Details

sample167.0ms

Algorithm

intervals

Results

33.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1530
4	489
3	158
2	71
1	36
0	18

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
0.1b	(pow (* -2 (log u1)) 0.5)
0.3b	(* PI u2)
0.4b	(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
14×	`add-sqr-sqrt`
9×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `associate-r`
7×	`prod-exp`
6×	`associate-l` `add-log-exp`
4×	`pow-exp` `insert-posit16`
3×	`pow-unpow` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `pow-pow` `pow-prod-down` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 73

Calls

4 calls:

27.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
11.0ms	(pow (* -2 (log u1)) 0.5)
7.0ms	(* PI u2)
22.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.1s

Counts

4 → 12

Calls

4 calls:

548.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
413.0ms	(pow (* -2 (log u1)) 0.5)
23.0ms	(* PI u2)
1.1s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify3.4s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	4829
2	1216
1	425
0	164

prune483.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2 (log u1)) 0.5)
0.2b	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
0.3b	(* PI u2)
0.3b	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`prod-exp`
15×	`associate-l`
13×	`add-cbrt-cube`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`insert-posit16` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `pow-unpow` `pow-prod-down` `*-commutative`
2×	`unpow-prod-down` `pow-pow`

Counts

4 → 90

Calls

4 calls:

13.0ms	(pow (* -2 (log u1)) 0.5)
34.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
19.0ms	(* PI u2)
21.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

series3.0s

Counts

4 → 12

Calls

4 calls:

359.0ms	(pow (* -2 (log u1)) 0.5)
1.5s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
38.0ms	(* PI u2)
1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify2.6s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	3262
2	978
1	352
0	145

prune580.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
0.1b	(pow (* -2 (log u1)) 0.5)
0.3b	(* PI u2)
0.4b	(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
14×	`add-sqr-sqrt`
9×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `associate-r`
7×	`prod-exp`
6×	`associate-l` `add-log-exp`
4×	`pow-exp` `insert-posit16`
3×	`pow-unpow` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `pow-pow` `pow-prod-down` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 73

Calls

4 calls:

12.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
6.0ms	(pow (* -2 (log u1)) 0.5)
6.0ms	(* PI u2)
24.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.0s

Counts

4 → 12

Calls

4 calls:

619.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
384.0ms	(pow (* -2 (log u1)) 0.5)
33.0ms	(* PI u2)
1.0s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify3.5s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	4829
2	1216
1	425
0	164

prune610.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize95.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
0.3b	(* (* (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
0.5b	(* (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
0.5b	(cbrt (* (* (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))))

rewrite625.0ms

Algorithm

rewrite-expression-head

Rules

791×	`add-exp-log`
715×	`prod-exp`
174×	`pow-exp`
87×	`pow-to-exp`
59×	`add-cbrt-cube`
40×	`cbrt-unprod`
30×	`pow1`
13×	`add-sqr-sqrt`
8×	`associate-l`
7×	`-un-lft-identity` `pow-plus` `associate-r*` `pow-prod-up` `add-cube-cbrt`
5×	`sqrt-prod`
4×	`pow-prod-down` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`pow2` `pow-sqr` `*-commutative` `sqr-pow`
2×	`pow3`
1×	`cbrt-prod` `unpow-prod-down` `pow1/3` `swap-sqr` `rem-cbrt-cube`

Counts

4 → 248

Calls

4 calls:

18.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
262.0ms	(* (* (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
100.0ms	(* (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
225.0ms	(cbrt (* (* (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))))

series4.6s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
1.3s	(* (* (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
1.1s	(* (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
1.1s	(cbrt (* (* (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))))

simplify2.1s

Counts

260 → 260

Iterations

Iter	Nodes
done	5001
2	1420
1	517
0	230

prune727.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes403.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	25
1	25
0	18

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.8s	8000×	body	80	valid
356.0ms	8000×	pre	80	true