Details

sample166.0ms

Algorithm

intervals

Results

51.0ms	256×	body	80	valid
10.0ms	256×	pre	80	true

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	2005
6	2005
5	1509
4	498
3	162
2	74
1	37
0	18

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)
0.1b	(pow (* -2 (log u1)) 0.5)
0.2b	(* u2 (* 2 PI))
0.3b	(* (pow (* -2 (log u1)) 0.5) 1/6)

rewrite66.0ms

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` `associate-l*` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-r` `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))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)
10.0ms	(pow (* -2 (log u1)) 0.5)
27.0ms	(* u2 (* 2 PI))
25.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)

series2.6s

Counts

4 → 12

Calls

4 calls:

572.0ms	(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)
866.0ms	(pow (* -2 (log u1)) 0.5)
49.0ms	(* u2 (* 2 PI))
1.1s	(* (pow (* -2 (log u1)) 0.5) 1/6)

simplify1.2s

Counts

90 → 90

Iterations

Iter	Nodes
done	2005
3	2005
2	1102
1	382
0	160

prune506.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
19×	`prod-exp`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
14×	`pow1`
13×	`associate-r`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-l`
8×	`sqrt-prod`
7×	`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:

5.0ms	(pow (* -2 (log u1)) 0.5)
17.0ms	(* u2 (* 2 PI))
51.0ms	(* (* (pow (* -2 (log u1)) 0.5) (sqrt 1/6)) (sqrt 1/6))
13.0ms	(* (pow (* -2 (log u1)) 0.5) (sqrt 1/6))

series2.5s

Counts

4 → 12

Calls

4 calls:

420.0ms	(pow (* -2 (log u1)) 0.5)
44.0ms	(* u2 (* 2 PI))
1.1s	(* (* (pow (* -2 (log u1)) 0.5) (sqrt 1/6)) (sqrt 1/6))
932.0ms	(* (pow (* -2 (log u1)) 0.5) (sqrt 1/6))

simplify1.1s

Counts

110 → 110

Iterations

Iter	Nodes
done	2010
3	2010
2	1210
1	406
0	165

prune608.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2 (log u1)) 0.5)
0.2b	(* u2 (* 2 PI))
0.3b	(* (pow (* -2 (log u1)) 0.5) 1/6)
0.8b	(exp (* (pow (* -2 (log u1)) 0.5) 1/6))

rewrite59.0ms

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` `associate-l*` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-r` `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:

10.0ms	(pow (* -2 (log u1)) 0.5)
26.0ms	(* u2 (* 2 PI))
11.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)
10.0ms	(exp (* (pow (* -2 (log u1)) 0.5) 1/6))

series2.4s

Counts

4 → 12

Calls

4 calls:

345.0ms	(pow (* -2 (log u1)) 0.5)
62.0ms	(* u2 (* 2 PI))
956.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)
1.1s	(exp (* (pow (* -2 (log u1)) 0.5) 1/6))

simplify1.1s

Counts

92 → 92

Iterations

Iter	Nodes
done	2001
3	2001
2	950
1	343
0	145

prune625.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* u2 (* 2 PI))
0.3b	(* (pow (* -2 (log u1)) (/ 0.5 2)) (* (pow (* -2 (log u1)) (/ 0.5 2)) 1/6))
0.4b	(* (pow (* -2 (log u1)) (/ 0.5 2)) 1/6)
0.8b	(exp (* (pow (* -2 (log u1)) (/ 0.5 2)) (* (pow (* -2 (log u1)) (/ 0.5 2)) 1/6)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

17.0ms	(* u2 (* 2 PI))
32.0ms	(* (pow (* -2 (log u1)) (/ 0.5 2)) (* (pow (* -2 (log u1)) (/ 0.5 2)) 1/6))
12.0ms	(* (pow (* -2 (log u1)) (/ 0.5 2)) 1/6)
41.0ms	(exp (* (pow (* -2 (log u1)) (/ 0.5 2)) (* (pow (* -2 (log u1)) (/ 0.5 2)) 1/6)))

series3.1s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* u2 (* 2 PI))
1.0s	(* (pow (* -2 (log u1)) (/ 0.5 2)) (* (pow (* -2 (log u1)) (/ 0.5 2)) 1/6))
903.0ms	(* (pow (* -2 (log u1)) (/ 0.5 2)) 1/6)
1.1s	(exp (* (pow (* -2 (log u1)) (/ 0.5 2)) (* (pow (* -2 (log u1)) (/ 0.5 2)) 1/6)))

simplify1.3s

Counts

111 → 111

Iterations

Iter	Nodes
done	2007
3	2007
2	1112
1	384
0	166

prune649.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes407.0ms

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
done	22
1	22
0	17

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.6s	8000×	body	80	valid
402.0ms	8000×	pre	80	true