Details

sample180.0ms

Algorithm

intervals

Results

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

simplify3.6s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
0.2b	(* PI u2)
0.2b	(pow (* -2 (log u1)) 0.5)
0.4b	(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite73.0ms

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	(* PI u2)
10.0ms	(pow (* -2 (log u1)) 0.5)
24.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.0s

Counts

4 → 12

Calls

4 calls:

523.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
41.0ms	(* PI u2)
379.0ms	(pow (* -2 (log u1)) 0.5)
1.1s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify3.6s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
3	4839
2	1224
1	423
0	164

prune612.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

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:

10.0ms	(* PI u2)
10.0ms	(pow (* -2 (log u1)) 0.5)
54.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
12.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

series2.4s

Counts

4 → 12

Calls

4 calls:

41.0ms	(* PI u2)
403.0ms	(pow (* -2 (log u1)) 0.5)
935.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
1.0s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify2.6s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	3186
2	959
1	347
0	145

prune635.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
0.2b	(* PI u2)
0.2b	(pow (* -2 (log u1)) 0.5)
0.4b	(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite39.0ms

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:

18.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
5.0ms	(* PI u2)
5.0ms	(pow (* -2 (log u1)) 0.5)
10.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.2s

Counts

4 → 12

Calls

4 calls:

493.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
355.0ms	(* PI u2)
387.0ms	(pow (* -2 (log u1)) 0.5)
936.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify3.1s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
3	4839
2	1224
1	423
0	164

prune483.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize73.0ms

Local error

Found 4 expressions with local error:

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

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

202×	`add-exp-log`
166×	`prod-exp`
46×	`add-cbrt-cube`
43×	`pow1`
29×	`cbrt-unprod`
28×	`pow-exp`
23×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt`
14×	`pow-to-exp`
12×	`times-frac`
11×	`associate-r`
7×	`associate-l`
4×	`pow-sqr` `pow-prod-up` `insert-posit16` `associate-/l*` `add-log-exp` `difference-of-squares` `unswap-sqr` `sqr-pow`
3×	`associate-/r` `-commutative`
2×	`unpow-prod-down` `pow-plus` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow2` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `swap-sqr` `div-exp` `div-inv`

Counts

4 → 157

Calls

4 calls:

11.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
10.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
29.0ms	(/ (- (* 0.5 0.5) (* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))) (- 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5)))))
243.0ms	(* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))

series3.4s

Counts

4 → 12

Calls

4 calls:

1.0s	(* 1/6 (pow (* -2 (log u1)) 0.5))
975.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
939.0ms	(/ (- (* 0.5 0.5) (* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))) (- 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5)))))
469.0ms	(* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))

simplify3.0s

Counts

169 → 169

Iterations

Iter	Nodes
done	5001
2	2756
1	747
0	275

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes446.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	22
1	22
0	16

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
300.0ms	8000×	pre	80	true