Details

sample218.0ms

Algorithm

halfpoints

Results

simplify656.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

655.0ms

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

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize170.0ms

Local error

Found 4 expressions with local error:

1.1b	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
0.4b	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))
0.3b	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
0.3b	(-.p16 (.p16 b_2 b_2) (.p16 c a))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 5

Calls

4 calls:

Slowest

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

series1.0ms

Counts

4 → 4

Calls

4 calls:

Slowest

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

simplify1.5s

Counts

5 → 9

Calls

5 calls:

Slowest

571.0ms	(-.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))
265.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
263.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
260.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)
173.0ms	(/.p16 (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2) a)

prune199.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.4b

localize177.0ms

Local error

Found 4 expressions with local error:

2.8b	(-.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))
1.1b	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
0.5b	(/.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	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 6

Calls

4 calls:

Slowest

10.0ms	(/.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))
5.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
4.0ms	(-.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	(sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a)))

series0.0ms

Counts

4 → 4

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

simplify450.0ms

Counts

4 → 10

Calls

4 calls:

Slowest

181.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
118.0ms	(-.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)))
87.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
62.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

prune181.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.4b

localize291.0ms

Local error

Found 4 expressions with local error:

1.1b	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
1.1b	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
1.1b	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
0.8b	(/.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))) b_2) (-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 6

Calls

4 calls:

Slowest

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

series0.0ms

Counts

4 → 4

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) (/.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)))
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)

simplify842.0ms

Counts

6 → 10

Calls

6 calls:

Slowest

249.0ms	(-.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
129.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
127.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
126.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)
111.0ms	(+.p16 (sqrt.p16 (-.p16 (.p16 b_2 b_2) (.p16 c a))) b_2)

prune234.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.4b

localize282.0ms

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)))
1.1b	(-.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	(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))))
0.3b	(/.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)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 5

Calls

4 calls:

Slowest

8.0ms	(/.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)))
2.0ms	(/.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

Counts

4 → 4

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))))

simplify1.8s

Counts

3 → 9

Calls

3 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))

750.0ms

(-.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))))

9.0ms

(+.p16 (*.p16 b_2 b_2) (*.p16 c a))

prune137.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 1.4b

regimes467.0ms

Accuracy

-∞% (-62.3b remaining)

Error of 1.7b against oracle of 64.0b and baseline of 64.0b

bsearch1.0ms

end0.0ms

sample2.9s

Algorithm

halfpoints

Results