Details

sample301.0ms

Algorithm

intervals

Results

52.0ms	256×	body	80	valid
10.0ms	256×	pre	80	true

simplify4.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1534
4	385
3	145
2	69
1	34
0	18

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize61.0ms

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)
0.2b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-sqr-sqrt`
14×	`-un-lft-identity` `add-cbrt-cube` `associate-l*` `prod-exp` `add-cube-cbrt`
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` `sum-log` `flip3-+` `associate-*l/` `flip-+` `div-inv`

Counts

4 → 87

Calls

4 calls:

59.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
12.0ms	(pow (* -2.0 (log u1)) 0.5)
17.0ms	(* (* 2.0 PI) u2)
39.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.3s

Counts

4 → 12

Calls

4 calls:

738.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
421.0ms	(pow (* -2.0 (log u1)) 0.5)
62.0ms	(* (* 2.0 PI) u2)
1.1s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify1.7s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	1834
1	555
0	206

prune783.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* (* 2.0 PI) u2)
0.2b	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

36.0ms	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
5.0ms	(pow (* -2.0 (log u1)) 0.5)
13.0ms	(* (* 2.0 PI) u2)
12.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

series2.4s

Counts

4 → 12

Calls

4 calls:

767.0ms	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
403.0ms	(pow (* -2.0 (log u1)) 0.5)
49.0ms	(* (* 2.0 PI) u2)
1.1s	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify1.8s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1734
1	520
0	187

prune618.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize93.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

3606×	`add-exp-log`
2379×	`prod-exp`
979×	`div-exp`
594×	`add-cbrt-cube`
326×	`pow-exp` `cbrt-unprod`
175×	`cbrt-undiv`
163×	`pow-to-exp`
33×	`add-sqr-sqrt`
32×	`pow1`
30×	`times-frac`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
19×	`associate-r`
15×	`associate-l`
9×	`pow3`
8×	`frac-times`
7×	`pow-plus` `swap-sqr` `associate-*l/` `pow-prod-up` `div-inv`
6×	`associate-*r/`
5×	`pow-prod-down`
4×	`sum-cubes` `associate-/l*` `add-log-exp`
3×	`pow2` `associate-/r` `pow-sqr` `-commutative` `unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`clear-num` `frac-2neg` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 633

Calls

4 calls:

957.0ms	(/ (+ (* (* (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0) (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0)) (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0)) (* (* 0.5 0.5) 0.5)) (+ (* 0.5 0.5) (* (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0) (- (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0) 0.5))))
343.0ms	(* (* (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0) (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0)) (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0))
107.0ms	(* (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0) (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0))
132.0ms	(* (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0) (- (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0) 0.5))

series5.3s

Counts

4 → 12

Calls

4 calls:

2.3s	(/ (+ (* (* (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0) (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0)) (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0)) (* (* 0.5 0.5) 0.5)) (+ (* 0.5 0.5) (* (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0) (- (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0) 0.5))))
717.0ms	(* (* (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0) (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0)) (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0))
725.0ms	(* (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0) (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0))
1.5s	(* (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0) (- (/ (* (* (pow (* -2.0 (log u1)) 0.5) 1.0) (cos (* (* u2 2.0) PI))) 6.0) 0.5))

simplify3.2s

Counts

645 → 645

Iterations

Iter	Nodes
done	5001
1	2112
0	743

prune4.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.2b	(log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.4b	(exp (log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

17.0ms	(* (* 2.0 PI) u2)
67.0ms	(log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
35.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
85.0ms	(exp (log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)))

series2.5s

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (* 2.0 PI) u2)
750.0ms	(log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
1.0s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
634.0ms	(exp (log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)))

simplify2.0s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1636
1	529
0	230

prune841.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes1.2s

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	36
1	36
0	26

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
264.0ms	8000×	pre	80	true