Details

analyze307.0ms (6.1%)

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 (1%)

Algorithm

1×

intervals

Results

29.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify506.0ms (10%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

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

localize28.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(+ 0.5 (* 1.0 (* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))))
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* PI u2)
0.4b	(* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log`
25×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`prod-exp`
11×	`times-frac` `add-cbrt-cube`
9×	`pow1`
8×	`associate-l`
6×	`pow-exp` `add-log-exp`
5×	`unswap-sqr`
4×	`div-exp` `sqr-pow`
3×	`pow-to-exp` `pow-unpow` `cbrt-unprod`
2×	`unpow-prod-down` `pow-pow` `pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `associate-*r/` `sum-log` `flip-+` `div-inv`

Counts

4 → 87

Calls

4 calls:

11.0ms	(* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))
4.0ms	(+ 0.5 (* 1.0 (* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))))
4.0ms	(pow (* -2.0 (log u1)) 0.5)
3.0ms	(* PI u2)

series206.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))
79.0ms	(+ 0.5 (* 1.0 (* (pow (* -2.0 (log u1)) 0.5) (/ (cos (* 2.0 (* PI u2))) 6.0))))
35.0ms	(pow (* -2.0 (log u1)) 0.5)
2.0ms	(* PI u2)

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4957	1396
1	4957	1396

prune281.0ms (5.6%)

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

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+ 0.5 (* 1.0 (/ (* (cos (* 2.0 (* PI u2))) (pow (* -2.0 (log u1)) 0.5)) 6.0)))
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* PI u2)
0.3b	(/ (* (cos (* 2.0 (* PI u2))) (pow (* -2.0 (log u1)) 0.5)) 6.0)

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-exp-log`
11×	`add-sqr-sqrt` `add-cbrt-cube`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
7×	`prod-exp`
6×	`add-log-exp`
5×	`div-exp`
4×	`pow-exp`
3×	`pow-unpow` `times-frac` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow` `pow-prod-down` `cbrt-unprod`
1×	`+-commutative` `unpow-prod-down` `frac-2neg` `flip3-+` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `associate-/l` `unswap-sqr` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

7.0ms	(/ (* (cos (* 2.0 (* PI u2))) (pow (* -2.0 (log u1)) 0.5)) 6.0)
4.0ms	(+ 0.5 (* 1.0 (/ (* (cos (* 2.0 (* PI u2))) (pow (* -2.0 (log u1)) 0.5)) 6.0)))
4.0ms	(pow (* -2.0 (log u1)) 0.5)
4.0ms	(* PI u2)

series182.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ 0.5 (* 1.0 (/ (* (cos (* 2.0 (* PI u2))) (pow (* -2.0 (log u1)) 0.5)) 6.0)))
71.0ms	(/ (* (cos (* 2.0 (* PI u2))) (pow (* -2.0 (log u1)) 0.5)) 6.0)
36.0ms	(pow (* -2.0 (log u1)) 0.5)
2.0ms	(* PI u2)

simplify50.0ms (1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4968	1043
1	4968	1043

prune211.0ms (4.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	83	8	91

Merged error: 0b

Counts

91 → 8

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`associate-r`
30×	`add-exp-log` `sqrt-prod`
25×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
17×	`prod-exp`
15×	`add-cbrt-cube`
12×	`associate-l`
10×	`pow1`
8×	`unswap-sqr`
6×	`cbrt-unprod`
5×	`sqrt-div`
4×	`associate-r/` `pow-exp` `-commutative` `add-log-exp` `sqr-pow`
3×	`pow-prod-down`
2×	`pow-to-exp` `div-inv`
1×	`frac-times` `unpow-prod-down` `associate-*l/`

Counts

4 → 113

Calls

4 calls:

13.0ms	(* (* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ (cos (* 2.0 (* PI u2))) 6.0))) (sqrt (/ (cos (* 2.0 (* PI u2))) 6.0)))
10.0ms	(* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ (cos (* 2.0 (* PI u2))) 6.0)))
4.0ms	(* PI u2)
4.0ms	(* PI u2)

series166.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ (cos (* 2.0 (* PI u2))) 6.0)))
79.0ms	(* (* (pow (* -2.0 (log u1)) 0.5) (sqrt (/ (cos (* 2.0 (* PI u2))) 6.0))) (sqrt (/ (cos (* 2.0 (* PI u2))) 6.0)))
2.0ms	(* PI u2)
2.0ms	(* PI u2)

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4976	1843
1	4976	1843

prune428.0ms (8.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	125	8	133

Merged error: 0b

Counts

133 → 8

localize17.0ms (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	(* PI u2)
0.3b	(/ (cos (* 2.0 (* PI u2))) (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`times-frac`
75×	`add-sqr-sqrt`
73×	`add-cube-cbrt` `*-un-lft-identity`
31×	`add-exp-log`
24×	`associate-/r*`
17×	`unpow-prod-down` `sqr-pow`
13×	`div-exp` `add-cbrt-cube`
9×	`pow1`
6×	`pow-exp` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `prod-exp` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `associate-r` `associate-l`
2×	`pow-pow` `frac-2neg` `pow-prod-down` `clear-num`
1×	`associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 170

Calls

4 calls:

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

series223.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
67.0ms	(/ (cos (* 2.0 (* PI u2))) (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
35.0ms	(pow (* -2.0 (log u1)) 0.5)
2.0ms	(* PI u2)

simplify83.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4941	3391
1	4941	3391

prune526.0ms (10.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	182	8	190

Merged error: 0b

Counts

190 → 8

regimes359.0ms (7.1%)

Accuracy

Total 0.4b remaining (95.2%)

Threshold costs 0.4b (95.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	30
1	27	30

end0.0ms (0%)

sample1.1s (22.4%)

Algorithm

1×

intervals

Results

777.0ms	8000×	body	80	valid
196.0ms	8000×	pre	80	true

Details

analyze307.0ms (6.1%)

sample48.0ms (1%)

simplify506.0ms (10%)

prune14.0ms (0.3%)

localize28.0ms (0.6%)

rewrite26.0ms (0.5%)

series206.0ms (4.1%)

simplify76.0ms (1.5%)

prune281.0ms (5.6%)

localize18.0ms (0.3%)

rewrite21.0ms (0.4%)

series182.0ms (3.6%)

simplify50.0ms (1%)

prune211.0ms (4.2%)

localize20.0ms (0.4%)

rewrite34.0ms (0.7%)

series166.0ms (3.3%)

simplify54.0ms (1.1%)

prune428.0ms (8.5%)

localize17.0ms (0.3%)

rewrite30.0ms (0.6%)

series223.0ms (4.4%)

simplify83.0ms (1.6%)

prune526.0ms (10.4%)

regimes359.0ms (7.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.1s (22.4%)

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