Details

analyze315.0ms

Algorithm: search

sample44.0ms

Algorithm

intervals

Results

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

simplify407.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	10
1	71	10
2	154	10
3	469	10
4	1812	10
5	5001	10

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

localize31.0ms

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)))
0.1b	(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))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-exp-log`
33×	`prod-exp`
23×	`add-sqr-sqrt` `add-cbrt-cube`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
14×	`pow1`
11×	`times-frac` `associate-r`
10×	`pow-exp` `cbrt-unprod`
8×	`div-exp`
5×	`pow-to-exp` `pow-prod-down`
4×	`add-log-exp` `unswap-sqr` `sqr-pow`
3×	`pow-unpow` `associate-l/` `-commutative`
2×	`cbrt-undiv` `unpow-prod-down` `pow-pow`
1×	`div-inv`

Counts

4 → 102

Calls

4 calls:

9.0ms	(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))
4.0ms	(pow (* -2.0 (log u1)) 0.5)
5.0ms	(* (* 2.0 PI) u2)
10.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series220.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))
34.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
108.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify60.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	515	865
1	2258	738
2	5002	730

prune195.0ms

Filtered

68 candidates to 114 candidates (-67.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	106	8	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	8	115

Merged error: 0.0b

Counts

115 → 8

localize17.0ms

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log`
20×	`add-cbrt-cube`
17×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `prod-exp`
15×	`times-frac`
8×	`div-exp` `cbrt-unprod`
7×	`pow-prod-down`
6×	`associate-r` `pow-exp`
5×	`unpow-prod-down` `associate-/l*` `sqr-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-unpow` `associate-/r*`
2×	`cbrt-undiv` `pow-pow` `associate-l` `*-commutative`
1×	`frac-2neg` `associate-r/` `associate-l/` `clear-num` `div-inv`

Counts

4 → 97

Calls

4 calls:

9.0ms	(* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))
4.0ms	(pow (* -2.0 (log u1)) 0.5)
5.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
5.0ms	(* (* 2.0 PI) u2)

series209.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2)))
36.0ms	(pow (* -2.0 (log u1)) 0.5)
96.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
3.0ms	(* (* 2.0 PI) u2)

simplify56.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	485	830
1	2104	713
2	5002	705

prune193.0ms

Filtered

69 candidates to 109 candidates (-58.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Merged error: 0.0b

Counts

117 → 8

localize20.0ms

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

rewrite37.0ms

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)
12.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
5.0ms	(* (* 2.0 PI) u2)
11.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series241.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (* -2.0 (log u1)) 0.5)
101.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
3.0ms	(* (* 2.0 PI) u2)
103.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify56.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	454	932
1	1787	832
2	5001	819

prune266.0ms

Filtered

83 candidates to 124 candidates (-49.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	124	8	132

Merged error: 0b

Counts

132 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
0.3b	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
0.3b	(* (* 2.0 PI) u2)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
72×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
52×	`add-exp-log`
26×	`div-exp`
24×	`associate-/r*`
17×	`unpow-prod-down` `sqr-pow`
16×	`add-cbrt-cube`
13×	`pow1`
10×	`pow-exp`
8×	`prod-exp`
6×	`div-inv` `associate-/l*`
5×	`pow-to-exp` `rec-exp` `1-exp`
4×	`cbrt-undiv` `pow-prod-down` `add-log-exp`
3×	`pow-unpow` `associate-r` `cbrt-unprod`
2×	`pow-pow` `frac-2neg` `clear-num`
1×	`pow-flip` `associate-l` `associate-/r/` `*-commutative` `inv-pow`

Counts

4 → 182

Calls

4 calls:

4.0ms	(pow (* -2.0 (log u1)) 0.5)
8.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
4.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
7.0ms	(* (* 2.0 PI) u2)

series246.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (* -2.0 (log u1)) 0.5)
95.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
112.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
3.0ms	(* (* 2.0 PI) u2)

simplify70.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	660	1618
1	2852	1464
2	5001	1363

prune261.0ms

Filtered

105 candidates to 194 candidates (-84.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	194	8	202

Merged error: 0b

Counts

202 → 8

regimes503.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	14
1	27	14

end0.0ms

analyze119.0ms

Algorithm: search

sample1.2s

Algorithm

intervals

Results

816.0ms	8000×	body	80	valid
204.0ms	8000×	pre	80	true

Details

analyze315.0ms

sample44.0ms

simplify407.0ms

prune5.0ms

localize31.0ms

rewrite31.0ms

series220.0ms

simplify60.0ms

prune195.0ms

localize17.0ms

rewrite25.0ms

series209.0ms

simplify56.0ms

prune193.0ms

localize20.0ms

rewrite37.0ms

series241.0ms

simplify56.0ms

prune266.0ms

localize18.0ms

rewrite30.0ms

series246.0ms

simplify70.0ms

prune261.0ms

regimes503.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze119.0ms

sample1.2s

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