Details

sample216.0ms

Algorithm

intervals

Results

71.0ms	256×	body	80	valid
15.0ms	256×	pre	80	true

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	2190
6	2190
5	1530
4	489
3	158
2	71
1	36
0	18

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize62.0ms

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

rewrite88.0ms

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:

39.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
11.0ms	(pow (* -2 (log u1)) 0.5)
11.0ms	(* PI u2)
24.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.0s

Counts

4 → 12

Calls

4 calls:

559.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
349.0ms	(pow (* -2 (log u1)) 0.5)
33.0ms	(* PI u2)
1.1s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	2000
3	2000
2	1216
1	425
0	164

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

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)
35.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
10.0ms	(* PI u2)
12.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

series2.6s

Counts

4 → 12

Calls

4 calls:

409.0ms	(pow (* -2 (log u1)) 0.5)
1.1s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
47.0ms	(* PI u2)
1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
done	2034
3	2034
2	978
1	352
0	145

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize49.0ms

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

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-exp-log`
85×	`prod-exp`
24×	`pow-exp`
20×	`add-cbrt-cube`
14×	`add-sqr-sqrt`
12×	`pow-to-exp`
11×	`pow1` `associate-r`
10×	`cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l`
4×	`insert-posit16` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`*-commutative`
2×	`unpow-prod-down`
1×	`cbrt-prod` `pow2` `pow-plus` `pow1/3` `swap-sqr` `pow3` `pow-prod-down` `pow-sqr` `pow-prod-up` `rem-cbrt-cube`

Counts

4 → 105

Calls

4 calls:

21.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
21.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
154.0ms	(cbrt (* (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
62.0ms	(* (* 1/6 (pow (* -2 (log u1)) 0.5)) (* 1/6 (pow (* -2 (log u1)) 0.5)))

series4.8s

Counts

4 → 12

Calls

4 calls:

1.1s	(* 1/6 (pow (* -2 (log u1)) 0.5))
1.1s	(* 1/6 (pow (* -2 (log u1)) 0.5))
1.6s	(cbrt (* (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
1.1s	(* (* 1/6 (pow (* -2 (log u1)) 0.5)) (* 1/6 (pow (* -2 (log u1)) 0.5)))

simplify1.2s

Counts

117 → 117

Iterations

Iter	Nodes
done	2001
3	2001
2	762
1	275
0	127

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 1/36 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 1.0)) (* 1/6 (pow (* -2 (log u1)) 0.5)))
0.4b	(* 1/6 (pow (* -2 (log u1)) 0.5))
0.4b	(* 1/36 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 1.0))
0.5b	(cbrt (* (* 1/36 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 1.0)) (* 1/6 (pow (* -2 (log u1)) 0.5))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

290×	`add-exp-log`
261×	`prod-exp`
124×	`pow-exp`
56×	`pow-to-exp`
20×	`add-cbrt-cube`
14×	`add-sqr-sqrt`
11×	`associate-r`
10×	`cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l`
6×	`pow1`
4×	`insert-posit16` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`*-commutative`
2×	`unpow-prod-down`
1×	`cbrt-prod` `pow1/3` `pow-prod-down`

Counts

4 → 147

Calls

4 calls:

56.0ms	(* (* 1/36 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 1.0)) (* 1/6 (pow (* -2 (log u1)) 0.5)))
17.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
30.0ms	(* 1/36 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 1.0))
36.0ms	(cbrt (* (* 1/36 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 1.0)) (* 1/6 (pow (* -2 (log u1)) 0.5))))

series4.1s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (* 1/36 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 1.0)) (* 1/6 (pow (* -2 (log u1)) 0.5)))
1.0s	(* 1/6 (pow (* -2 (log u1)) 0.5))
950.0ms	(* 1/36 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 1.0))
1.1s	(cbrt (* (* 1/36 (pow (* (pow -2 1.0) (pow (log u1) 1.0)) 1.0)) (* 1/6 (pow (* -2 (log u1)) 0.5))))

simplify1.4s

Counts

159 → 159

Iterations

Iter	Nodes
done	2000
3	2000
2	1491
1	488
0	204

prune2.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes458.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	25
1	25
0	18

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.7s	8000×	body	80	valid
389.0ms	8000×	pre	80	true