->posit16 1.0) (real->posit16 3.0)) (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (real->posit16 9))
219.0ms
(*.p16 rand (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (real->posit16 9)))) a))
166.0ms
(*.p16 (real->posit16 1) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes1.1s

Accuracy

-∞% (-63.5b remaining)

Error of 0.5b against oracle of 64.0b and baseline of 64.0b

bsearch5.0ms

end0.0ms

sample11.4s

Algorithm
halfpoints
Results