Details

sample183.0ms

Algorithm

intervals

Results

100.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify4.2s

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize52.0ms

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))

rewrite160.0ms

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:

87.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
9.0ms	(pow (* -2.0 (log u1)) 0.5)
27.0ms	(* (* 2.0 PI) u2)
32.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series2.2s

Counts

4 → 12

Calls

4 calls:

709.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
382.0ms	(pow (* -2.0 (log u1)) 0.5)
65.0ms	(* (* 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

prune791.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.2b	(* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2))
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
38.8b	(cbrt (* (* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2)) (* (* 2.0 PI) u2)))

rewrite521.0ms

Algorithm

rewrite-expression-head

Rules

123×	`pow1`
69×	`pow-prod-down`
65×	`add-exp-log`
50×	`add-cbrt-cube`
40×	`prod-exp`
32×	`cbrt-unprod`
21×	`add-sqr-sqrt`
15×	`associate-l`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`times-frac`
9×	`associate-r` `pow-sqr` `pow-prod-up`
4×	`div-exp` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`pow-plus` `*-commutative` `sqr-pow`
2×	`pow-to-exp`
1×	`cbrt-prod` `pow2` `cbrt-undiv` `unpow-prod-down` `pow1/3` `swap-sqr` `pow3` `associate-*l/` `rem-cbrt-cube` `div-inv`

Counts

4 → 129

Calls

4 calls:

19.0ms	(* (* 2.0 PI) u2)
92.0ms	(* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2))
18.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
381.0ms	(cbrt (* (* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2)) (* (* 2.0 PI) u2)))

series1.5s

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* 2.0 PI) u2)
88.0ms	(* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2))
1.3s	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
106.0ms	(cbrt (* (* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2)) (* (* 2.0 PI) u2)))

simplify1.8s

Counts

141 → 141

Iterations

Iter	Nodes
done	5000
2	1801
1	515
0	204

prune880.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

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	(* (sqrt (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
38.8b	(cbrt (* (* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2)) (* (* 2.0 PI) u2)))

rewrite505.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-exp-log`
42×	`add-sqr-sqrt`
30×	`associate-l`
24×	`*-un-lft-identity` `add-cube-cbrt`
22×	`times-frac`
21×	`prod-exp`
19×	`pow1`
16×	`add-cbrt-cube`
14×	`associate-r`
9×	`unswap-sqr`
8×	`sqrt-pow1` `pow1/2` `div-exp` `pow-exp`
7×	`associate-*l/`
6×	`sqr-pow`
5×	`pow-prod-up` `cbrt-unprod`
4×	`pow-to-exp` `sqrt-div` `swap-sqr` `sqrt-prod` `add-log-exp`
3×	`pow-prod-down` `pow-sqr` `*-commutative`
2×	`cbrt-undiv` `unpow-prod-down` `div-inv`
1×	`cbrt-prod` `pow2` `frac-times` `rem-square-sqrt` `pow-plus` `pow1/3` `sqrt-unprod` `pow3` `associate-*r/` `rem-cbrt-cube`

Counts

4 → 133

Calls

4 calls:

18.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
29.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
92.0ms	(* (sqrt (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
359.0ms	(cbrt (* (* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2)) (* (* 2.0 PI) u2)))

series3.5s

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))
1.2s	(* (sqrt (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))) (sqrt (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
118.0ms	(cbrt (* (* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2)) (* (* 2.0 PI) u2)))

simplify1.7s

Counts

145 → 145

Iterations

Iter	Nodes
done	5000
2	1391
1	432
0	187

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.2b	(* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2))
0.3b	(* (pow (* (pow -2.0 1.0) (pow (log u1) 1.0)) 0.5) 0.16666666666666666)
38.8b	(cbrt (* (* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2)) (* (* 2.0 PI) u2)))

rewrite570.0ms

Algorithm

rewrite-expression-head

Rules

123×	`pow1`
71×	`add-exp-log`
69×	`pow-prod-down`
51×	`prod-exp`
47×	`add-cbrt-cube`
31×	`cbrt-unprod`
16×	`pow-exp`
10×	`add-sqr-sqrt`
9×	`pow-sqr` `pow-prod-up`
7×	`pow-to-exp` `-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
4×	`add-log-exp`
3×	`pow-plus` `*-commutative`
2×	`unswap-sqr` `sqr-pow`
1×	`cbrt-prod` `pow2` `unpow-prod-down` `pow1/3` `swap-sqr` `pow3` `rem-cbrt-cube`

Counts

4 → 119

Calls

4 calls:

26.0ms	(* (* 2.0 PI) u2)
132.0ms	(* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2))
15.0ms	(* (pow (* (pow -2.0 1.0) (pow (log u1) 1.0)) 0.5) 0.16666666666666666)
386.0ms	(cbrt (* (* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2)) (* (* 2.0 PI) u2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* 2.0 PI) u2)
113.0ms	(* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2))
1.0s	(* (pow (* (pow -2.0 1.0) (pow (log u1) 1.0)) 0.5) 0.16666666666666666)
131.0ms	(cbrt (* (* (* (* 2.0 PI) u2) (* (* 2.0 PI) u2)) (* (* 2.0 PI) u2)))

simplify1.8s

Counts

131 → 131

Iterations

Iter	Nodes
done	5003
2	1430
1	415
0	176

prune720.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes1.5s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	29
1	29
0	22

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
688.0ms	8000×	pre	80	true