Details

sample227.0ms

Algorithm

halfpoints

Results

simplify187.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

187.0ms

(/.p16 (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (*.p16 (real->posit16 2) a))

prune45.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

localize308.0ms

Local error

Found 4 expressions with local error:

0.9b	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))) b)
0.3b	(sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4))))
0.3b	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (.p16 c a) (real->posit16 4)))) b) (.p16 (real->posit16 2) a))
0.3b	(-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 6

Calls

4 calls:

Slowest

6.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (.p16 c a) (real->posit16 4)))) b) (.p16 (real->posit16 2) a))
6.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))) b)
4.0ms	(-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))
0.0ms	(sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

0.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))) b)
0.0ms	(sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4))))
0.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (.p16 c a) (real->posit16 4)))) b) (.p16 (real->posit16 2) a))
0.0ms	(-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))

simplify2.1s

Counts

5 → 10

Calls

5 calls:

Slowest

683.0ms	(-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (.p16 c a) (real->posit16 4)))) (sqrt.p16 (-.p16 (.p16 b b) (.p16 (.p16 c a) (real->posit16 4))))) (.p16 b b))
389.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (.p16 c a) (real->posit16 4)))) b) (.p16 (real->posit16 2) a))
373.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (.p16 c a) (real->posit16 4)))) b) (.p16 (real->posit16 2) a))
367.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (.p16 c a) (real->posit16 4)))) b) (.p16 (real->posit16 2) a))
326.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (.p16 c a) (real->posit16 4)))) b) (.p16 (real->posit16 2) a))

prune427.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.1b

localize232.0ms

Local error

Found 4 expressions with local error:

0.9b	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))) b)
0.3b	(sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4))))
0.3b	(-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))
0.3b	(.p16 (.p16 c a) (real->posit16 4))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 6

Calls

4 calls:

Slowest

9.0ms	(-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))
7.0ms	(.p16 (.p16 c a) (real->posit16 4))
3.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))) b)
0.0ms	(sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

0.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))) b)
0.0ms	(sqrt.p16 (-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4))))
0.0ms	(-.p16 (.p16 b b) (.p16 (*.p16 c a) (real->posit16 4)))
0.0ms	(.p16 (.p16 c a) (real->posit16 4))

simplify1.0ms

Counts

0 → 10

Calls

0 calls:

Slowest

prune454.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.1b

localize314.0ms

Local error

Found 4 expressions with local error:

0.9b	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))) b)
0.3b	(sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4)))))
0.3b	(-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))
0.2b	(/.p16 (/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))) b) (real->posit16 2)) a)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 5

Calls

4 calls:

Slowest

18.0ms	(-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))
6.0ms	(/.p16 (/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))) b) (real->posit16 2)) a)
3.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))) b)
0.0ms	(sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

0.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))) b)
0.0ms	(/.p16 (/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))) b) (real->posit16 2)) a)
0.0ms	(sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4)))))
0.0ms	(-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))

simplify347.0ms

Counts

1 → 9

Calls

1 calls:

Slowest

346.0ms

(-.p16 (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 c (*.p16 a (real->posit16 4))))) b)

prune478.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

localize218.0ms

Local error

Found 4 expressions with local error:

0.9b	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))) b)
0.3b	(sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4)))))
0.3b	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (.p16 a (real->posit16 4))))) b) (.p16 a (real->posit16 2)))
0.3b	(-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 6

Calls

4 calls:

Slowest

11.0ms	(-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))
6.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (.p16 a (real->posit16 4))))) b) (.p16 a (real->posit16 2)))
3.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))) b)
0.0ms	(sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

0.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))) b)
0.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (.p16 a (real->posit16 4))))) b) (.p16 a (real->posit16 2)))
0.0ms	(sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4)))))
0.0ms	(-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))

simplify2.4s

Counts

6 → 10

Calls

6 calls:

Slowest

1.3s	(-.p16 (.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (.p16 a (real->posit16 4))))) (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (.p16 a (real->posit16 4)))))) (.p16 b b))
306.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))) b)
293.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))) b)
261.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))) b)
241.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b b) (.p16 c (*.p16 a (real->posit16 4))))) b)

prune371.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.0b

regimes644.0ms

Accuracy

-∞% (-62.4b remaining)

Error of 1.6b against oracle of 64.0b and baseline of 64.0b

bsearch3.0ms

end0.0ms

sample3.2s

Algorithm

halfpoints

Results