Details

sample217.0ms

Algorithm

intervals

Results

79.0ms	256×	body	80	valid
16.0ms	256×	pre	80	true

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
5	1530
4	489
3	158
2	71
1	36
0	18

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize70.0ms

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))

rewrite38.0ms

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:

13.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
5.0ms	(pow (* -2 (log u1)) 0.5)
5.0ms	(* PI u2)
12.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series1.9s

Counts

4 → 12

Calls

4 calls:

512.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
378.0ms	(pow (* -2 (log u1)) 0.5)
39.0ms	(* PI u2)
970.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify867.0ms

Counts

85 → 85

Iterations

Iter	Nodes
done	2000
2	1216
1	425
0	164

prune514.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

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))

rewrite77.0ms

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:

5.0ms	(pow (* -2 (log u1)) 0.5)
29.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
17.0ms	(* PI u2)
25.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

series2.6s

Counts

4 → 12

Calls

4 calls:

410.0ms	(pow (* -2 (log u1)) 0.5)
1.1s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
23.0ms	(* PI u2)
1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify692.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	2000
2	978
1	352
0	145

prune628.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize129.0ms

Local error

Found 4 expressions with local error:

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

rewrite743.0ms

Algorithm

rewrite-expression-head

Rules

221×	`add-exp-log`
182×	`prod-exp`
53×	`add-cbrt-cube`
48×	`pow1`
35×	`cbrt-unprod`
30×	`pow-exp`
20×	`pow-prod-down`
15×	`add-sqr-sqrt` `pow-to-exp`
14×	`associate-l`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-r`
4×	`pow-sqr` `*-commutative` `pow-prod-up` `insert-posit16` `add-log-exp` `unswap-sqr` `sqr-pow`
2×	`unpow-prod-down` `pow-plus` `associate-*l/`
1×	`pow2` `flip3--` `swap-sqr` `flip--`

Counts

4 → 146

Calls

4 calls:

21.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)
19.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)
403.0ms	(* (- (* (cos (* 2 (* PI u2))) (* (pow (* -2 (log u1)) 0.5) 1/6)) 0.5) (* (cos (* 2 (* PI u2))) (* (pow (* -2 (log u1)) 0.5) 1/6)))
294.0ms	(* (* (cos (* 2 (* PI u2))) (* (pow (* -2 (log u1)) 0.5) 1/6)) (* (cos (* 2 (* PI u2))) (* (pow (* -2 (log u1)) 0.5) 1/6)))

series3.9s

Counts

4 → 12

Calls

4 calls:

937.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)
1.0s	(* (pow (* -2 (log u1)) 0.5) 1/6)
1.5s	(* (- (* (cos (* 2 (* PI u2))) (* (pow (* -2 (log u1)) 0.5) 1/6)) 0.5) (* (cos (* 2 (* PI u2))) (* (pow (* -2 (log u1)) 0.5) 1/6)))
526.0ms	(* (* (cos (* 2 (* PI u2))) (* (pow (* -2 (log u1)) 0.5) 1/6)) (* (cos (* 2 (* PI u2))) (* (pow (* -2 (log u1)) 0.5) 1/6)))

simplify709.0ms

Counts

158 → 158

Iterations

Iter	Nodes
done	2002
1	584
0	218

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize126.0ms

Local error

Found 4 expressions with local error:

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

rewrite466.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
31×	`prod-exp`
20×	`add-sqr-sqrt`
19×	`add-cbrt-cube`
18×	`associate-l`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-r`
9×	`pow1` `cbrt-unprod`
8×	`pow-exp`
6×	`unswap-sqr` `sqr-pow`
4×	`pow-to-exp` `*-commutative` `insert-posit16` `add-log-exp`
3×	`unpow-prod-down` `pow-prod-down`
2×	`associate-*l/`
1×	`flip3--` `flip--`

Counts

4 → 98

Calls

4 calls:

22.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)
13.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)
11.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)
417.0ms	(* (- (* (cos (* 2 (* PI u2))) (* (pow (* -2 (log u1)) 0.5) 1/6)) 0.5) (* (cos (* 2 (* PI u2))) (* (pow (* -2 (log u1)) 0.5) 1/6)))

series4.3s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (pow (* -2 (log u1)) 0.5) 1/6)
1.1s	(* (pow (* -2 (log u1)) 0.5) 1/6)
960.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)
1.2s	(* (- (* (cos (* 2 (* PI u2))) (* (pow (* -2 (log u1)) 0.5) 1/6)) 0.5) (* (cos (* 2 (* PI u2))) (* (pow (* -2 (log u1)) 0.5) 1/6)))

simplify1.1s

Counts

110 → 110

Iterations

Iter	Nodes
done	2003
2	1340
1	401
0	162

prune1.5s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes384.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	25
1	25
0	18

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.6s	8000×	body	80	valid
381.0ms	8000×	pre	80	true