Details

sample331.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify64.0ms

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

prune7.0ms

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: 0.3b

Counts

2 → 1

localize42.0ms

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

rewrite31.0ms

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))

series230.0ms

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)
34.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)
113.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify59.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (50.0ms)

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

prune545.0ms

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

localize20.0ms

Local error

Found 4 expressions with local error:

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

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)
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))

series239.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (* -2.0 (log u1)) 0.5)
101.0ms	(* (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))

simplify54.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (44.0ms)

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

prune852.0ms

Filtered

124 candidates to 83 candidates (33.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	126	8	134

Merged error: 0.0b

Counts

134 → 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)))
0.3b	(* (* 2.0 PI) u2)
0.3b	(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite26.0ms

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:

121.0ms	(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))))
97.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify43.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (36.0ms)

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

prune638.0ms

Filtered

104 candidates to 67 candidates (35.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	5	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:

0.3b	(* (* 2.0 PI) u2)
0.3b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
0.6b	(cbrt (pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3))
0.7b	(pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3)

rewrite28.0ms

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))
7.0ms	(pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3)

series307.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) u2)
96.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
96.0ms	(cbrt (pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3))
111.0ms	(pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3)

simplify57.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	474	787
1	1975	743
2	5001	738

prune700.0ms

Filtered

119 candidates to 74 candidates (37.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	119	8	127

Merged error: 0.0b

Counts

127 → 8

regimes875.0ms

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

771.0ms	8000×	body	80	valid
178.0ms	8000×	pre	80	true

Details

sample331.0ms

simplify64.0ms

prune7.0ms

localize42.0ms

rewrite31.0ms

series230.0ms

simplify59.0ms

prune545.0ms

localize20.0ms

rewrite35.0ms

series239.0ms

simplify54.0ms

prune852.0ms

localize22.0ms

rewrite26.0ms

series318.0ms

simplify43.0ms

prune638.0ms

localize22.0ms

rewrite28.0ms

series307.0ms

simplify57.0ms

prune700.0ms

regimes875.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

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