Details

sample340.0ms

Algorithm

intervals

Results

158.0ms	256×	body	80	valid
20.0ms	256×	pre	80	true

simplify3.3s

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize42.0ms

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))

rewrite47.0ms

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)
6.0ms	(pow (* -2 (log u1)) 0.5)
15.0ms	(* u2 (* 2 PI))
24.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.3s

Counts

4 → 12

Calls

4 calls:

509.0ms	(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* -2 (log u1)) 0.5)) 0.5)
346.0ms	(pow (* -2 (log u1)) 0.5)
63.0ms	(* u2 (* 2 PI))
1.4s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.2s

Counts

90 → 90

Iterations

Iter	Nodes
3	3314
2	972
1	351
0	159

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite126.0ms

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:

6.0ms	(pow (* -2 (log u1)) 0.5)
27.0ms	(* u2 (* 2 PI))
64.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
28.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

series2.6s

Counts

4 → 12

Calls

4 calls:

442.0ms	(pow (* -2 (log u1)) 0.5)
39.0ms	(* u2 (* 2 PI))
1.1s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))
996.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))

simplify1.3s

Counts

110 → 110

Iterations

Iter	Nodes
3	3211
2	1073
1	360
0	159

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (* 1/6 (pow (* -2 (log u1)) 0.5)))
0.3b	(* u2 (* 2 PI))
0.4b	(* 1/6 (pow (* -2 (log u1)) 0.5))
0.5b	(expm1 (log1p (* 1/6 (pow (* -2 (log u1)) 0.5))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`pow1`
8×	`prod-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `associate-l`
5×	`expm1-log1p-u`
4×	`cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`pow-exp` `*-commutative` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `log1p-udef` `expm1-log1p` `unpow-prod-down` `log1p-expm1` `expm1-udef`

Counts

4 → 71

Calls

4 calls:

1.0ms	(log1p (* 1/6 (pow (* -2 (log u1)) 0.5)))
28.0ms	(* u2 (* 2 PI))
22.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
1.0ms	(expm1 (log1p (* 1/6 (pow (* -2 (log u1)) 0.5))))

series4.0s

Counts

4 → 12

Calls

4 calls:

1.3s	(log1p (* 1/6 (pow (* -2 (log u1)) 0.5)))
62.0ms	(* u2 (* 2 PI))
1.2s	(* 1/6 (pow (* -2 (log u1)) 0.5))
1.5s	(expm1 (log1p (* 1/6 (pow (* -2 (log u1)) 0.5))))

simplify774.0ms

Counts

83 → 83

Iterations

Iter	Nodes
3	2158
2	726
1	297
0	146

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize80.0ms

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))

rewrite211.0ms

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×	`expm1-log1p-u` `pow-prod-down` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`cbrt-prod` `pow2` `pow3` `pow-sqr`
1×	`pow-plus` `pow1/3` `rem-cbrt-cube`

Counts

4 → 180

Calls

4 calls:

46.0ms	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
89.0ms	(* 1/6 (cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))
26.0ms	(cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))
43.0ms	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))

series4.2s

Counts

4 → 12

Calls

4 calls:

956.0ms	(* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
1.1s	(* 1/6 (cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))))
1.1s	(cbrt (* (* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))
1.1s	(* (pow (* -2 (log u1)) 0.5) (pow (* -2 (log u1)) 0.5))

simplify2.4s

Counts

192 → 192

Iterations

Iter	Nodes
3	4122
2	1288
1	557
0	226

prune3.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes370.0ms

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

sample2.8s

Algorithm

intervals

Results

2.2s	8000×	body	80	valid
414.0ms	8000×	pre	80	true