Details

sample893.0ms

Algorithm

intervals

Results

255.0ms	256×	body	80	valid
37.0ms	256×	pre	80	true

simplify24.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1528
4	386
3	145
2	69
1	34
0	18

prune286.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize632.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite641.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `prod-exp` `add-cbrt-cube`
12×	`pow1`
11×	`times-frac`
8×	`associate-r`
6×	`pow-exp` `add-log-exp`
5×	`cbrt-unprod`
4×	`div-exp` `pow-prod-down` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-*l/` `sum-log` `flip-+` `div-inv`

Counts

4 → 87

Calls

4 calls:

216.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
55.0ms	(pow (* -2.0 (log u1)) 0.5)
38.0ms	(* (* 2.0 PI) u2)
73.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series7.0s

Counts

4 → 12

Calls

4 calls:

3.1s	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
1.1s	(pow (* -2.0 (log u1)) 0.5)
92.0ms	(* (* 2.0 PI) u2)
2.6s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify9.7s

Counts

99 → 99

Iterations

Iter	Nodes
done	5003
2	1764
1	545
0	203

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize88.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
0.3b	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`pow1`
9×	`prod-exp`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`div-exp`
4×	`pow-prod-down` `pow-exp` `cbrt-unprod`
3×	`pow-unpow` `times-frac` `associate-r` `associate-/r*`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow`
1×	`+-commutative` `unpow-prod-down` `frac-2neg` `flip3-+` `associate-l` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `associate-/l` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

136.0ms	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
9.0ms	(pow (* -2.0 (log u1)) 0.5)
53.0ms	(* (* 2.0 PI) u2)
35.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

series9.6s

Counts

4 → 12

Calls

4 calls:

2.1s	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
1.5s	(pow (* -2.0 (log u1)) 0.5)
514.0ms	(* (* 2.0 PI) u2)
5.4s	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify7.3s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1689
1	510
0	184

prune2.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize590.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
0.3b	(* (* 2.0 PI) u2)
0.3b	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

rewrite498.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log` `add-sqr-sqrt`
33×	`associate-l`
30×	`sqrt-prod`
23×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
19×	`prod-exp`
16×	`add-cbrt-cube`
14×	`pow1`
9×	`associate-r`
7×	`cbrt-unprod`
6×	`pow-exp` `unswap-sqr`
5×	`sqrt-div` `pow-prod-down` `sqr-pow`
4×	`associate-*l/` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow` `div-inv`
1×	`frac-times` `associate-*r/`

Counts

4 → 112

Calls

4 calls:

16.0ms	(pow (* -2.0 (log u1)) 0.5)
227.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
34.0ms	(* (* 2.0 PI) u2)
120.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series8.8s

Counts

4 → 12

Calls

4 calls:

1.2s	(pow (* -2.0 (log u1)) 0.5)
3.9s	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
49.0ms	(* (* 2.0 PI) u2)
3.7s	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify17.7s

Counts

124 → 124

Iterations

Iter	Nodes
done	5002
3	4993
2	1444
1	485
0	200

prune3.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize336.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
0.3b	(/ 1.0 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
0.3b	(* (* 2.0 PI) u2)

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
72×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log`
24×	`associate-/r*`
17×	`unpow-prod-down` `sqr-pow`
16×	`add-cbrt-cube`
13×	`div-exp`
12×	`pow1`
6×	`pow-exp` `prod-exp` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `pow-prod-down` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `associate-r` `cbrt-unprod`
2×	`pow-pow` `frac-2neg` `clear-num`
1×	`associate-l` `associate-/r/` `*-commutative`

Counts

4 → 170

Calls

4 calls:

13.0ms	(pow (* -2.0 (log u1)) 0.5)
16.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
44.0ms	(/ 1.0 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
110.0ms	(* (* 2.0 PI) u2)

series11.2s

Counts

4 → 12

Calls

4 calls:

1.7s	(pow (* -2.0 (log u1)) 0.5)
5.4s	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
4.1s	(/ 1.0 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
75.0ms	(* (* 2.0 PI) u2)

simplify15.9s

Counts

182 → 182

Iterations

Iter	Nodes
done	5000
2	2629
1	828
0	311

prune5.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes3.9s

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

simplify334.0ms

Iterations

Iter	Nodes
done	30
1	30
0	22

end11.0ms

sample9.1s

Algorithm

intervals

Results

7.1s	8000×	body	80	valid
1.5s	8000×	pre	80	true