Details

sample221.0ms

Algorithm

intervals

Results

64.0ms	256×	body	80	valid
13.0ms	256×	pre	80	true

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1530
4	489
3	158
2	71
1	36
0	18

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
14×	`add-sqr-sqrt`
9×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `associate-r`
7×	`prod-exp`
6×	`associate-l` `add-log-exp`
4×	`pow-exp` `insert-posit16`
3×	`pow-unpow` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `pow-pow` `pow-prod-down` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 73

Calls

4 calls:

26.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
10.0ms	(pow (* -2 (log u1)) 0.5)
11.0ms	(* PI u2)
30.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series1.9s

Counts

4 → 12

Calls

4 calls:

474.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
371.0ms	(pow (* -2 (log u1)) 0.5)
24.0ms	(* PI u2)
1.1s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify3.3s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	4829
2	1216
1	425
0	164

prune516.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`prod-exp`
15×	`associate-l`
13×	`add-cbrt-cube`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`insert-posit16` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `pow-unpow` `pow-prod-down` `*-commutative`
2×	`unpow-prod-down` `pow-pow`

Counts

4 → 90

Calls

4 calls:

9.0ms	(pow (* -2 (log u1)) 0.5)
12.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
5.0ms	(* PI u2)
38.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))

series2.7s

Counts

4 → 12

Calls

4 calls:

384.0ms	(pow (* -2 (log u1)) 0.5)
1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
33.0ms	(* PI u2)
1.1s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))

simplify2.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
3	3226
2	963
1	347
0	145

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5))))
0.1b	(pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5)
0.3b	(* PI u2)
0.3b	(* 1/6 (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
32×	`pow-exp`
31×	`prod-exp`
14×	`add-sqr-sqrt` `pow-to-exp`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `associate-r`
7×	`pow1`
6×	`associate-l` `add-log-exp`
4×	`insert-posit16`
3×	`pow-unpow` `unswap-sqr` `sqr-pow`
2×	`unpow-prod-down` `pow-pow` `pow-prod-down` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 89

Calls

4 calls:

17.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5))))
11.0ms	(pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5)
5.0ms	(* PI u2)
16.0ms	(* 1/6 (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5))

series2.6s

Counts

4 → 12

Calls

4 calls:

486.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5))))
1.2s	(pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5)
34.0ms	(* PI u2)
935.0ms	(* 1/6 (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5))

simplify3.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	1541
1	542
0	207

prune575.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (pow (* -2 (log u1)) 0.5) 1/216) (pow (* -2 (log u1)) 0.5))
0.3b	(* (* (* (pow (* -2 (log u1)) 0.5) 1/216) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
0.4b	(* (pow (* -2 (log u1)) 0.5) 1/216)
0.6b	(cbrt (* (* (* (pow (* -2 (log u1)) 0.5) 1/216) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

380×	`add-exp-log`
335×	`prod-exp`
134×	`pow-exp`
67×	`pow-to-exp`
20×	`add-cbrt-cube`
13×	`associate-r`
11×	`add-sqr-sqrt`
10×	`cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l`
4×	`pow1` `insert-posit16` `add-log-exp` `sqr-pow`
3×	`unpow-prod-down` `*-commutative`
2×	`unswap-sqr`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 173

Calls

4 calls:

37.0ms	(* (* (pow (* -2 (log u1)) 0.5) 1/216) (pow (* -2 (log u1)) 0.5))
101.0ms	(* (* (* (pow (* -2 (log u1)) 0.5) 1/216) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
20.0ms	(* (pow (* -2 (log u1)) 0.5) 1/216)
55.0ms	(cbrt (* (* (* (pow (* -2 (log u1)) 0.5) 1/216) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))

series4.1s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (* (pow (* -2 (log u1)) 0.5) 1/216) (pow (* -2 (log u1)) 0.5))
914.0ms	(* (* (* (pow (* -2 (log u1)) 0.5) 1/216) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5))
1.1s	(* (pow (* -2 (log u1)) 0.5) 1/216)
1.0s	(cbrt (* (* (* (pow (* -2 (log u1)) 0.5) 1/216) (pow (* -2 (log u1)) 0.5)) (pow (* -2 (log u1)) 0.5)))

simplify3.7s

Counts

185 → 185

Iterations

Iter	Nodes
done	5002
3	4335
2	1305
1	480
0	193

prune768.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes505.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.0s	8000×	body	80	valid
740.0ms	8000×	pre	80	true