Details

sample170.0ms

Algorithm

intervals

Results

52.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1509
4	498
3	162
2	74
1	37
0	18

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
16×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
15×	`times-frac`
12×	`pow1`
11×	`add-cbrt-cube`
5×	`unpow-prod-down` `prod-exp` `associate-/l*` `sqr-pow`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `pow-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r` `associate-l*` `cbrt-unprod`
2×	`pow-to-exp` `pow-pow`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-r` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 93

Calls

4 calls:

0.0ms	(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
9.0ms	(pow (* -2 (log u1)) 0.5)
9.0ms	(/ (pow (* -2 (log u1)) 0.5) 6)
18.0ms	(* u2 (* 2 PI))

series2.1s

Counts

4 → 12

Calls

4 calls:

611.0ms	(fma (cos (* u2 (* 2 PI))) (/ (pow (* -2 (log u1)) 0.5) 6) 0.5)
374.0ms	(pow (* -2 (log u1)) 0.5)
1.1s	(/ (pow (* -2 (log u1)) 0.5) 6)
45.0ms	(* u2 (* 2 PI))

simplify3.0s

Counts

105 → 105

Iterations

Iter	Nodes
done	5088
3	4506
2	1192
1	417
0	189

prune661.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize28.0ms

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

rewrite38.0ms

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)
6.0ms	(pow (* -2 (log u1)) 0.5)
16.0ms	(* u2 (* 2 PI))
13.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)

series2.0s

Counts

4 → 12

Calls

4 calls:

560.0ms	(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)
409.0ms	(pow (* -2 (log u1)) 0.5)
57.0ms	(* u2 (* 2 PI))
959.0ms	(* (pow (* -2 (log u1)) 0.5) 1/6)

simplify3.0s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
3	4101
2	1102
1	382
0	160

prune603.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

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:

6.0ms	(pow (* -2 (log u1)) 0.5)
43.0ms	(* (* (pow (* -2 (log u1)) 0.5) (sqrt 1/6)) (sqrt 1/6))
38.0ms	(* u2 (* 2 PI))
17.0ms	(* (pow (* -2 (log u1)) 0.5) (sqrt 1/6))

series2.7s

Counts

4 → 12

Calls

4 calls:

417.0ms	(pow (* -2 (log u1)) 0.5)
1.1s	(* (* (pow (* -2 (log u1)) 0.5) (sqrt 1/6)) (sqrt 1/6))
56.0ms	(* u2 (* 2 PI))
1.2s	(* (pow (* -2 (log u1)) 0.5) (sqrt 1/6))

simplify3.6s

Counts

110 → 110

Iterations

Iter	Nodes
done	5006
3	4311
2	1203
1	407
0	165

prune624.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-exp-log`
43×	`add-sqr-sqrt` `times-frac`
34×	`prod-exp`
32×	`*-un-lft-identity` `add-cube-cbrt`
22×	`pow-exp`
20×	`div-exp` `associate-r`
16×	`add-cbrt-cube`
14×	`sqr-pow`
13×	`pow-unpow`
12×	`pow1`
11×	`pow-to-exp`
9×	`unpow-prod-down`
8×	`associate-l`
6×	`unswap-sqr`
5×	`cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `div-inv`
2×	`cbrt-undiv` `pow-pow` `*-commutative`
1×	`clear-num` `frac-2neg` `associate-*r/`

Counts

4 → 156

Calls

4 calls:

12.0ms	(pow (* -2 (log u1)) (/ 0.5 2))
9.0ms	(/ (pow (* -2 (log u1)) (/ 0.5 2)) 6)
16.0ms	(* u2 (* 2 PI))
32.0ms	(* (pow (* -2 (log u1)) (/ 0.5 2)) (/ (pow (* -2 (log u1)) (/ 0.5 2)) 6))

series2.6s

Counts

4 → 12

Calls

4 calls:

393.0ms	(pow (* -2 (log u1)) (/ 0.5 2))
1.1s	(/ (pow (* -2 (log u1)) (/ 0.5 2)) 6)
44.0ms	(* u2 (* 2 PI))
1.1s	(* (pow (* -2 (log u1)) (/ 0.5 2)) (/ (pow (* -2 (log u1)) (/ 0.5 2)) 6))

simplify2.0s

Counts

168 → 168

Iterations

Iter	Nodes
done	5001
2	1975
1	616
0	247

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes472.0ms

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
done	22
1	22
0	17

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
315.0ms	8000×	pre	80	true