Details

sample50.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify750.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4872	19
1	4872	19

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.4b

Counts

2 → 1

localize19.0ms

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)
0.3b	(* (* 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:

8.0ms	(+ (* (* (/ 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)
10.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series240.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
37.0ms	(pow (* -2.0 (log u1)) 0.5)
4.0ms	(* (* 2.0 PI) u2)
115.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify60.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4944	1174
1	4944	1174

prune197.0ms

Filtered

66 candidates to 99 candidates (-50.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	8	100

Merged error: 0.0b

Counts

100 → 8

localize16.0ms

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

8.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
4.0ms	(pow (* -2.0 (log u1)) 0.5)
4.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
5.0ms	(* (* 2.0 PI) u2)

series222.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
38.0ms	(pow (* -2.0 (log u1)) 0.5)
102.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
3.0ms	(* (* 2.0 PI) u2)

simplify36.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5008	1158

prune176.0ms

Filtered

66 candidates to 96 candidates (-45.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	97	7	104

Merged error: 0b

Counts

104 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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)
4.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
7.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
5.0ms	(* (* 2.0 PI) u2)

series264.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(pow (* -2.0 (log u1)) 0.5)
120.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
103.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
4.0ms	(* (* 2.0 PI) u2)

simplify65.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5216	2530

prune341.0ms

Filtered

119 candidates to 194 candidates (-63.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	194	7	201

Merged error: 0b

Counts

201 → 7

localize24.0ms

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)) (* 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)))

rewrite35.0ms

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:

5.0ms	(pow (* -2.0 (log u1)) (/ 0.5 2))
5.0ms	(* (* 2.0 PI) u2)
10.0ms	(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 1/2 0.5))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
8.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 1/2 0.5)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(pow (* -2.0 (log u1)) (/ 0.5 2))
3.0ms	(* (* 2.0 PI) u2)
102.0ms	(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 1/2 0.5))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
103.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (* 1/2 0.5)))

simplify68.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4919	1691
1	4919	1691

prune221.0ms

Filtered

80 candidates to 152 candidates (-90.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	152	7	159

Merged error: 0b

Counts

159 → 7

regimes398.0ms

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	21
1	27	21

end0.0ms

sample1.2s

Algorithm

intervals

Results

771.0ms	8000×	body	80	valid
180.0ms	8000×	pre	80	true

Details

sample50.0ms

simplify750.0ms

prune10.0ms

localize19.0ms

rewrite48.0ms

series240.0ms

simplify60.0ms

prune197.0ms

localize16.0ms

rewrite23.0ms

series222.0ms

simplify36.0ms

prune176.0ms

localize18.0ms

rewrite27.0ms

series264.0ms

simplify65.0ms

prune341.0ms

localize24.0ms

rewrite35.0ms

series245.0ms

simplify68.0ms

prune221.0ms

regimes398.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

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