Details

sample53.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify1.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	19
1	34	19
2	68	19
3	148	19
4	419	19
5	1419	19
done	5001	19

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.4b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (* (/ 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))

rewrite35.0ms

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:

10.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
4.0ms	(pow (* -2.0 (log u1)) 0.5)
5.0ms	(* (* 2.0 PI) u2)
11.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series259.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
39.0ms	(pow (* -2.0 (log u1)) 0.5)
4.0ms	(* (* 2.0 PI) u2)
127.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify576.0ms

Counts

99 → 99

Iterations

Useful iterations: done (573.0ms)

Iter	Nodes	Cost
0	208	1421
1	525	1360
2	1918	1231
done	5000	1211

prune253.0ms

Filtered

67 candidates to 99 candidates (-47.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	87	12	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	12	100

Merged error: 0b

Counts

100 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

4.0ms	(pow (* -2.0 (log u1)) 0.5)
10.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
5.0ms	(* (* 2.0 PI) u2)
14.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow (* -2.0 (log u1)) 0.5)
112.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
3.0ms	(* (* 2.0 PI) u2)
117.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))

simplify570.0ms

Counts

124 → 124

Iterations

Useful iterations: done (567.0ms)

Iter	Nodes	Cost
0	203	1783
1	461	1600
2	1595	1444
done	5000	1411

prune323.0ms

Filtered

87 candidates to 124 candidates (-42.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	8	3	11
Picked	0	1	1
Done	0	0	0
Total	129	7	136

Merged error: 0b

Counts

136 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) (/ 0.5 2))
0.3b	(* (* 2.0 PI) u2)
0.3b	(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

152×	`add-exp-log`
99×	`prod-exp`
40×	`pow-exp`
29×	`add-sqr-sqrt`
23×	`add-cbrt-cube`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`pow-to-exp` `times-frac` `div-exp`
15×	`associate-l`
13×	`pow-unpow` `associate-r`
12×	`pow1`
10×	`cbrt-unprod`
5×	`sqr-pow`
4×	`pow-prod-down` `add-log-exp` `unswap-sqr`
3×	`unpow-prod-down` `associate-l/` `-commutative`
2×	`cbrt-undiv` `pow-pow` `div-inv`

Counts

4 → 140

Calls

4 calls:

6.0ms	(pow (* -2.0 (log u1)) (/ 0.5 2))
5.0ms	(* (* 2.0 PI) u2)
11.0ms	(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
9.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow (* -2.0 (log u1)) (/ 0.5 2))
3.0ms	(* (* 2.0 PI) u2)
110.0ms	(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
112.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))

simplify622.0ms

Counts

152 → 152

Iterations

Useful iterations: done (617.0ms)

Iter	Nodes	Cost
0	238	2723
1	627	2397
2	2223	1985
done	5000	1717

prune297.0ms

Filtered

83 candidates to 152 candidates (-83.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	152	7	159

Merged error: 0b

Counts

159 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3)))
0.5b	(cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3))
0.7b	(pow (pow (* -2.0 (log u1)) 0.5) 3)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
44×	`cbrt-prod`
25×	`unpow-prod-down`
22×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
19×	`cube-prod`
18×	`add-exp-log`
16×	`times-frac`
15×	`sqr-pow`
14×	`associate-l` `unswap-sqr`
13×	`add-cbrt-cube`
11×	`pow1`
6×	`pow-exp` `prod-exp`
5×	`cbrt-unprod`
4×	`pow-prod-down` `add-log-exp`
3×	`cube-mult` `pow-unpow` `unpow3`
2×	`pow-to-exp` `*-commutative`
1×	`cbrt-undiv` `pow-pow` `pow1/3` `div-exp` `associate-*l/` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 133

Calls

4 calls:

5.0ms	(* (* 2.0 PI) u2)
15.0ms	(* (/ 1.0 6.0) (cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3)))
4.0ms	(cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3))
5.0ms	(pow (pow (* -2.0 (log u1)) 0.5) 3)

series270.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (* 2.0 PI) u2)
110.0ms	(* (/ 1.0 6.0) (cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3)))
103.0ms	(cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3))
53.0ms	(pow (pow (* -2.0 (log u1)) 0.5) 3)

simplify681.0ms

Counts

145 → 145

Iterations

Useful iterations: done (676.0ms)

Iter	Nodes	Cost
0	248	2277
1	621	1898
2	2458	1741
done	5001	1717

prune298.0ms

Filtered

94 candidates to 145 candidates (-54.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	145	7	152

Merged error: 0b

Counts

152 → 7

regimes682.0ms

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	20	25
1	27	25
done	27	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

769.0ms	8000×	body	80	valid
199.0ms	8000×	pre	80	true

Details

sample53.0ms

simplify1.0s

prune5.0ms

localize19.0ms

rewrite35.0ms

series259.0ms

simplify576.0ms

prune253.0ms

localize19.0ms

rewrite41.0ms

series271.0ms

simplify570.0ms

prune323.0ms

localize19.0ms

rewrite41.0ms

series264.0ms

simplify622.0ms

prune297.0ms

localize20.0ms

rewrite34.0ms

series270.0ms

simplify681.0ms

prune298.0ms

regimes682.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling