Details

sample53.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 93.756105%

Space saved by search: 93.756105%

Guaranteed chance to sample good point: 0%

Results

25.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify604.0ms

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

prune6.0ms

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

localize34.0ms

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)
0.2b	(* (* 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:

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

series233.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
35.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
114.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify59.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (51.0ms)

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

prune201.0ms

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

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* (* 2.0 PI) u2)
0.2b	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
0.3b	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

rewrite35.0ms

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)
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)))
9.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

series240.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
102.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
100.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify54.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	454	932
1	1787	832
2	5002	819

prune267.0ms

Filtered

83 candidates to 124 candidates (-49.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

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

Merged error: 0.0b

Counts

132 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) u2)
0.3b	(* (/ 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)

rewrite32.0ms

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)
13.0ms	(* (/ 1.0 6.0) (cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3)))
6.0ms	(cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3))
4.0ms	(pow (pow (* -2.0 (log u1)) 0.5) 3)

series239.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) u2)
98.0ms	(* (/ 1.0 6.0) (cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3)))
93.0ms	(cbrt (pow (pow (* -2.0 (log u1)) 0.5) 3))
44.0ms	(pow (pow (* -2.0 (log u1)) 0.5) 3)

simplify78.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	609	1029
1	2514	983
2	5001	964

prune239.0ms

Filtered

82 candidates to 145 candidates (-76.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	145	8	153

Merged error: 0.0b

Counts

153 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) (/ 0.5 2))
0.2b	(* (* 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)))

rewrite34.0ms

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)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
8.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (* -2.0 (log u1)) (/ 0.5 2))
3.0ms	(* (* 2.0 PI) u2)
100.0ms	(* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2))) (pow (* -2.0 (log u1)) (/ 0.5 2)))
99.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) (/ 0.5 2)))

simplify64.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	617	1345
1	2368	1017
2	5002	1007

prune225.0ms

Filtered

79 candidates to 152 candidates (-92.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	152	8	160

Merged error: 0.0b

Counts

160 → 8

regimes575.0ms

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	27	14
1	27	14

end0.0ms

sample1.2s

Algorithm

intervals

sampling

Space saved by range analysis: 93.756105%

Space saved by search: 93.756105%

Guaranteed chance to sample good point: 0%

Results

777.0ms	8000×	body	80	valid
192.0ms	8000×	pre	80	true

Details

sample53.0ms

simplify604.0ms

prune6.0ms

localize34.0ms

rewrite32.0ms

series233.0ms

simplify59.0ms

prune201.0ms

localize20.0ms

rewrite35.0ms

series240.0ms

simplify54.0ms

prune267.0ms

localize22.0ms

rewrite32.0ms

series239.0ms

simplify78.0ms

prune239.0ms

localize20.0ms

rewrite34.0ms

series238.0ms

simplify64.0ms

prune225.0ms

regimes575.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling