Details

sample333.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify67.0ms

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

localize40.0ms

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))

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:

10.0ms	(+ (* (* (/ 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))

series1.7s

Counts

4 → 12

Calls

4 calls:

558.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
299.0ms	(pow (* -2.0 (log u1)) 0.5)
46.0ms	(* (* 2.0 PI) u2)
823.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify61.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	507	728
1	2155	656
2	5001	656

prune611.0ms

Filtered

99 candidates to 71 candidates (28.3%)

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

localize23.0ms

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))

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))

series2.0s

Counts

4 → 12

Calls

4 calls:

306.0ms	(pow (* -2.0 (log u1)) 0.5)
861.0ms	(* (sqrt (/ 1.0 6.0)) (* (sqrt (/ 1.0 6.0)) (pow (* -2.0 (log u1)) 0.5)))
38.0ms	(* (* 2.0 PI) u2)
830.0ms	(* (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	447	924
1	1791	827
2	5002	823

prune964.0ms

Filtered

124 candidates to 89 candidates (28.2%)

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

localize25.0ms

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))

series2.8s

Counts

4 → 12

Calls

4 calls:

1.1s	(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))
38.0ms	(* (* 2.0 PI) u2)
825.0ms	(exp (log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
812.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify49.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	396	631
1	1598	565
2	5001	564

prune720.0ms

Filtered

104 candidates to 71 candidates (31.7%)

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

localize21.0ms

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)

rewrite27.0ms

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))
8.0ms	(pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3)

series2.6s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (* 2.0 PI) u2)
827.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
819.0ms	(cbrt (pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3))
923.0ms	(pow (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) 3)

simplify60.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	483	777
1	2025	738
2	5002	736

prune884.0ms

Filtered

119 candidates to 80 candidates (32.8%)

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

regimes840.0ms

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

776.0ms	8000×	body	80	valid
176.0ms	8000×	pre	80	true

Details

sample333.0ms

simplify67.0ms

prune7.0ms

localize40.0ms

rewrite33.0ms

series1.7s

simplify61.0ms

prune611.0ms

localize23.0ms

rewrite33.0ms

series2.0s

simplify53.0ms

prune964.0ms

localize25.0ms

rewrite26.0ms

series2.8s

simplify49.0ms

prune720.0ms

localize21.0ms

rewrite27.0ms

series2.6s

simplify60.0ms

prune884.0ms

regimes840.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling