Details

analyze789.0ms (14.2%)

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

sample94.0ms (1.7%)

Algorithm

1×

intervals

Results

18.0ms	39×	body	1280	invalid
14.0ms	33×	body	640	valid
13.0ms	29×	body	1280	valid
12.0ms	168×	body	80	valid
11.0ms	36×	body	640	invalid
4.0ms	19×	body	320	invalid
4.0ms	17×	body	320	valid
1.0ms	9×	body	160	valid
1.0ms	12×	body	80	invalid
1.0ms	6×	body	160	invalid

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

prune12.0ms (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: 0.6b

Counts

2 → 2

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite24.0ms (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:

11.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
6.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))
4.0ms	(+ (* a1 a1) (* a2 a2))

series58.0ms (1%)

Counts

3 → 9

Calls

3 calls:

42.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
11.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))
5.0ms	(+ (* a1 a1) (* a2 a2))

simplify67.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4965	1529
1	4965	1529

prune213.0ms (3.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	7	105

Merged error: 0.3b

Counts

105 → 7

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.3b	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
0.3b	(* (cos th) (+ (* a1 a1) (* a2 a2)))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

8.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
6.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
4.0ms	(+ (* a1 a1) (* a2 a2))

series68.0ms (1.2%)

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
26.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
5.0ms	(+ (* a1 a1) (* a2 a2))

simplify49.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4979	870
1	4979	870

prune126.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	71	7	78

Merged error: 0.3b

Counts

78 → 7

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)))
0.4b	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
7.3b	(sqrt (+ (* a1 a1) (* a2 a2)))
7.3b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`sqrt-prod`
72×	`times-frac`
61×	`add-sqr-sqrt`
59×	`add-cube-cbrt` `*-un-lft-identity`
40×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`sqrt-div`
6×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l`
5×	`flip3-+` `associate-*r/` `flip-+`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp` `pow-prod-down`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/` `div-inv` `associate-/l/`
1×	`sqrt-undiv` `frac-2neg` `associate-l` `clear-num` `*-commutative`

Counts

4 → 157

Calls

4 calls:

17.0ms	(* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)))
7.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series63.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)))
11.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4972	2849
1	4972	2849

prune285.0ms (5.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	169	7	176

Merged error: 0.3b

Counts

176 → 7

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (sqrt (+ (* a1 a1) (* a2 a2))))
0.2b	(* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0)))
7.3b	(sqrt (+ (* a1 a1) (* a2 a2)))
7.4b	(sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`sqrt-prod`
31×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-r`
19×	`times-frac`
13×	`pow1`
12×	`sqrt-div`
11×	`add-exp-log` `add-cbrt-cube`
7×	`associate-*r/`
4×	`flip3-+` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+` `add-log-exp`
3×	`rem-sqrt-square`
2×	`frac-times` `sqrt-pow1` `pow1/2` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

14.0ms	(* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0)))
7.0ms	(* (cos th) (sqrt (+ (* a1 a1) (* a2 a2))))
5.0ms	(sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series72.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0)))
23.0ms	(* (cos th) (sqrt (+ (* a1 a1) (* a2 a2))))
9.0ms	(sqrt (/ (+ (* a1 a1) (* a2 a2)) 2.0))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify31.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5399	1691

prune173.0ms (3.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	3	1	4
Picked	0	1	1
Done	0	2	2
Total	113	6	119

Merged error: 0.3b

Counts

119 → 6

regimes340.0ms (6.1%)

Accuracy

Total 0.3b remaining (88.6%)

Threshold costs 0.3b (88.6%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	22
1	16	22

end0.0ms (0%)

sample2.9s (51.6%)

Algorithm

1×

intervals

Results

605.0ms	1333×	body	1280	valid
557.0ms	1236×	body	1280	invalid
355.0ms	4721×	body	80	valid
352.0ms	1115×	body	640	valid
314.0ms	1009×	body	640	invalid
126.0ms	558×	body	320	valid
107.0ms	463×	body	320	invalid
45.0ms	273×	body	160	valid
42.0ms	527×	body	80	invalid
35.0ms	229×	body	160	invalid

Details

analyze789.0ms (14.2%)

sample94.0ms (1.7%)

simplify4.0ms (0.1%)

prune12.0ms (0.2%)

localize11.0ms (0.2%)

rewrite24.0ms (0.4%)

series58.0ms (1%)

simplify67.0ms (1.2%)

prune213.0ms (3.8%)

localize11.0ms (0.2%)

rewrite20.0ms (0.4%)

series68.0ms (1.2%)

simplify49.0ms (0.9%)

prune126.0ms (2.3%)

localize13.0ms (0.2%)

rewrite41.0ms (0.7%)

series63.0ms (1.1%)

simplify73.0ms (1.3%)

prune285.0ms (5.1%)

localize14.0ms (0.2%)

rewrite33.0ms (0.6%)

series72.0ms (1.3%)

simplify31.0ms (0.6%)

prune173.0ms (3.1%)

regimes340.0ms (6.1%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample2.9s (51.6%)

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