Details

sample169.0ms

Algorithm

intervals

Results

46.0ms	256×	body	80	valid
10.0ms	256×	pre	80	true

simplify3.0s

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize39.0ms

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

rewrite120.0ms

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:

59.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
5.0ms	(pow (* -2 (log u1)) 0.5)
14.0ms	(* (* 2 PI) u2)
37.0ms	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

series2.2s

Counts

4 → 12

Calls

4 calls:

648.0ms	(+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5)
475.0ms	(pow (* -2 (log u1)) 0.5)
54.0ms	(* (* 2 PI) u2)
1.0s	(* (/ 1 6) (pow (* -2 (log u1)) 0.5))

simplify2.9s

Counts

113 → 113

Iterations

Iter	Nodes
3	5048
2	1526
1	545
0	218

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2 (log u1)) 0.5)
0.2b	(* (* 2 PI) u2)
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))

rewrite135.0ms

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:

5.0ms	(pow (* -2 (log u1)) 0.5)
26.0ms	(* (* 2 PI) u2)
79.0ms	(* (sqrt (/ 1 6)) (* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5)))
23.0ms	(* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5))

series2.6s

Counts

4 → 12

Calls

4 calls:

405.0ms	(pow (* -2 (log u1)) 0.5)
56.0ms	(* (* 2 PI) u2)
1.1s	(* (sqrt (/ 1 6)) (* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5)))
1.1s	(* (sqrt (/ 1 6)) (pow (* -2 (log u1)) 0.5))

simplify1.9s

Counts

130 → 130

Iterations

Iter	Nodes
3	3584
2	1237
1	464
0	201

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 1 (* 1/6 (pow (* (log u1) -2) 0.5))) (cos (* (* 2 PI) u2))) 0.5)
0.1b	(pow (* (log u1) -2) 0.5)
0.2b	(* (* 2 PI) u2)
0.4b	(* 1/6 (pow (* (log u1) -2) 0.5))

rewrite101.0ms

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:

69.0ms	(+ (* (* 1 (* 1/6 (pow (* (log u1) -2) 0.5))) (cos (* (* 2 PI) u2))) 0.5)
5.0ms	(pow (* (log u1) -2) 0.5)
14.0ms	(* (* 2 PI) u2)
11.0ms	(* 1/6 (pow (* (log u1) -2) 0.5))

series2.4s

Counts

4 → 12

Calls

4 calls:

605.0ms	(+ (* (* 1 (* 1/6 (pow (* (log u1) -2) 0.5))) (cos (* (* 2 PI) u2))) 0.5)
362.0ms	(pow (* (log u1) -2) 0.5)
39.0ms	(* (* 2 PI) u2)
1.4s	(* 1/6 (pow (* (log u1) -2) 0.5))

simplify2.0s

Counts

85 → 85

Iterations

Iter	Nodes
3	4289
2	1327
1	433
0	173

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite114.0ms

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:

6.0ms	(pow (* (log u1) -2) 0.5)
14.0ms	(* (* 2 PI) u2)
74.0ms	(* (sqrt (/ 1 6)) (* (sqrt (/ 1 6)) (pow (* (log u1) -2) 0.5)))
17.0ms	(* (sqrt (/ 1 6)) (pow (* (log u1) -2) 0.5))

series2.8s

Counts

4 → 12

Calls

4 calls:

407.0ms	(pow (* (log u1) -2) 0.5)
51.0ms	(* (* 2 PI) u2)
1.2s	(* (sqrt (/ 1 6)) (* (sqrt (/ 1 6)) (pow (* (log u1) -2) 0.5)))
1.1s	(* (sqrt (/ 1 6)) (pow (* (log u1) -2) 0.5))

simplify1.9s

Counts

130 → 130

Iterations

Iter	Nodes
3	3280
2	1197
1	467
0	203

prune1.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes471.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	25
1	25
0	18

end0.0ms

sample3.2s

Algorithm

intervals

Results

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