Details

sample466.0ms

Algorithm

halfpoints

Results

simplify1.2s

Calls

1 calls:

Slowest

1.2s	(/.p16 (+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 a c)))) a)

prune57.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.0b

localize330.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
0.4b	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
0.4b	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
0.2b	(-.p16 (.p16 b_2 b_2) (.p16 c a))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

3×	`p16-flip--`
2×	`sub-neg`
1×	`associate-/l/`

Calls

4 calls:

Slowest

5.0ms	(-.p16 (.p16 b_2 b_2) (.p16 c a))
5.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
3.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
0.0ms	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))

series0.0ms

Calls

4 calls:

Slowest

0.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
0.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
0.0ms	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
0.0ms	(-.p16 (.p16 b_2 b_2) (.p16 c a))

simplify1.5s

Calls

5 calls:

Slowest

618.0ms	(-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2))
218.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
216.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
216.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
189.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)

prune459.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.6b

localize219.0ms

Local error

Found 4 expressions with local error:

1.8b	(/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))
1.2b	(-.p16 (sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))) b_2)
0.4b	(/.p16 (-.p16 (sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))) b_2) a)
0.4b	(sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

4×	`-commutative` `associate-/l` `difference-of-squares`
3×	`p16-flip--`
2×	`associate-/l/`
1×	`sub-neg`

Calls

4 calls:

Slowest

28.0ms	(/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))
4.0ms	(/.p16 (-.p16 (sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))) b_2) a)
2.0ms	(-.p16 (sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))) b_2)
0.0ms	(sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a))))

series0.0ms

Calls

4 calls:

Slowest

0.0ms	(/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))
0.0ms	(/.p16 (-.p16 (sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))) b_2) a)
0.0ms	(-.p16 (sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))) b_2)
0.0ms	(sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a))))

simplify1.6s

Calls

6 calls:

Slowest

1.0s	(-.p16 (.p16 (sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a)))) (sqrt.p16 (/.p16 (-.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 c a) (.p16 c a))) (+.p16 (.p16 b_2 b_2) (.p16 c a))))) (.p16 b_2 b_2))
538.0ms	(-.p16 (.p16 (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)) (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2))) (.p16 (.p16 (.p16 c a) (.p16 c a)) (.p16 (.p16 c a) (.p16 c a))))
7.0ms	(+.p16 (.p16 b_2 b_2) (.p16 c a))
7.0ms	(+.p16 (.p16 b_2 b_2) (.p16 c a))
6.0ms	(+.p16 (.p16 b_2 b_2) (.p16 c a))

prune612.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.6b

localize162.0ms

Local error

Found 4 expressions with local error:

3.4b	(-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2))
1.6b	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
0.8b	(/.p16 (-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2)) (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2))
0.4b	(/.p16 (/.p16 (-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2)) (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)) a)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-commutative` `difference-of-squares`
8×	`associate-/l*` `associate-/l/`
3×	`p16-flip--`
1×	`+-commutative` `sub-neg`

Calls

4 calls:

Slowest

31.0ms	(/.p16 (/.p16 (-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2)) (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)) a)
20.0ms	(/.p16 (-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2)) (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2))
11.0ms	(-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2))
5.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

series0.0ms

Calls

4 calls:

Slowest

0.0ms	(-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2))
0.0ms	(/.p16 (/.p16 (-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2)) (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)) a)
0.0ms	(/.p16 (-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2)) (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2))
0.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

simplify2.5s

Calls

19 calls:

Slowest

513.0ms	(-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 b_2 b_2))
234.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
201.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
172.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
157.0ms	(-.p16 (.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))))) (.p16 (.p16 b_2 b_2) (.p16 b_2 b_2)))

prune1.2s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 1.5b

localize167.0ms

Local error

Found 4 expressions with local error:

1.6b	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
1.6b	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
1.2b	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
0.8b	(/.p16 (.p16 (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)) (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (*.p16 c a))) b_2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

2×	`+-commutative` `p16-flip--` `associate-/l*`
1×	`sub-neg` `associate-r/` `-commutative` `associate-/l/`

Calls

4 calls:

Slowest

16.0ms	(/.p16 (.p16 (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)) (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (*.p16 c a))) b_2))
5.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
5.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
3.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

series0.0ms

Calls

4 calls:

Slowest

0.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
0.0ms	(/.p16 (.p16 (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)) (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (*.p16 c a))) b_2))
0.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
0.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

simplify2.2s

Calls

11 calls:

Slowest

840.0ms	(.p16 (+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) (-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))) (*.p16 b_2 b_2)))
263.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
192.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
157.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
139.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

prune290.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 1.4b

regimes1.3s

Accuracy

-∞% (-61.7b remaining)

Error of 2.3b against oracle of 64.0b and baseline of 64.0b

bsearch1.0ms

end0.0ms

sample5.7s

Algorithm

halfpoints

Results