Details

sample287.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	19
1	34	19
2	68	19
3	147	19
4	395	19
5	1291	19
done	5000	19

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

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))

rewrite48.0ms

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:

18.0ms	(+ (* (* (/ 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)
6.0ms	(* (* 2.0 PI) u2)
12.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.5s

Counts

4 → 12

Calls

4 calls:

471.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
269.0ms	(pow (* -2.0 (log u1)) 0.5)
38.0ms	(* (* 2.0 PI) u2)
711.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify627.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (177.0ms)

Iter	Nodes	Cost
0	203	1408
1	506	1344
2	1721	1222
done	5000	1222

prune337.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ (* 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)
0.3b	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

11.0ms	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
2.0ms	(pow (* -2.0 (log u1)) 0.5)
6.0ms	(* (* 2.0 PI) u2)
5.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

series1.5s

Counts

4 → 12

Calls

4 calls:

468.0ms	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
275.0ms	(pow (* -2.0 (log u1)) 0.5)
39.0ms	(* (* 2.0 PI) u2)
709.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)

simplify541.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (145.0ms)

Iter	Nodes	Cost
0	184	1168
1	455	1121
2	1566	986
done	5000	986

prune271.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.3b	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
0.5b	(cbrt (pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3))
0.7b	(pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
20×	`cbrt-prod` `add-cbrt-cube`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
14×	`unpow-prod-down` `cube-prod`
13×	`prod-exp`
10×	`pow1` `div-exp` `pow-exp`
5×	`cbrt-unprod` `div-inv`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `associate-r` `pow-prod-down` `associate-/r*` `rem-cube-cbrt`
2×	`cube-div` `cube-mult` `unpow3` `sqr-pow`
1×	`cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `associate-l` `clear-num` `-commutative` `rem-cbrt-cube` `associate-/l`

Counts

4 → 111

Calls

4 calls:

6.0ms	(* (* 2.0 PI) u2)
4.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
3.0ms	(cbrt (pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3))
5.0ms	(pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3)

series2.2s

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* 2.0 PI) u2)
712.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
699.0ms	(cbrt (pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3))
786.0ms	(pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3)

simplify598.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (191.0ms)

Iter	Nodes	Cost
0	203	1950
1	492	1652
2	1783	1486
done	5001	1486

prune396.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.3b	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
0.5b	(pow (pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3) 1/3)
0.7b	(pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log`
34×	`unpow-prod-down`
26×	`pow-exp`
20×	`add-cbrt-cube`
18×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `prod-exp`
15×	`times-frac` `div-exp`
14×	`cube-prod`
10×	`pow1`
6×	`pow-to-exp` `pow-unpow`
5×	`cbrt-unprod` `div-inv`
4×	`cbrt-undiv` `add-log-exp`
3×	`associate-r` `pow-prod-down` `associate-/r*` `rem-cube-cbrt` `sqr-pow`
2×	`cube-mult` `pow-pow` `unpow3`
1×	`cube-div` `frac-2neg` `unpow1/3` `associate-l` `clear-num` `-commutative` `associate-/l`

Counts

4 → 123

Calls

4 calls:

7.0ms	(* (* 2.0 PI) u2)
4.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
7.0ms	(pow (pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3) 1/3)
4.0ms	(pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3)

series2.6s

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* 2.0 PI) u2)
712.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
992.0ms	(pow (pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3) 1/3)
911.0ms	(pow (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) 3)

simplify720.0ms

Counts

135 → 135

Iterations

Useful iterations: 2 (260.0ms)

Iter	Nodes	Cost
0	225	2218
1	603	1811
2	2052	1646
done	5000	1646

prune363.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes425.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	19
1	24	19
done	24	19

end0.0ms

sample934.0ms

Algorithm

intervals

Results

671.0ms	8000×	body	80	valid
117.0ms	8000×	pre	80	true