Details

sample929.0ms

Algorithm

halfpoints

Results

simplify397.0ms

Calls

1 calls:

Slowest

397.0ms

(*.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)))

prune78.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize441.0ms

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)))))
0.2b	(*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
0.2b	(/.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

2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `p16-flip--` `*-commutative`
1×	`associate-l/` `associate-r/`

Calls

4 calls:

Slowest

11.0ms	(.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)))
3.0ms	(*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
1.0ms	(/.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))))

simplify2.3s

Calls

10 calls:

Slowest

446.0ms	(.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)))
424.0ms	(.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)))
415.0ms	(.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)))
397.0ms	(.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)))
214.0ms	(.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))))

prune884.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize360.0ms

Local error

Found 4 expressions with local error:

0.5b	(.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 (real->posit16 1) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (.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)))))
0.3b	(sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
0.2b	(*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`sub-neg`
4×	`distribute-rgt-in` `distribute-lft-in`
2×	`associate-+l+` `associate-+r+` `associate-l/` `associate-r/` `p16-flip--` `*-commutative`
1×	`+-commutative` `distribute-rgt-out` `associate-l`

Calls

4 calls:

Slowest

7.0ms	(+.p16 (.p16 (real->posit16 1) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (.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)))))
4.0ms	(*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
4.0ms	(.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	(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) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (.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 (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	(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

18 calls:

Slowest

1.0s	(/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))))
780.0ms	(.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))))
610.0ms	(.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))))
309.0ms	(.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))))
268.0ms	(.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))))

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize524.0ms

Local error

Found 4 expressions with local error:

0.5b	(.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 (real->posit16 1) (neg.p16 (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (.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)))))
0.3b	(sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
0.2b	(*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`sub-neg`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`associate-+r+` `associate-l/` `associate-r/` `p16-flip--` `*-commutative`
1×	`+-commutative` `associate-l`

Calls

4 calls:

Slowest

6.0ms	(+.p16 (.p16 (real->posit16 1) (neg.p16 (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (.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 (.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))))
4.0ms	(*.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 (real->posit16 1) (neg.p16 (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (.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	(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))))

simplify3.2s

Calls

14 calls:

Slowest

1.1s	(/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))))
861.0ms	(.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))))
814.0ms	(.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))))
194.0ms	(.p16 (.p16 (real->posit16 1) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
132.0ms	(.p16 (neg.p16 (/.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))

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize443.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.p16 (.p16 (.p16 (real->posit16 1) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))))
0.4b	(+.p16 (.p16 (real->posit16 1) (neg.p16 (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (/.p16 (.p16 (.p16 (real->posit16 1) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (sqrt.p16 (.p16 (real->posit16 9) (-.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)))))
0.2b	(.p16 (.p16 (real->posit16 1) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

13.0ms	(+.p16 (.p16 (real->posit16 1) (neg.p16 (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (/.p16 (.p16 (.p16 (real->posit16 1) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (sqrt.p16 (.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))))
4.0ms	(/.p16 (.p16 (.p16 (real->posit16 1) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))))
4.0ms	(.p16 (.p16 (real->posit16 1) rand) (-.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) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))))
0.0ms	(+.p16 (.p16 (real->posit16 1) (neg.p16 (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (/.p16 (.p16 (.p16 (real->posit16 1) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))) (sqrt.p16 (.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))))
0.0ms	(.p16 (.p16 (real->posit16 1) rand) (-.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)))))

simplify1.7s

Calls

10 calls:

Slowest

965.0ms	(.p16 (.p16 (real->posit16 1) rand) (-.p16 (.p16 a a) (.p16 (/.p16 (real->posit16 1.0) (real->posit16 3.0)) (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))
172.0ms	(.p16 (.p16 (real->posit16 1) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
160.0ms	(.p16 (.p16 (real->posit16 1) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
160.0ms	(.p16 (.p16 (real->posit16 1) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))
146.0ms	(.p16 (.p16 (real->posit16 1) rand) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))))

prune869.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes976.0ms

Accuracy

-∞% (-63.6b remaining)

Error of 0.4b against oracle of 64.0b and baseline of 64.0b

bsearch7.0ms

end0.0ms

sample9.2s

Algorithm

halfpoints

Results