Details

sample161.0ms

Algorithm

intervals

Results

41.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
6	3940
5	1361
4	464
3	162
2	74
1	37
0	18

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
0.1b	(pow (* -2 (log u1)) 0.5)
0.3b	(* u2 (* 2 PI))
0.4b	(* 1/6 (pow (* -2 (log u1)) 0.5))

rewrite69.0ms

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` `insert-posit16` `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 → 78

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)
27.0ms	(* u2 (* 2 PI))
34.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.1s

Counts

4 → 12

Calls

4 calls:

530.0ms	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
446.0ms	(pow (* -2 (log u1)) 0.5)
35.0ms	(* u2 (* 2 PI))
1.1s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.3s

Counts

90 → 90

Iterations

Iter	Nodes
3	3314
2	972
1	351
0	159

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

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

rewrite108.0ms

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` `insert-posit16` `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 → 98

Calls

4 calls:

9.0ms	(pow (* -2 (log u1)) 0.5)
51.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
23.0ms	(* u2 (* 2 PI))
22.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

series2.8s

Counts

4 → 12

Calls

4 calls:

354.0ms	(pow (* -2 (log u1)) 0.5)
1.4s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
46.0ms	(* u2 (* 2 PI))
1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify1.3s

Counts

110 → 110

Iterations

Iter	Nodes
3	3250
2	1073
1	361
0	159

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2 (log u1)) 0.5)
0.3b	(* u2 (* 2 PI))
0.4b	(* 1/6 (pow (* -2 (log u1)) 0.5))
0.9b	(exp (* 1/6 (pow (* -2 (log u1)) 0.5)))

rewrite39.0ms

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×	`expm1-log1p-u` `pow-prod-down` `pow-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `pow-pow` `*-commutative` `unswap-sqr`
1×	`exp-prod` `exp-to-pow` `rem-exp-log`

Counts

4 → 80

Calls

4 calls:

5.0ms	(pow (* -2 (log u1)) 0.5)
13.0ms	(* u2 (* 2 PI))
10.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
10.0ms	(exp (* 1/6 (pow (* -2 (log u1)) 0.5)))

series2.8s

Counts

4 → 12

Calls

4 calls:

432.0ms	(pow (* -2 (log u1)) 0.5)
63.0ms	(* u2 (* 2 PI))
1.2s	(* 1/6 (pow (* -2 (log u1)) 0.5))
1.1s	(exp (* 1/6 (pow (* -2 (log u1)) 0.5)))

simplify983.0ms

Counts

92 → 92

Iterations

Iter	Nodes
3	2390
2	827
1	310
0	145

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize78.0ms

Local error

Found 4 expressions with local error:

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

rewrite521.0ms

Algorithm

rewrite-expression-head

Rules

577×	`add-exp-log`
525×	`prod-exp`
212×	`pow-exp`
106×	`pow-to-exp`
25×	`add-cbrt-cube`
15×	`add-sqr-sqrt`
14×	`cbrt-unprod`
11×	`associate-r`
10×	`*-un-lft-identity` `add-cube-cbrt` `sqr-pow`
9×	`pow1` `associate-l`
6×	`pow-prod-down` `unswap-sqr`
5×	`unpow-prod-down` `swap-sqr`
4×	`expm1-log1p-u` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow2` `pow-sqr`
1×	`cbrt-prod` `pow-plus` `pow1/3` `pow3`

Counts

4 → 248

Calls

4 calls:

253.0ms	(* 1/6 (* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (sqrt 1/6)))
43.0ms	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
32.0ms	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
186.0ms	(cbrt (* 1/6 (* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (sqrt 1/6))))

series4.6s

Counts

4 → 12

Calls

4 calls:

1.2s	(* 1/6 (* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (sqrt 1/6)))
988.0ms	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
979.0ms	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))
1.5s	(cbrt (* 1/6 (* (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)) (sqrt 1/6))))

simplify4.3s

Counts

260 → 260

Iterations

Iter	Nodes
3	7059
2	1792
1	788
0	310

prune4.5s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes822.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	22
1	22
0	17

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.2s	8000×	body	80	valid
464.0ms	8000×	pre	80	true