Details

sample368.0ms

Algorithm

intervals

Results

93.0ms	256×	body	80	valid
15.0ms	256×	pre	80	true

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
6	4008
5	1348
4	443
3	220
2	117
1	72
0	18

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 0.5 (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* u2 (* 2 PI)))))
0.1b	(pow (* -2 (log u1)) 0.5)
0.2b	(* u2 (* 2 PI))
0.4b	(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

12.0ms	(+ 0.5 (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* u2 (* 2 PI)))))
8.0ms	(pow (* -2 (log u1)) 0.5)
29.0ms	(* u2 (* 2 PI))
11.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.3s

Counts

4 → 12

Calls

4 calls:

543.0ms	(+ 0.5 (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* u2 (* 2 PI)))))
700.0ms	(pow (* -2 (log u1)) 0.5)
47.0ms	(* u2 (* 2 PI))
977.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify2.3s

Counts

85 → 85

Iterations

Iter	Nodes
3	5512
2	1686
1	708
0	168

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize62.0ms

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
19×	`prod-exp`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
15×	`associate-l`
14×	`pow1`
11×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-prod`
7×	`associate-r` `cbrt-unprod`
6×	`pow-exp`
5×	`pow-prod-down`
4×	`insert-posit16` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow`

Counts

4 → 90

Calls

4 calls:

5.0ms	(pow (* -2 (log u1)) 0.5)
37.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
14.0ms	(* u2 (* 2 PI))
12.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

series2.7s

Counts

4 → 12

Calls

4 calls:

420.0ms	(pow (* -2 (log u1)) 0.5)
1.1s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
34.0ms	(* u2 (* 2 PI))
1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
3	3791
2	1487
1	610
0	151

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 0.5 (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* u2 (* 2 PI)))))
0.1b	(pow (* -2 (log u1)) 0.5)
0.2b	(* u2 (* 2 PI))
0.4b	(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

25.0ms	(+ 0.5 (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* u2 (* 2 PI)))))
10.0ms	(pow (* -2 (log u1)) 0.5)
25.0ms	(* u2 (* 2 PI))
30.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.1s

Counts

4 → 12

Calls

4 calls:

625.0ms	(+ 0.5 (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* u2 (* 2 PI)))))
418.0ms	(pow (* -2 (log u1)) 0.5)
63.0ms	(* u2 (* 2 PI))
1.0s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify2.4s

Counts

85 → 85

Iterations

Iter	Nodes
3	5512
2	1686
1	708
0	168

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize91.0ms

Local error

Found 4 expressions with local error:

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

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`add-exp-log`
24×	`pow1`
19×	`associate-l`
15×	`-un-lft-identity` `add-cbrt-cube` `associate-r*` `add-cube-cbrt`
14×	`prod-exp` `sqrt-prod`
9×	`unswap-sqr`
8×	`sqrt-pow1` `pow1/2`
6×	`pow-prod-down` `cbrt-unprod` `sqr-pow`
5×	`pow-prod-up`
4×	`swap-sqr` `pow-exp` `*-commutative` `insert-posit16` `add-log-exp`
3×	`pow-sqr`
2×	`pow-to-exp` `unpow-prod-down`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod`

Counts

4 → 116

Calls

4 calls:

12.0ms	(* u2 (* 2 PI))
12.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
25.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
63.0ms	(* (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))) (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))))

series3.3s

Counts

4 → 12

Calls

4 calls:

53.0ms	(* u2 (* 2 PI))
1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
1.0s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
1.0s	(* (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))) (sqrt (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))))

simplify1.5s

Counts

128 → 128

Iterations

Iter	Nodes
3	4369
2	1388
1	585
0	153

prune2.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes386.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	22
1	22
0	16

end0.0ms

sample2.7s

Algorithm

intervals

Results

2.2s	8000×	body	80	valid
354.0ms	8000×	pre	80	true