Details

sample152.0ms

Algorithm

intervals

Results

53.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
6	3468
5	1272
4	432
3	156
2	69
1	34
0	18

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
25×	`add-sqr-sqrt`
24×	`prod-exp`
16×	`*-un-lft-identity`
14×	`add-cbrt-cube` `associate-l` `add-cube-cbrt`
13×	`times-frac`
12×	`pow1`
10×	`pow-exp`
8×	`div-exp` `associate-r`
6×	`add-log-exp` `unswap-sqr`
5×	`pow-to-exp` `cbrt-unprod` `sqr-pow`
4×	`rec-exp` `1-exp` `pow-prod-down` `insert-posit16`
3×	`pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `sum-log` `flip3-+` `associate-*l/` `flip-+` `div-inv`

Counts

4 → 101

Calls

4 calls:

77.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
11.0ms	(pow (* -2 (log u1)) 0.5)
29.0ms	(* (* 2 PI) u2)
26.0ms	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

series2.2s

Counts

4 → 12

Calls

4 calls:

591.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
279.0ms	(pow (* -2 (log u1)) 0.5)
386.0ms	(* (* 2 PI) u2)
965.0ms	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

simplify3.0s

Counts

113 → 113

Iterations

Iter	Nodes
3	5048
2	1526
1	545
0	218

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize51.0ms

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

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
34×	`add-exp-log`
33×	`associate-l`
32×	`sqrt-prod`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
22×	`times-frac`
19×	`prod-exp`
16×	`add-cbrt-cube`
14×	`pow1`
9×	`associate-r`
8×	`unswap-sqr`
7×	`cbrt-unprod`
6×	`pow-exp` `sqr-pow`
5×	`sqrt-div` `pow-prod-down`
4×	`associate-*l/` `insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow` `div-inv`
1×	`frac-times` `associate-*r/`

Counts

4 → 118

Calls

4 calls:

11.0ms	(pow (* -2 (log u1)) 0.5)
87.0ms	(* (sqrt (/ 1 6)) (* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5)))
15.0ms	(* (* 2 PI) u2)
30.0ms	(* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5))

series2.6s

Counts

4 → 12

Calls

4 calls:

421.0ms	(pow (* -2 (log u1)) 0.5)
1.1s	(* (sqrt (/ 1 6)) (* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5)))
63.0ms	(* (* 2 PI) u2)
1.0s	(* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5))

simplify2.0s

Counts

130 → 130

Iterations

Iter	Nodes
3	3605
2	1213
1	462
0	201

prune2.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

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-r*` `add-cube-cbrt`
6×	`add-log-exp`
4×	`associate-l` `pow-prod-down` `pow-exp` `cbrt-unprod` `insert-posit16`
3×	`pow-unpow` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `pow-pow` `*-commutative` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 73

Calls

4 calls:

38.0ms	(+ (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
13.0ms	(pow (* -2 (log u1)) 0.5)
15.0ms	(* (* 2 PI) u2)
11.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series1.9s

Counts

4 → 12

Calls

4 calls:

603.0ms	(+ (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
377.0ms	(pow (* -2 (log u1)) 0.5)
45.0ms	(* (* 2 PI) u2)
875.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify2.2s

Counts

85 → 85

Iterations

Iter	Nodes
3	4614
2	1292
1	420
0	170

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize88.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

202×	`add-exp-log`
166×	`prod-exp`
46×	`add-cbrt-cube`
43×	`pow1`
29×	`cbrt-unprod`
28×	`pow-exp`
23×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt`
14×	`pow-to-exp`
12×	`times-frac`
11×	`associate-r`
7×	`associate-l`
4×	`pow-sqr` `pow-prod-up` `insert-posit16` `associate-/l*` `add-log-exp` `difference-of-squares` `unswap-sqr` `sqr-pow`
3×	`associate-/r` `-commutative`
2×	`unpow-prod-down` `pow-plus` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow2` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `swap-sqr` `div-exp` `div-inv`

Counts

4 → 157

Calls

4 calls:

22.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
22.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
645.0ms	(/ (- (* (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2)))) (* 0.5 0.5)) (- (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5))
343.0ms	(* (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))))

series4.3s

Counts

4 → 12

Calls

4 calls:

1.4s	(* 1/6 (pow (* -2 (log u1)) 0.5))
1.1s	(* 1/6 (pow (* -2 (log u1)) 0.5))
1.1s	(/ (- (* (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2)))) (* 0.5 0.5)) (- (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5))
654.0ms	(* (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) (* (* 1/6 (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))))

simplify1.2s

Counts

169 → 169

Iterations

Iter	Nodes
2	2566
1	737
0	277

prune2.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes426.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
2	25
1	25
0	20

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.2s	8000×	body	80	valid
392.0ms	8000×	pre	80	true