Details

analyze811.0ms (13.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

sample100.0ms (1.6%)

Algorithm

1×

intervals

Results

18.0ms	40×	body	1280	invalid
17.0ms	38×	body	1280	valid
15.0ms	154×	body	80	valid
12.0ms	36×	body	640	valid
11.0ms	33×	body	640	invalid
5.0ms	20×	body	320	valid
4.0ms	17×	body	320	invalid
1.0ms	17×	body	80	invalid
1.0ms	8×	body	160	invalid
1.0ms	8×	body	160	valid

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	105	13
1	105	13

prune13.0ms (0.2%)

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

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
0.4b	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
32×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-r` `sqrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1` `add-log-exp`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

3 → 94

Calls

3 calls:

13.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
7.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))
4.0ms	(+ (* a1 a1) (* a2 a2))

series52.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

35.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
11.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))
6.0ms	(+ (* a1 a1) (* a2 a2))

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4965	1529
1	4965	1529

prune227.0ms (3.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Merged error: 0.0b

Counts

105 → 8

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* (cos th) (+ (* (/ a1 (sqrt 2.0)) a1) (* (/ a2 (sqrt 2.0)) a2)))
0.2b	(* (/ a2 (sqrt 2.0)) a2)
0.4b	(/ a2 (sqrt 2.0))
0.5b	(/ a1 (sqrt 2.0))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
56×	`times-frac`
50×	`add-cube-cbrt` `*-un-lft-identity`
34×	`sqrt-prod`
25×	`associate-l`
15×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
8×	`pow1`
6×	`associate-r` `associate-/l*`
4×	`add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `div-inv`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `frac-add` `flip-+`

Counts

4 → 143

Calls

4 calls:

10.0ms	(* (cos th) (+ (* (/ a1 (sqrt 2.0)) a1) (* (/ a2 (sqrt 2.0)) a2)))
8.0ms	(* (/ a2 (sqrt 2.0)) a2)
4.0ms	(/ a1 (sqrt 2.0))
4.0ms	(/ a2 (sqrt 2.0))

series57.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos th) (+ (* (/ a1 (sqrt 2.0)) a1) (* (/ a2 (sqrt 2.0)) a2)))
6.0ms	(* (/ a2 (sqrt 2.0)) a2)
5.0ms	(/ a1 (sqrt 2.0))
5.0ms	(/ a2 (sqrt 2.0))

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4959	1377
1	4959	1377

prune350.0ms (5.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	157	6	163

Merged error: 0.0b

Counts

163 → 6

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* a1 (* (/ a1 (sqrt 2.0)) (cos th)))
0.2b	(* (/ a2 (sqrt 2.0)) (cos th))
0.4b	(/ a2 (sqrt 2.0))
0.5b	(/ a1 (sqrt 2.0))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
56×	`times-frac`
49×	`add-cube-cbrt` `*-un-lft-identity`
34×	`sqrt-prod`
25×	`associate-l`
22×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*`
4×	`cbrt-undiv` `div-exp` `associate-r` `pow-prod-down` `add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`associate-*r/`

Counts

4 → 141

Calls

4 calls:

8.0ms	(* (/ a2 (sqrt 2.0)) (cos th))
8.0ms	(* a1 (* (/ a1 (sqrt 2.0)) (cos th)))
4.0ms	(/ a1 (sqrt 2.0))
4.0ms	(/ a2 (sqrt 2.0))

series37.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (/ a2 (sqrt 2.0)) (cos th))
11.0ms	(* a1 (* (/ a1 (sqrt 2.0)) (cos th)))
5.0ms	(/ a1 (sqrt 2.0))
5.0ms	(/ a2 (sqrt 2.0))

simplify62.0ms (1%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4984	1282
1	4984	1282

prune345.0ms (5.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	152	7	159

Merged error: 0b

Counts

159 → 7

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(* a2 (* (/ a2 (sqrt 2.0)) (cos th)))
0.2b	(* (/ a2 (sqrt 2.0)) (cos th))
0.2b	(/ (* a1 (* a1 (cos th))) (sqrt 2.0))
0.4b	(/ a2 (sqrt 2.0))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
44×	`times-frac`
38×	`add-cube-cbrt` `*-un-lft-identity`
29×	`add-exp-log` `add-cbrt-cube`
28×	`sqrt-prod`
25×	`associate-l`
12×	`associate-/r*`
11×	`pow1`
10×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
4×	`associate-r` `pow-prod-down` `associate-/l*` `add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`associate-*r/`

Counts

4 → 131

Calls

4 calls:

8.0ms	(* (/ a2 (sqrt 2.0)) (cos th))
7.0ms	(* a2 (* (/ a2 (sqrt 2.0)) (cos th)))
7.0ms	(/ (* a1 (* a1 (cos th))) (sqrt 2.0))
4.0ms	(/ a2 (sqrt 2.0))

series43.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ (* a1 (* a1 (cos th))) (sqrt 2.0))
12.0ms	(* (/ a2 (sqrt 2.0)) (cos th))
12.0ms	(* a2 (* (/ a2 (sqrt 2.0)) (cos th)))
5.0ms	(/ a2 (sqrt 2.0))

simplify49.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5094	1298

prune283.0ms (4.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	143	7	150

Merged error: 0b

Counts

150 → 7

regimes528.0ms (8.5%)

Accuracy

Total 0.4b remaining (94.8%)

Threshold costs 0.4b (94.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	19
1	18	19

end0.0ms (0%)

sample2.9s (47.3%)

Algorithm

1×

intervals

Results

612.0ms	1314×	body	1280	valid
539.0ms	1144×	body	1280	invalid
368.0ms	1136×	body	640	valid
364.0ms	4722×	body	80	valid
333.0ms	989×	body	640	invalid
137.0ms	559×	body	320	valid
120.0ms	495×	body	320	invalid
48.0ms	527×	body	80	invalid
43.0ms	269×	body	160	valid
38.0ms	238×	body	160	invalid

Details

analyze811.0ms (13.1%)

sample100.0ms (1.6%)

simplify4.0ms (0.1%)

prune13.0ms (0.2%)

localize11.0ms (0.2%)

rewrite27.0ms (0.4%)

series52.0ms (0.8%)

simplify63.0ms (1%)

prune227.0ms (3.7%)

localize15.0ms (0.2%)

rewrite30.0ms (0.5%)

series57.0ms (0.9%)

simplify67.0ms (1.1%)

prune350.0ms (5.7%)

localize14.0ms (0.2%)

rewrite28.0ms (0.5%)

series37.0ms (0.6%)

simplify62.0ms (1%)

prune345.0ms (5.6%)

localize14.0ms (0.2%)

rewrite31.0ms (0.5%)

series43.0ms (0.7%)

simplify49.0ms (0.8%)

prune283.0ms (4.6%)

regimes528.0ms (8.5%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample2.9s (47.3%)

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