Details

sample177.0ms

Algorithm

intervals

Results

102.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify3.7s

Counts

1 → 1

Iterations

Iter	Nodes
6	3778
5	1307
4	450
3	160
2	72
1	35
0	18

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
0.2b	(pow (* -2 (log u1)) 0.5)
0.3b	(* u2 (* 2 PI))
0.4b	(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite67.0ms

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`
4×	`expm1-log1p-u` `pow-prod-down` `pow-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `pow-pow` `*-commutative` `unswap-sqr`
1×	`fma-udef`

Counts

4 → 74

Calls

4 calls:

0.0ms	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
8.0ms	(pow (* -2 (log u1)) 0.5)
25.0ms	(* u2 (* 2 PI))
31.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.1s

Counts

4 → 12

Calls

4 calls:

533.0ms	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
396.0ms	(pow (* -2 (log u1)) 0.5)
55.0ms	(* u2 (* 2 PI))
1.1s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.3s

Counts

86 → 86

Iterations

Iter	Nodes
3	3343
2	971
1	346
0	155

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* -2 (log u1)) 0.5)
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))
0.3b	(* u2 (* 2 PI))

rewrite75.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow`

Counts

4 → 94

Calls

4 calls:

5.0ms	(pow (* -2 (log u1)) 0.5)
32.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
23.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
13.0ms	(* u2 (* 2 PI))

series2.5s

Counts

4 → 12

Calls

4 calls:

336.0ms	(pow (* -2 (log u1)) 0.5)
1.1s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
50.0ms	(* u2 (* 2 PI))

simplify1.5s

Counts

106 → 106

Iterations

Iter	Nodes
3	3432
2	1076
1	353
0	155

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
0.2b	(pow (* -2 (log u1)) 0.5)
0.3b	(* u2 (* 2 PI))
0.4b	(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite32.0ms

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`
4×	`expm1-log1p-u` `pow-prod-down` `pow-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `pow-pow` `*-commutative` `unswap-sqr`
1×	`fma-udef`

Counts

4 → 74

Calls

4 calls:

0.0ms	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
5.0ms	(pow (* -2 (log u1)) 0.5)
13.0ms	(* u2 (* 2 PI))
13.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.0s

Counts

4 → 12

Calls

4 calls:

543.0ms	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
421.0ms	(pow (* -2 (log u1)) 0.5)
42.0ms	(* u2 (* 2 PI))
983.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.4s

Counts

86 → 86

Iterations

Iter	Nodes
3	3343
2	971
1	346
0	155

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

151×	`add-exp-log`
119×	`prod-exp`
38×	`pow-exp`
25×	`add-cbrt-cube`
19×	`pow-to-exp`
17×	`add-sqr-sqrt`
16×	`associate-l`
13×	`cbrt-unprod`
12×	`associate-r`
11×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-prod`
4×	`expm1-log1p-u` `pow-prod-down` `*-commutative` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
2×	`unpow-prod-down`

Counts

4 → 130

Calls

4 calls:

91.0ms	(* (sqrt 1/6) (* (* (sqrt 1/6) (pow (* -2 (log u1)) (/ 0.5 2))) (pow (* -2 (log u1)) (/ 0.5 2))))
14.0ms	(* u2 (* 2 PI))
30.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) (/ 0.5 2)))
62.0ms	(* (* (sqrt 1/6) (pow (* -2 (log u1)) (/ 0.5 2))) (pow (* -2 (log u1)) (/ 0.5 2)))

series3.0s

Counts

4 → 12

Calls

4 calls:

890.0ms	(* (sqrt 1/6) (* (* (sqrt 1/6) (pow (* -2 (log u1)) (/ 0.5 2))) (pow (* -2 (log u1)) (/ 0.5 2))))
42.0ms	(* u2 (* 2 PI))
1.0s	(* (sqrt 1/6) (pow (* -2 (log u1)) (/ 0.5 2)))
1.1s	(* (* (sqrt 1/6) (pow (* -2 (log u1)) (/ 0.5 2))) (pow (* -2 (log u1)) (/ 0.5 2)))

simplify3.3s

Counts

142 → 142

Iterations

Iter	Nodes
3	5066
2	1388
1	461
0	188

prune2.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes463.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	22
1	22
0	17

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.6s	8000×	body	80	valid
371.0ms	8000×	pre	80	true