Details

sample321.0ms

Algorithm

intervals

Results

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

simplify320.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	34	10
1	71	10
2	154	10
3	469	10
4	1812	10
5	5001	10

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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 → 1

localize20.0ms

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))

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:

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))

series223.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
34.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
107.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify61.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (52.0ms)

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

prune214.0ms

Filtered

99 candidates to 66 candidates (33.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	89	10	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	10	100

Merged error: 0.0b

Counts

100 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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

series238.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (* -2.0 (log u1)) 0.5)
100.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
3.0ms	(* (* 2.0 PI) u2)
100.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify55.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	454	932
1	1787	832
2	5001	819

prune277.0ms

Filtered

124 candidates to 83 candidates (33.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	126	8	134

Merged error: 0.0b

Counts

134 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
0.3b	(* (* 2.0 PI) u2)
0.3b	(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
23×	`prod-exp`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `add-cbrt-cube`
11×	`pow1` `times-frac`
9×	`rem-log-exp`
8×	`div-exp` `associate-r` `pow-exp`
5×	`cbrt-unprod`
4×	`pow-to-exp` `exp-prod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-*l/` `sqr-pow`
2×	`log-div` `log-prod` `log-pow` `*-commutative`
1×	`cbrt-undiv` `unpow-prod-down` `exp-diff` `exp-sum` `div-inv` `rem-exp-log`

Counts

4 → 92

Calls

4 calls:

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

series318.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
3.0ms	(* (* 2.0 PI) u2)
97.0ms	(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
98.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify46.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	394	637
1	1577	568
2	5001	564

prune200.0ms

Filtered

104 candidates to 66 candidates (36.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	104	8	112

Merged error: 0.0b

Counts

112 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (sqrt (/ 1.0 6.0)) (/ (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)) (sqrt 6.0)))
0.3b	(* (* 2.0 PI) u2)
0.6b	(/ (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)) (sqrt 6.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-exp-log`
28×	`add-sqr-sqrt`
24×	`sqrt-prod`
23×	`add-cbrt-cube`
22×	`times-frac`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`prod-exp`
17×	`associate-l`
14×	`pow1`
13×	`associate-r`
10×	`div-exp`
8×	`cbrt-unprod`
6×	`pow-exp` `associate-/r*`
5×	`pow-prod-down`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `div-inv` `unswap-sqr`
2×	`pow-pow` `sqrt-div` `*-commutative`
1×	`frac-times` `unpow-prod-down` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/l*` `sqr-pow`

Counts

4 → 115

Calls

4 calls:

4.0ms	(pow (* -2.0 (log u1)) 0.5)
14.0ms	(* (sqrt (/ 1.0 6.0)) (/ (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)) (sqrt 6.0)))
5.0ms	(* (* 2.0 PI) u2)
7.0ms	(/ (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)) (sqrt 6.0))

series247.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (* -2.0 (log u1)) 0.5)
106.0ms	(* (sqrt (/ 1.0 6.0)) (/ (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)) (sqrt 6.0)))
3.0ms	(* (* 2.0 PI) u2)
102.0ms	(/ (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)) (sqrt 6.0))

simplify61.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	553	1117
1	2371	1010
2	5001	995

prune244.0ms

Filtered

127 candidates to 78 candidates (38.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	127	8	135

Merged error: 0.0b

Counts

135 → 8

regimes763.0ms

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

sample1.3s

Algorithm

intervals

Results

809.0ms	8000×	body	80	valid
197.0ms	8000×	pre	80	true

Details

sample321.0ms

simplify320.0ms

prune6.0ms

localize20.0ms

rewrite48.0ms

series223.0ms

simplify61.0ms

prune214.0ms

localize19.0ms

rewrite33.0ms

series238.0ms

simplify55.0ms

prune277.0ms

localize21.0ms

rewrite28.0ms

series318.0ms

simplify46.0ms

prune200.0ms

localize22.0ms

rewrite34.0ms

series247.0ms

simplify61.0ms

prune244.0ms

regimes763.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling