Details

analyze310.0ms (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

simplify508.0ms (9.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4872	19
1	4872	19

prune9.0ms (0.2%)

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

localize19.0ms (0.4%)

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))

rewrite38.0ms (0.7%)

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:

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

series222.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
78.0ms	(+ (* (* (/ 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)

simplify50.0ms (1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4949	1174
1	4949	1174

prune282.0ms (5.4%)

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

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

series212.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (pow (* -2.0 (log u1)) 0.5) 6.0)
78.0ms	(+ (* (* 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)

simplify54.0ms (1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4979	1158
1	4979	1158

prune261.0ms (5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	96	9	105

Merged error: 0b

Counts

105 → 9

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.2b	(* (* 2.0 PI) u2)
0.2b	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
0.3b	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))

rewrite28.0ms (0.5%)

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

series248.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
95.0ms	(/ 1 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
36.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* (* 2.0 PI) u2)

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4944	2530
1	4944	2530

prune574.0ms (11%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	195	8	203

Merged error: 0b

Counts

203 → 8

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-exp-log`
23×	`prod-exp`
22×	`add-sqr-sqrt`
16×	`associate-r`
14×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
11×	`pow1` `times-frac`
9×	`rem-log-exp`
8×	`div-exp` `pow-exp`
6×	`associate-l`
5×	`cbrt-unprod`
4×	`pow-to-exp` `exp-prod` `add-log-exp` `unswap-sqr`
3×	`associate-*r/` `pow-prod-down` `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:

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

series314.0ms (6%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(log (* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0)))
97.0ms	(* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0))
95.0ms	(exp (log (* (pow (* -2.0 (log u1)) 0.5) (/ 1.0 6.0))))
3.0ms	(* (* 2.0 PI) u2)

simplify36.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5367	1026

prune274.0ms (5.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	104	8	112

Merged error: 0b

Counts

112 → 8

regimes448.0ms (8.5%)

Accuracy

Total 0.3b remaining (96.1%)

Threshold costs 0.3b (96.1%)

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

780.0ms	8000×	body	80	valid
193.0ms	8000×	pre	80	true

Details

analyze310.0ms (5.9%)

sample48.0ms (0.9%)

simplify508.0ms (9.7%)

prune9.0ms (0.2%)

localize19.0ms (0.4%)

rewrite38.0ms (0.7%)

series222.0ms (4.2%)

simplify50.0ms (1%)

prune282.0ms (5.4%)

localize17.0ms (0.3%)

rewrite26.0ms (0.5%)

series212.0ms (4.1%)

simplify54.0ms (1%)

prune261.0ms (5%)

localize18.0ms (0.4%)

rewrite28.0ms (0.5%)

series248.0ms (4.7%)

simplify63.0ms (1.2%)

prune574.0ms (11%)

localize21.0ms (0.4%)

rewrite26.0ms (0.5%)

series314.0ms (6%)

simplify36.0ms (0.7%)

prune274.0ms (5.2%)

regimes448.0ms (8.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.1s (21.7%)

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