Details

sample54.0ms

Algorithm

intervals

Results

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

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4872	19
1	4872	19

prune14.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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 → 2

localize27.0ms

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)
4.0ms	(pow (* -2.0 (log u1)) 0.5)
5.0ms	(* (* 2.0 PI) u2)
12.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series262.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
42.0ms	(pow (* -2.0 (log u1)) 0.5)
4.0ms	(* (* 2.0 PI) u2)
128.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify43.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4947	1174
1	4947	1174

prune227.0ms

Filtered

66 candidates to 99 candidates (-50.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	89	10	99
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	91	10	101

Merged error: 0b

Counts

101 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log` `add-sqr-sqrt`
30×	`sqrt-prod`
23×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-l`
20×	`times-frac` `associate-r`
19×	`prod-exp`
16×	`add-cbrt-cube`
14×	`pow1`
7×	`cbrt-unprod`
6×	`pow-exp` `unswap-sqr`
5×	`sqrt-div` `pow-prod-down` `sqr-pow`
4×	`associate-*r/` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow` `div-inv`
1×	`frac-times` `associate-*l/`

Counts

4 → 112

Calls

4 calls:

5.0ms	(pow (* -2.0 (log u1)) 0.5)
10.0ms	(* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ 1.0 6.0)))
8.0ms	(* (* 2.0 PI) u2)
14.0ms	(* (sqrt (/ 1.0 6.0)) (* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ 1.0 6.0))))

series274.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow (* -2.0 (log u1)) 0.5)
113.0ms	(* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ 1.0 6.0)))
4.0ms	(* (* 2.0 PI) u2)
117.0ms	(* (sqrt (/ 1.0 6.0)) (* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ 1.0 6.0))))

simplify44.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4995	1398
1	4995	1398

prune290.0ms

Filtered

81 candidates to 124 candidates (-53.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	127	7	134

Merged error: 0b

Counts

134 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
1.2b	(pow (exp (pow (* -2.0 (log u1)) 0.5)) (/ 1.0 6.0))
2.5b	(exp (pow (* -2.0 (log u1)) 0.5))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
13×	`pow1`
12×	`add-exp-log`
10×	`exp-prod`
9×	`times-frac` `add-cbrt-cube`
8×	`pow-pow`
6×	`unpow-prod-down`
5×	`add-log-exp`
4×	`pow-prod-down` `prod-exp` `sqr-pow`
3×	`associate-r` `pow-exp` `cbrt-unprod`
2×	`pow-to-exp`
1×	`associate-l` `*-commutative` `div-inv` `rem-exp-log`

Counts

4 → 80

Calls

4 calls:

5.0ms	(pow (* -2.0 (log u1)) 0.5)
6.0ms	(* (* 2.0 PI) u2)
7.0ms	(pow (exp (pow (* -2.0 (log u1)) 0.5)) (/ 1.0 6.0))
4.0ms	(exp (pow (* -2.0 (log u1)) 0.5))

series177.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow (* -2.0 (log u1)) 0.5)
4.0ms	(* (* 2.0 PI) u2)
83.0ms	(pow (exp (pow (* -2.0 (log u1)) 0.5)) (/ 1.0 6.0))
51.0ms	(exp (pow (* -2.0 (log u1)) 0.5))

simplify52.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4984	859
1	4984	859

prune449.0ms

Filtered

61 candidates to 92 candidates (-50.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	93	6	99

Merged error: 0b

Counts

99 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) (* 1/2 0.5))
0.3b	(* (* 2.0 PI) u2)
0.3b	(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 1/2 0.5))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 1/2 0.5)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

152×	`add-exp-log`
99×	`prod-exp`
40×	`pow-exp`
23×	`add-cbrt-cube`
22×	`add-sqr-sqrt`
20×	`pow-to-exp` `div-exp`
15×	`associate-l`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
12×	`pow1`
11×	`times-frac`
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`
1×	`pow-unpow` `div-inv`

Counts

4 → 128

Calls

4 calls:

5.0ms	(pow (* -2.0 (log u1)) (* 1/2 0.5))
6.0ms	(* (* 2.0 PI) u2)
12.0ms	(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 1/2 0.5))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
9.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 1/2 0.5)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(pow (* -2.0 (log u1)) (* 1/2 0.5))
4.0ms	(* (* 2.0 PI) u2)
114.0ms	(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 1/2 0.5))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
115.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 1/2 0.5)))

simplify59.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4889	1573
1	4889	1573

prune208.0ms

Filtered

69 candidates to 140 candidates (-102.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	140	6	146

Merged error: 0b

Counts

146 → 6

regimes412.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	25
1	27	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

723.0ms	8000×	body	80	valid
196.0ms	8000×	pre	80	true

Details

sample54.0ms

simplify72.0ms

prune14.0ms

localize27.0ms

rewrite36.0ms

series262.0ms

simplify43.0ms

prune227.0ms

localize18.0ms

rewrite41.0ms

series274.0ms

simplify44.0ms

prune290.0ms

localize21.0ms

rewrite24.0ms

series177.0ms

simplify52.0ms

prune449.0ms

localize23.0ms

rewrite38.0ms

series275.0ms

simplify59.0ms

prune208.0ms

regimes412.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

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