Details

sample696.0ms

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

24.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify419.0ms

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

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)
0.2b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite29.0ms

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

series225.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ (* (* (/ 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)
4.0ms	(* (* 2.0 PI) u2)
110.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify61.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (50.0ms)

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

prune202.0ms

Filtered

66 candidates to 99 candidates (-50.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	90	9	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	9	100

Merged error: 0b

Counts

100 → 9

localize19.0ms

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)

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

series207.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
34.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
95.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (43.0ms)

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

prune182.0ms

Filtered

67 candidates to 96 candidates (-43.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	97	8	105

Merged error: 0b

Counts

105 → 8

localize17.0ms

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)))

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	(* (* 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)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
110.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
95.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))

simplify69.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (52.0ms)

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

prune289.0ms

Filtered

106 candidates to 194 candidates (-83.0%)

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

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) (/ 0.5 2))
0.2b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2))))
0.5b	(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

161×	`add-exp-log`
110×	`prod-exp`
50×	`pow-exp`
30×	`add-sqr-sqrt`
25×	`pow-to-exp`
23×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
19×	`times-frac` `associate-l`
17×	`div-exp`
14×	`pow1`
13×	`pow-unpow`
10×	`cbrt-unprod`
9×	`associate-r` `sqr-pow`
6×	`pow-prod-down` `unswap-sqr`
5×	`unpow-prod-down` `swap-sqr`
4×	`add-log-exp`
3×	`*-commutative`
2×	`cbrt-undiv` `pow-pow` `div-inv`
1×	`pow2` `associate-*l/` `pow-sqr` `pow-prod-up`

Counts

4 → 157

Calls

4 calls:

5.0ms	(pow (* -2.0 (log u1)) (/ 0.5 2))
7.0ms	(* (* 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))))
7.0ms	(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (* -2.0 (log u1)) (/ 0.5 2))
3.0ms	(* (* 2.0 PI) u2)
95.0ms	(* (/ 1.0 6.0) (* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2))))
92.0ms	(* (pow (* -2.0 (log u1)) (/ 0.5 2)) (pow (* -2.0 (log u1)) (/ 0.5 2)))

simplify74.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	694	1399
1	2572	1071
2	5001	1047

prune216.0ms

Filtered

81 candidates to 169 candidates (-108.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	169	8	177

Merged error: 0b

Counts

177 → 8

regimes804.0ms

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

sample1.7s

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

781.0ms	8000×	body	80	valid
196.0ms	8000×	pre	80	true

Details

sample696.0ms

simplify419.0ms

prune5.0ms

localize19.0ms

rewrite29.0ms

series225.0ms

simplify61.0ms

prune202.0ms

localize19.0ms

rewrite23.0ms

series207.0ms

simplify52.0ms

prune182.0ms

localize17.0ms

rewrite27.0ms

series244.0ms

simplify69.0ms

prune289.0ms

localize19.0ms

rewrite36.0ms

series225.0ms

simplify74.0ms

prune216.0ms

regimes804.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.7s

Profiling