Details

sample53.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify787.0ms

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	1403	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))

rewrite36.0ms

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

series265.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
40.0ms	(pow (* -2.0 (log u1)) 0.5)
4.0ms	(* (* 2.0 PI) u2)
130.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify526.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (150.0ms)

Iter	Nodes	Cost
0	208	1421
1	525	1350
2	1857	1211
done	5001	1211

prune267.0ms

Filtered

69 candidates to 99 candidates (-43.5%)

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)))

rewrite38.0ms

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:

5.0ms	(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)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(pow (* -2.0 (log u1)) 0.5)
116.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))
4.0ms	(* (* 2.0 PI) u2)
118.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))

simplify787.0ms

Counts

124 → 124

Iterations

Useful iterations: 2 (131.0ms)

Iter	Nodes	Cost
0	203	1783
1	461	1555
2	1499	1411
done	5000	1411

prune330.0ms

Filtered

85 candidates to 124 candidates (-45.9%)

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)))

rewrite39.0ms

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)
12.0ms	(* (* (/ 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)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow (* -2.0 (log u1)) (/ 0.5 2))
3.0ms	(* (* 2.0 PI) u2)
114.0ms	(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
116.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))

simplify548.0ms

Counts

152 → 152

Iterations

Useful iterations: 2 (172.0ms)

Iter	Nodes	Cost
0	238	2723
1	627	1921
2	2069	1717
done	5000	1717

prune300.0ms

Filtered

81 candidates to 152 candidates (-87.7%)

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)

series284.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (* 2.0 PI) u2)
117.0ms	(* (/ 1.0 6.0) (cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3)))
109.0ms	(cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3))
55.0ms	(pow (pow (* -2.0 (log u1)) 0.5) 3)

simplify618.0ms

Counts

145 → 145

Iterations

Useful iterations: done (613.0ms)

Iter	Nodes	Cost
0	248	2277
1	621	1802
2	2220	1721
done	5000	1717

prune286.0ms

Filtered

90 candidates to 145 candidates (-61.1%)

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

regimes707.0ms

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

741.0ms	8000×	body	80	valid
199.0ms	8000×	pre	80	true

Details

sample53.0ms

simplify787.0ms

prune5.0ms

localize19.0ms

rewrite36.0ms

series265.0ms

simplify526.0ms

prune267.0ms

localize19.0ms

rewrite38.0ms

series281.0ms

simplify787.0ms

prune330.0ms

localize19.0ms

rewrite39.0ms

series275.0ms

simplify548.0ms

prune300.0ms

localize20.0ms

rewrite34.0ms

series284.0ms

simplify618.0ms

prune286.0ms

regimes707.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling