Details

sample106.0ms

Algorithm

intervals

Results

32.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	3198
4	477
3	155
2	71
1	34
0	18

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize38.0ms

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))

rewrite124.0ms

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:

65.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
5.0ms	(pow (* -2.0 (log u1)) 0.5)
14.0ms	(* (* 2.0 PI) u2)
33.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts

4 → 12

Calls

4 calls:

681.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
353.0ms	(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))

simplify2.0s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	2644
1	557
0	206

prune730.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

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

rewrite69.0ms

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:

29.0ms	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
10.0ms	(pow (* -2.0 (log u1)) 0.5)
15.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
13.0ms	(* (* 2.0 PI) u2)

series2.1s

Counts

4 → 12

Calls

4 calls:

642.0ms	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
427.0ms	(pow (* -2.0 (log u1)) 0.5)
1.0s	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
48.0ms	(* (* 2.0 PI) u2)

simplify2.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5002
2	2526
1	526
0	187

prune662.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
0.2b	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
0.3b	(* (* 2.0 PI) u2)

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt` `add-exp-log`
33×	`associate-l`
30×	`sqrt-prod`
23×	`*-un-lft-identity` `add-cube-cbrt`
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:

5.0ms	(pow (* -2.0 (log u1)) 0.5)
57.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
31.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
14.0ms	(* (* 2.0 PI) u2)

series2.7s

Counts

4 → 12

Calls

4 calls:

400.0ms	(pow (* -2.0 (log u1)) 0.5)
1.1s	(* (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))
58.0ms	(* (* 2.0 PI) u2)

simplify1.6s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	2087
1	484
0	200

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) u2)
0.3b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
41.1b	(cbrt (* (* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2)) (* (* 2.0 PI) u2)))

rewrite506.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
22×	`add-sqr-sqrt`
19×	`add-cbrt-cube`
16×	`prod-exp`
15×	`associate-l`
14×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
11×	`times-frac` `associate-r`
8×	`cbrt-unprod`
6×	`pow-prod-down`
4×	`div-exp` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`*-commutative` `sqr-pow`
2×	`pow-to-exp`
1×	`cbrt-prod` `cbrt-undiv` `unpow-prod-down` `pow1/3` `pow3` `associate-*l/` `rem-cbrt-cube` `div-inv`

Counts

4 → 87

Calls

4 calls:

14.0ms	(* (* 2.0 PI) u2)
20.0ms	(* (* 2.0 PI) u2)
17.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
451.0ms	(cbrt (* (* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2)) (* (* 2.0 PI) u2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (* 2.0 PI) u2)
35.0ms	(* (* 2.0 PI) u2)
991.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
117.0ms	(cbrt (* (* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2)) (* (* 2.0 PI) u2)))

simplify1.5s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	1811
1	393
0	171

prune770.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes693.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	27
1	27
0	20

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
271.0ms	8000×	pre	80	true