Details

sample241.0ms

Algorithm

intervals

Results

66.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	18	19
1	34	19
2	71	19
3	152	19
4	440	19
5	1385	19
done	5000	19

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `prod-exp` `add-cbrt-cube`
12×	`pow1`
11×	`times-frac`
8×	`associate-r`
6×	`pow-exp` `add-log-exp`
5×	`cbrt-unprod`
4×	`div-exp` `pow-prod-down` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-*l/` `sum-log` `flip-+` `div-inv`

Counts

4 → 87

Calls

4 calls:

91.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
7.0ms	(pow (* -2.0 (log u1)) 0.5)
31.0ms	(* (* 2.0 PI) u2)
61.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.4s

Counts

4 → 12

Calls

4 calls:

720.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
448.0ms	(pow (* -2.0 (log u1)) 0.5)
54.0ms	(* (* 2.0 PI) u2)
1.1s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify2.0s

Counts

99 → 99

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	203	1408
1	499	1344
2	1655	1222
done	5000	1191

prune575.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
0.3b	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
0.3b	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log` `add-sqr-sqrt`
33×	`associate-l`
30×	`sqrt-prod`
23×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
19×	`prod-exp`
16×	`add-cbrt-cube`
14×	`pow1`
9×	`associate-r`
7×	`cbrt-unprod`
6×	`pow-exp` `unswap-sqr`
5×	`sqrt-div` `pow-prod-down` `sqr-pow`
4×	`associate-*l/` `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 → 112

Calls

4 calls:

13.0ms	(pow (* -2.0 (log u1)) 0.5)
39.0ms	(* (* 2.0 PI) u2)
114.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
44.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series2.8s

Counts

4 → 12

Calls

4 calls:

421.0ms	(pow (* -2.0 (log u1)) 0.5)
65.0ms	(* (* 2.0 PI) u2)
1.2s	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
1.2s	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify1.9s

Counts

124 → 124

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	200	1773
1	442	1551
2	1420	1428
done	5000	1413

prune701.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 1) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `prod-exp` `add-cbrt-cube`
12×	`pow1`
11×	`times-frac`
8×	`associate-r`
6×	`pow-exp` `add-log-exp`
5×	`cbrt-unprod`
4×	`div-exp` `pow-prod-down` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-*l/` `sum-log` `flip-+` `div-inv`

Counts

4 → 87

Calls

4 calls:

46.0ms	(+ (* (pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 1) (cos (* (* 2.0 PI) u2))) 0.5)
6.0ms	(pow (* -2.0 (log u1)) 0.5)
31.0ms	(* (* 2.0 PI) u2)
45.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.1s

Counts

4 → 12

Calls

4 calls:

656.0ms	(+ (* (pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 1) (cos (* (* 2.0 PI) u2))) 0.5)
386.0ms	(pow (* -2.0 (log u1)) 0.5)
46.0ms	(* (* 2.0 PI) u2)
1.0s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.4s

Counts

99 → 99

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	204	1444
1	500	1344
2	1660	1214
done	5000	1187

prune493.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.5b	(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
0.8b	(pow (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 3)

rewrite887.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-exp-log`
68×	`prod-exp`
38×	`add-sqr-sqrt` `add-cbrt-cube`
27×	`associate-l`
26×	`pow-exp`
22×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`cbrt-unprod`
16×	`div-exp`
13×	`associate-r`
12×	`pow1`
11×	`associate-*l/`
9×	`pow-to-exp`
8×	`unswap-sqr`
7×	`sqr-pow`
4×	`cbrt-undiv` `pow-prod-down` `add-log-exp` `rem-cube-cbrt`
3×	`unpow-prod-down` `pow-unpow` `*-commutative`
2×	`distribute-rgt-in` `frac-times` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `associate-*r/` `flip--` `div-inv`
1×	`cube-div` `cube-mult` `unpow3` `cube-prod`

Counts

4 → 152

Calls

4 calls:

48.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
22.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
726.0ms	(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
77.0ms	(pow (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 3)

series4.6s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.1s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.6s	(* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
825.0ms	(pow (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 3)

simplify2.0s

Counts

164 → 164

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	269	4188
1	683	3829
2	2654	3369
done	5002	3354

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes484.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: done (5.0ms)

Iter	Nodes	Cost
0	20	21
1	28	21
done	28	19

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.8s	8000×	body	80	valid
325.0ms	8000×	pre	80	true