Details

sample51.0ms

Algorithm

intervals

Results

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

simplify256.0ms

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

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:

0.0b	(+ (* (* (/ 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)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite33.0ms

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

series243.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
39.0ms	(pow (* -2.0 (log u1)) 0.5)
4.0ms	(* (* 2.0 PI) u2)
119.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify64.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (55.0ms)

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

prune208.0ms

Filtered

99 candidates to 66 candidates (33.3%)

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

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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)
12.0ms	(* (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))

series254.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
107.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
106.0ms	(* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5))

simplify53.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (43.0ms)

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

prune281.0ms

Filtered

124 candidates to 83 candidates (33.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	124	8	132

Merged error: 0b

Counts

132 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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)
5.0ms	(* (* 2.0 PI) u2)
14.0ms	(* (sqrt (/ 1.0 6.0)) (/ (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)) (sqrt 6.0)))
8.0ms	(/ (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)) (sqrt 6.0))

series267.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(pow (* -2.0 (log u1)) 0.5)
4.0ms	(* (* 2.0 PI) u2)
114.0ms	(* (sqrt (/ 1.0 6.0)) (/ (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)) (sqrt 6.0)))
111.0ms	(/ (* (sqrt 1.0) (pow (* -2.0 (log u1)) 0.5)) (sqrt 6.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (49.0ms)

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

prune285.0ms

Filtered

127 candidates to 78 candidates (38.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	127	8	135

Merged error: 0b

Counts

135 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log`
24×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
14×	`associate-l` `add-cbrt-cube`
13×	`prod-exp`
11×	`pow1` `times-frac`
8×	`associate-r`
6×	`log-prod`
5×	`cbrt-unprod`
4×	`log-div` `exp-prod` `div-exp` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`exp-sum` `pow-prod-down` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `exp-diff` `log-pow` `*-commutative` `flip-+`
1×	`cbrt-undiv` `unpow-prod-down` `rem-log-exp` `associate-*l/` `div-inv` `rem-exp-log`

Counts

4 → 90

Calls

4 calls:

8.0ms	(log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
5.0ms	(* (* 2.0 PI) u2)
9.0ms	(exp (log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)))
8.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series290.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))
3.0ms	(* (* 2.0 PI) u2)
81.0ms	(exp (log (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)))
103.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify58.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	509	1091
1	1969	975
2	5001	956

prune217.0ms

Filtered

102 candidates to 71 candidates (30.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	103	7	110

Merged error: 0b

Counts

110 → 7

regimes742.0ms

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

Results

778.0ms	8000×	body	80	valid
178.0ms	8000×	pre	80	true

Details

sample51.0ms

simplify256.0ms

prune6.0ms

localize20.0ms

rewrite33.0ms

series243.0ms

simplify64.0ms

prune208.0ms

localize21.0ms

rewrite34.0ms

series254.0ms

simplify53.0ms

prune281.0ms

localize26.0ms

rewrite35.0ms

series267.0ms

simplify60.0ms

prune285.0ms

localize22.0ms

rewrite34.0ms

series290.0ms

simplify58.0ms

prune217.0ms

regimes742.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

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