Details

analyze322.0ms

Algorithm

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
0%	6.2%	93.8%	3
3.1%	3.1%	93.8%	4
3.1%	3.1%	93.8%	5
4.7%	1.6%	93.8%	6
4.7%	1.6%	93.8%	7
5.5%	0.8%	93.8%	8
5.5%	0.8%	93.8%	9
5.8%	0.4%	93.8%	10
5.8%	0.4%	93.8%	11
6%	0.2%	93.8%	12
6%	0.2%	93.8%	13
6.1%	0.1%	93.8%	14

sample50.0ms

Algorithm

intervals

Results

31.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify498.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4872	19
1	4872	19

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.4b

Counts

2 → 1

localize29.0ms

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)
0.2b	(* (* 2.0 PI) u2)
0.4b	(* (/ 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)
9.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series227.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+ (* (* (/ 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)
108.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify50.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4949	1174
1	4949	1174

prune210.0ms

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: 0.0b

Counts

100 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

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:

11.0ms	(+ (* (* 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	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
5.0ms	(* (* 2.0 PI) u2)

series215.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
35.0ms	(pow (* -2.0 (log u1)) 0.5)
96.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
3.0ms	(* (* 2.0 PI) u2)

simplify50.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4979	1158
1	4979	1158

prune194.0ms

Filtered

66 candidates to 96 candidates (-45.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Merged error: 0.0b

Counts

105 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log` `add-sqr-sqrt`
30×	`sqrt-prod`
23×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-l`
20×	`times-frac` `associate-r`
19×	`prod-exp`
16×	`add-cbrt-cube`
14×	`pow1`
7×	`cbrt-unprod`
6×	`pow-exp` `unswap-sqr`
5×	`sqrt-div` `pow-prod-down` `sqr-pow`
4×	`associate-*r/` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `*-commutative`
2×	`unpow-prod-down` `pow-pow` `div-inv`
1×	`frac-times` `associate-*l/`

Counts

4 → 112

Calls

4 calls:

4.0ms	(pow (* -2.0 (log u1)) 0.5)
12.0ms	(* (sqrt (/ 1.0 6.0)) (* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ 1.0 6.0))))
5.0ms	(* (* 2.0 PI) u2)
10.0ms	(* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ 1.0 6.0)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (* -2.0 (log u1)) 0.5)
100.0ms	(* (sqrt (/ 1.0 6.0)) (* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ 1.0 6.0))))
3.0ms	(* (* 2.0 PI) u2)
102.0ms	(* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ 1.0 6.0)))

simplify36.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5090	1398

prune269.0ms

Filtered

82 candidates to 124 candidates (-51.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	124	8	132

Merged error: 0.0b

Counts

132 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
0.2b	(* (* 2.0 PI) u2)
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	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
5.0ms	(* (* 2.0 PI) u2)
7.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (* -2.0 (log u1)) 0.5)
111.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
3.0ms	(* (* 2.0 PI) u2)
96.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))

simplify69.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4944	2530
1	4944	2530

prune332.0ms

Filtered

119 candidates to 194 candidates (-63.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	194	8	202

Merged error: 0.0b

Counts

202 → 8

regimes467.0ms

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	25
1	27	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

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

Details

analyze322.0ms

sample50.0ms

simplify498.0ms

prune9.0ms

localize29.0ms

rewrite31.0ms

series227.0ms

simplify50.0ms

prune210.0ms

localize18.0ms

rewrite26.0ms

series215.0ms

simplify50.0ms

prune194.0ms

localize25.0ms

rewrite34.0ms

series241.0ms

simplify36.0ms

prune269.0ms

localize22.0ms

rewrite27.0ms

series246.0ms

simplify69.0ms

prune332.0ms

regimes467.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling