Details

sample1.0s

Algorithm

halfpoints

Results

simplify628.0ms

Calls

1 calls:

Slowest

628.0ms

(/.p16 (/.p16 (*.p16 (*.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i)))) (*.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))) (-.p16 (*.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))) (real->posit16 1.0)))

prune120.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize556.0ms

Local error

Found 4 expressions with local error:

3.4b	(/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))
1.5b	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
0.2b	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))
0.2b	(*.p16 i (+.p16 (+.p16 alpha beta) i))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

4×	`p16-times-frac`
2×	`distribute-rgt-in` `associate-+r+` `associate-/r` `distribute-lft-in` `difference-of-sqr-1` `associate-/l`
1×	`+-commutative` `p16-flip--` `associate-/r/` `*-commutative` `associate-/l/`

Calls

4 calls:

Slowest

6.0ms	(/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))
5.0ms	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
2.0ms	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))
2.0ms	(*.p16 i (+.p16 (+.p16 alpha beta) i))

series0.0ms

Calls

4 calls:

Slowest

0.0ms	(/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))
0.0ms	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
0.0ms	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))
0.0ms	(*.p16 i (+.p16 (+.p16 alpha beta) i))

simplify5.1s

Calls

18 calls:

Slowest

1.0s	(-.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0))
751.0ms	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
612.0ms	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
589.0ms	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
572.0ms	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.0b

localize257.0ms

Local error

Found 4 expressions with local error:

1.4b	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))
1.4b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
0.6b	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.5b	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

2×	`associate-/l/`
1×	`p16-flip--` `associate-/r/` `associate-/l*`

Calls

4 calls:

Slowest

8.0ms	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
7.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
3.0ms	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))
2.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

series0.0ms

Calls

4 calls:

Slowest

0.0ms	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))
0.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
0.0ms	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))

simplify3.9s

Calls

11 calls:

Slowest

1.1s	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
641.0ms	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
566.0ms	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
535.0ms	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
297.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))

prune965.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.8b

localize135.0ms

Local error

Found 4 expressions with local error:

1.4b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.0b	(/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) i))
0.6b	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.5b	(/.p16 (/.p16 i (/.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

2×	`associate-/r/` `associate-/l/`
1×	`p16-flip--` `associate-/l*`

Calls

4 calls:

Slowest

10.0ms	(/.p16 (/.p16 i (/.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
6.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
4.0ms	(/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) i))
3.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

series0.0ms

Calls

4 calls:

Slowest

0.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
0.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.0ms	(/.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) i))
0.0ms	(/.p16 (/.p16 i (/.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))

simplify84.0ms

Calls

3 calls:

Slowest

37.0ms

(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0))

31.0ms

(+.p16 (*.p16 beta alpha) (*.p16 i (+.p16 (+.p16 alpha beta) i)))

15.0ms

(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

prune748.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.7b

localize202.0ms

Local error

Found 4 expressions with local error:

1.4b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.0b	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) i))
0.8b	(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
0.6b	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

1×	`p16-flip--` `associate-/r/` `associate-/l/`

Calls

4 calls:

Slowest

11.0ms	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) i))
6.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
2.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.0ms	(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

series0.0ms

Calls

4 calls:

Slowest

0.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
0.0ms	(/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)) (+.p16 (+.p16 alpha beta) i))
0.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.0ms	(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

simplify220.0ms

Calls

6 calls:

Slowest

64.0ms	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))
40.0ms	(+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0))
30.0ms	(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
29.0ms	(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
28.0ms	(/.p16 i (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

prune338.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 0.7b

regimes2.6s

Accuracy

-∞% (-62.5b remaining)

Error of 1.5b against oracle of 64.0b and baseline of 64.0b

bsearch7.0ms

end0.0ms

sample32.9s

Algorithm

halfpoints

Results