Details

sample481.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 93.756105%

Space saved by search: 93.756105%

Guaranteed chance to sample good point: 99.21875%

Results

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

simplify417.0ms

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))) 0.5)
0.2b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* (* 2.0 PI) u2)
0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite32.0ms

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:

9.0ms	(+ (* (* (/ 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))

series257.0ms

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)
40.0ms	(pow (* -2.0 (log u1)) 0.5)
4.0ms	(* (* 2.0 PI) u2)
123.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify62.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	514	738
1	2154	656
2	5001	648

prune201.0ms

Filtered

66 candidates to 99 candidates (-50.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	9	100

Merged error: 0b

Counts

100 → 9

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

rewrite25.0ms

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:

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

series241.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
40.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
110.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	445	720
1	1835	655
2	5001	647

prune181.0ms

Filtered

67 candidates to 96 candidates (-43.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	98	7	105

Merged error: 0b

Counts

105 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

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

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)
5.0ms	(* (* 2.0 PI) u2)
4.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
8.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
128.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
114.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))

simplify74.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (56.0ms)

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

prune286.0ms

Filtered

106 candidates to 194 candidates (-83.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	194	7	201

Merged error: 0b

Counts

201 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.5b	(cbrt (pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3))
0.8b	(pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
23×	`add-sqr-sqrt` `prod-exp`
20×	`add-cbrt-cube`
17×	`pow-exp`
15×	`add-cube-cbrt` `*-un-lft-identity`
14×	`associate-l`
11×	`times-frac`
10×	`pow1`
8×	`cbrt-prod` `div-exp` `associate-r`
7×	`cbrt-unprod`
5×	`pow-to-exp` `sqr-pow`
4×	`add-log-exp` `unswap-sqr`
3×	`unpow-prod-down` `pow-unpow` `pow-prod-down` `associate-*l/` `rem-cube-cbrt`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `cube-prod` `*-commutative`
1×	`cbrt-div` `pow-pow` `pow1/3` `rem-cbrt-cube` `div-inv`

Counts

4 → 107

Calls

4 calls:

5.0ms	(* (* 2.0 PI) u2)
8.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
3.0ms	(cbrt (pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3))
9.0ms	(pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3)

series351.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) u2)
109.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
110.0ms	(cbrt (pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3))
128.0ms	(pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3)

simplify58.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	474	783
1	1975	741
2	5002	736

prune203.0ms

Filtered

74 candidates to 119 candidates (-60.8%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	119	7	126

Merged error: 0b

Counts

126 → 7

regimes714.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.5s

Algorithm

intervals

sampling

Space saved by range analysis: 93.756105%

Space saved by search: 93.756105%

Guaranteed chance to sample good point: 99.21875%

Results

834.0ms	8000×	body	80	valid
211.0ms	8000×	pre	80	true

Details

sample481.0ms

simplify417.0ms

prune5.0ms

localize31.0ms

rewrite32.0ms

series257.0ms

simplify62.0ms

prune201.0ms

localize17.0ms

rewrite25.0ms

series241.0ms

simplify55.0ms

prune181.0ms

localize19.0ms

rewrite30.0ms

series284.0ms

simplify74.0ms

prune286.0ms

localize21.0ms

rewrite29.0ms

series351.0ms

simplify58.0ms

prune203.0ms

regimes714.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling