Details

sample286.0ms

Algorithm

intervals

Results

68.0ms	256×	body	80	valid
15.0ms	256×	pre	80	true

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
6	3527
5	1264
4	443
3	158
2	71
1	36
0	18

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

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))

rewrite41.0ms

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:

17.0ms	(+ 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))

series2.6s

Counts

4 → 12

Calls

4 calls:

1.0s	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
400.0ms	(pow (* -2 (log u1)) 0.5)
36.0ms	(* PI u2)
1.1s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.6s

Counts

85 → 85

Iterations

Iter	Nodes
3	4270
2	1098
1	383
0	164

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2 (log u1)) 0.5)
0.3b	(* PI u2)
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))

rewrite87.0ms

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	(pow (* -2 (log u1)) 0.5)
10.0ms	(* PI u2)
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))

series2.5s

Counts

4 → 12

Calls

4 calls:

371.0ms	(pow (* -2 (log u1)) 0.5)
39.0ms	(* PI u2)
1.1s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
1.0s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
3	2345
2	865
1	316
0	145

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize121.0ms

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	(* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
0.7b	(pow (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) 3)

rewrite359.0ms

Algorithm

rewrite-expression-head

Rules

215×	`add-exp-log`
176×	`prod-exp`
50×	`add-cbrt-cube`
46×	`pow1`
36×	`pow-exp`
32×	`cbrt-unprod`
18×	`pow-prod-down`
16×	`pow-to-exp`
15×	`add-sqr-sqrt`
11×	`associate-r`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l`
5×	`sqr-pow`
4×	`pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `unpow-prod-down` `*-commutative` `rem-cube-cbrt`
2×	`pow-pow` `pow-plus`
1×	`pow2` `cube-mult` `unpow3` `cube-prod` `swap-sqr`

Counts

4 → 148

Calls

4 calls:

11.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
10.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
290.0ms	(* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
43.0ms	(pow (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) 3)

series3.3s

Counts

4 → 12

Calls

4 calls:

941.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
1.2s	(* 1/6 (pow (* -2 (log u1)) 0.5))
570.0ms	(* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
658.0ms	(pow (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) 3)

simplify6.4s

Counts

160 → 160

Iterations

Iter	Nodes
3	10744
2	1917
1	561
0	217

prune3.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize71.0ms

Local error

Found 4 expressions with local error:

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

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

238×	`add-exp-log`
206×	`prod-exp`
114×	`pow-exp`
57×	`pow-to-exp`
18×	`add-sqr-sqrt`
14×	`associate-r`
12×	`add-cbrt-cube`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqr-pow`
9×	`associate-l`
7×	`unswap-sqr`
6×	`pow1`
5×	`unpow-prod-down` `swap-sqr` `cbrt-unprod`
4×	`pow-prod-down` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`*-commutative`
2×	`cbrt-prod` `pow2` `pow3` `pow-sqr`
1×	`pow-plus` `pow1/3` `rem-cbrt-cube`

Counts

4 → 172

Calls

4 calls:

35.0ms	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
57.0ms	(* 1/6 (cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))
19.0ms	(cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))
20.0ms	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))

series4.5s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
1.0s	(* 1/6 (cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))
1.0s	(cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))
1.4s	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))

simplify2.9s

Counts

184 → 184

Iterations

Iter	Nodes
3	4033
2	1214
1	547
0	218

prune2.5s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes383.0ms

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
2	25
1	25
0	18

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.0s	8000×	body	80	valid
774.0ms	8000×	pre	80	true