Details

analyze311.0ms (5.9%)

Algorithm

1×

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

sample48.0ms (0.9%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify481.0ms (9.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4872	19
1	4872	19

prune14.0ms (0.3%)

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 → 2

localize29.0ms (0.5%)

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

rewrite31.0ms (0.6%)

Algorithm

1×	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))
9.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
4.0ms	(* (* 2.0 PI) u2)
4.0ms	(pow (* -2.0 (log u1)) 0.5)

series228.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
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)

simplify49.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4949	1174
1	4949	1174

prune274.0ms (5.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	90	9	99
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	92	9	101

Merged error: 0.0b

Counts

101 → 9

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 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)
0.3b	(* (* 2.0 PI) u2)
0.3b	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)

rewrite26.0ms (0.5%)

Algorithm

1×	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:

9.0ms	(+ (* (* 1.0 (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (cos (* (* 2.0 PI) u2))) 0.5)
6.0ms	(* (* 2.0 PI) u2)
4.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
4.0ms	(pow (* -2.0 (log u1)) 0.5)

series216.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
79.0ms	(+ (* (* 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)
3.0ms	(* (* 2.0 PI) u2)

simplify52.0ms (1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4979	1158
1	4979	1158

prune253.0ms (4.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Merged error: 0b

Counts

105 → 8

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite33.0ms (0.6%)

Algorithm

1×	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:

11.0ms	(* (sqrt (/ 1.0 6.0)) (* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ 1.0 6.0))))
9.0ms	(* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ 1.0 6.0)))
5.0ms	(* (* 2.0 PI) u2)
4.0ms	(pow (* -2.0 (log u1)) 0.5)

series244.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ 1.0 6.0)))
102.0ms	(* (sqrt (/ 1.0 6.0)) (* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ 1.0 6.0))))
36.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)

simplify36.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5090	1398

prune391.0ms (7.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	125	7	132

Merged error: 0b

Counts

132 → 7

localize18.0ms (0.3%)

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))
0.3b	(* (* 2.0 PI) u2)
0.3b	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))

rewrite29.0ms (0.6%)

Algorithm

1×	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:

7.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
6.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
4.0ms	(* (* 2.0 PI) u2)
4.0ms	(pow (* -2.0 (log u1)) 0.5)

series250.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
99.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
35.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4944	2530
1	4944	2530

prune547.0ms (10.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	194	7	201

Merged error: 0b

Counts

201 → 7

regimes430.0ms (8.2%)

Accuracy

Total 0.3b remaining (94.4%)

Threshold costs 0.3b (94.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	21
1	27	21

end0.0ms (0%)

sample1.1s (21.7%)

Algorithm

1×

intervals

Results

785.0ms	8000×	body	80	valid
190.0ms	8000×	pre	80	true

Details

analyze311.0ms (5.9%)

sample48.0ms (0.9%)

simplify481.0ms (9.2%)

prune14.0ms (0.3%)

localize29.0ms (0.5%)

rewrite31.0ms (0.6%)

series228.0ms (4.4%)

simplify49.0ms (0.9%)

prune274.0ms (5.2%)

localize17.0ms (0.3%)

rewrite26.0ms (0.5%)

series216.0ms (4.1%)

simplify52.0ms (1%)

prune253.0ms (4.8%)

localize23.0ms (0.4%)

rewrite33.0ms (0.6%)

series244.0ms (4.7%)

simplify36.0ms (0.7%)

prune391.0ms (7.5%)

localize18.0ms (0.3%)

rewrite29.0ms (0.6%)

series250.0ms (4.8%)

simplify70.0ms (1.3%)

prune547.0ms (10.4%)

regimes430.0ms (8.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.1s (21.7%)

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