Details

sample322.0ms

Algorithm

intervals

Results

57.0ms	256×	body	80	valid
13.0ms	256×	pre	80	true

simplify3.7s

Counts

1 → 1

Iterations

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

prune15.0ms

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))

rewrite375.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

286.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
12.0ms	(pow (* -2 (log u1)) 0.5)
11.0ms	(* PI u2)
61.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))

series2.1s

Counts

4 → 12

Calls

4 calls:

552.0ms	(+ 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))
406.0ms	(pow (* -2 (log u1)) 0.5)
48.0ms	(* PI u2)
1.1s	(* 1/6 (pow (* -2 (log u1)) 0.5))

simplify1.9s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	1527
1	553
0	205

prune640.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize32.0ms

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)))

rewrite417.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
85×	`associate-r`
62×	`unswap-sqr`
55×	`unpow-prod-down`
34×	`sqrt-prod`
31×	`add-exp-log`
30×	`associate-l`
25×	`*-un-lft-identity` `add-cube-cbrt`
19×	`pow1`
17×	`prod-exp`
13×	`add-cbrt-cube`
11×	`sqr-pow`
7×	`*-commutative`
6×	`pow-prod-down` `pow-exp`
5×	`cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `log-pow`
2×	`pow-pow`

Counts

4 → 173

Calls

4 calls:

24.0ms	(pow (* -2 (log u1)) 0.5)
78.0ms	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
13.0ms	(* PI u2)
292.0ms	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))

series2.9s

Counts

4 → 12

Calls

4 calls:

733.0ms	(pow (* -2 (log u1)) 0.5)
1.1s	(* (sqrt 1/6) (pow (* -2 (log u1)) 0.5))
24.0ms	(* PI u2)
1.0s	(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))

simplify2.1s

Counts

185 → 185

Iterations

Iter	Nodes
done	5001
2	1691
1	585
0	220

prune920.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize90.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.9s

Algorithm

rewrite-expression-head

Rules

20972×	`add-sqr-sqrt`
13722×	`unswap-sqr`
4134×	`difference-of-squares`
2618×	`times-frac`
2288×	`unpow-prod-down`
1603×	`*-un-lft-identity`
1107×	`sqr-pow`
1046×	`swap-sqr`
617×	`*-commutative`
598×	`distribute-lft-out--`
491×	`associate-l`
308×	`associate-r`
297×	`add-cube-cbrt`
238×	`associate-/l*`
202×	`add-exp-log`
166×	`prod-exp`
130×	`pow1`
68×	`pow-prod-down`
46×	`add-cbrt-cube`
29×	`cbrt-unprod`
28×	`pow-exp`
14×	`pow-to-exp`
11×	`associate-/r*`
9×	`pow-sqr` `pow-prod-up`
8×	`log-pow`
4×	`insert-posit16` `add-log-exp`
3×	`pow-plus`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow2` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

4 → 3218

Calls

4 calls:

69.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
67.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
7.8s	(/ (- (* 0.5 0.5) (* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))) (- 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5)))))
2.1s	(* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))

series3.5s

Counts

4 → 12

Calls

4 calls:

985.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
1.1s	(* 1/6 (pow (* -2 (log u1)) 0.5))
923.0ms	(/ (- (* 0.5 0.5) (* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))) (- 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5)))))
530.0ms	(* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))))

simplify8.2s

Counts

3230 → 3230

Iterations

Iter	Nodes
done	5000
0	2963

prune16.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize84.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.7s

Algorithm

rewrite-expression-head

Rules

20330×	`add-sqr-sqrt`
13669×	`unswap-sqr`
3930×	`difference-of-squares`
2464×	`times-frac`
2100×	`unpow-prod-down`
1864×	`log-prod` `exp-sum`
1312×	`*-un-lft-identity`
1028×	`sqr-pow`
527×	`*-commutative`
522×	`distribute-lft-out--`
516×	`swap-sqr`
405×	`associate-l`
268×	`add-cube-cbrt`
224×	`associate-/l*`
191×	`associate-r`
91×	`add-exp-log`
70×	`prod-exp`
33×	`pow1`
31×	`add-cbrt-cube`
17×	`pow-prod-down` `cbrt-unprod`
11×	`associate-/r*`
10×	`pow-exp`
5×	`pow-to-exp`
4×	`log-pow` `insert-posit16` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

4 → 2964

Calls

4 calls:

50.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
48.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
9.7s	(/ (- (* 0.5 0.5) (* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (exp (log (* 1/6 (pow (* -2 (log u1)) 0.5))))))) (- 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5)))))
3.1s	(* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (exp (log (* 1/6 (pow (* -2 (log u1)) 0.5))))))

series3.2s

Counts

4 → 12

Calls

4 calls:

948.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
959.0ms	(* 1/6 (pow (* -2 (log u1)) 0.5))
819.0ms	(/ (- (* 0.5 0.5) (* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (exp (log (* 1/6 (pow (* -2 (log u1)) 0.5))))))) (- 0.5 (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5)))))
492.0ms	(* (* (cos (* 2 (* PI u2))) (* 1/6 (pow (* -2 (log u1)) 0.5))) (* (cos (* 2 (* PI u2))) (exp (log (* 1/6 (pow (* -2 (log u1)) 0.5))))))

simplify6.4s

Counts

2976 → 2976

Iterations

Iter	Nodes
done	5001
0	3292

prune18.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes369.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	25
1	25
0	18

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.2s	8000×	body	80	valid
434.0ms	8000×	pre	80	true