Details

analyze673.0ms (15.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

sample58.0ms (1.3%)

Algorithm

1×

intervals

Results

24.0ms	63×	body	1280	valid
14.0ms	60×	body	640	valid
5.0ms	93×	body	80	valid
3.0ms	21×	body	320	valid
2.0ms	19×	body	160	valid
0.0ms	1×	body	80	invalid

simplify495.0ms (11.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5131	12

prune10.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 40.1b

Counts

2 → 1

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
0.0b	(pow (exp x) 2.0)
5.3b	(- (pow (exp x) 2.0) 1.0)
5.4b	(- (exp x) 1.0)

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
35×	`times-frac`
30×	`difference-of-squares`
21×	`add-cube-cbrt`
16×	`distribute-lft-out--`
10×	`unpow-prod-down`
8×	`add-log-exp` `sqr-pow`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*`
4×	`flip3--` `pow-pow` `flip--`
3×	`pow-unpow` `exp-prod`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `div-sub` `div-exp` `pow-exp` `clear-num` `div-inv`

Counts

4 → 112

Calls

4 calls:

11.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
6.0ms	(- (exp x) 1.0)
5.0ms	(- (pow (exp x) 2.0) 1.0)
3.0ms	(pow (exp x) 2.0)

series54.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (pow (exp x) 2.0) 1.0)
15.0ms	(pow (exp x) 2.0)
10.0ms	(- (exp x) 1.0)
10.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))

simplify91.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4908	1696
1	4908	1696

prune278.0ms (6.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	2	125

Merged error: 0.0b

Counts

125 → 2

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+ x (+ 2 (* x (* x 1/2))))
9.9b	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `sqrt-prod`
3×	`pow1` `add-cube-cbrt` `sum-log`
2×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `associate-+r+` `sqrt-pow1` `pow1/2`

Counts

2 → 30

Calls

2 calls:

5.0ms	(+ x (+ 2 (* x (* x 1/2))))
5.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

series8.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

5.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))
2.0ms	(+ x (+ 2 (* x (* x 1/2))))

simplify39.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5225	486

prune69.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	35	3	38

Merged error: 0b

Counts

38 → 3

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ x (+ 2 (* x (* x 1/2))))))
0.8b	(* (sqrt (sqrt (+ x (+ 2 (* x (* x 1/2)))))) (sqrt (sqrt (+ x (+ 2 (* x (* x 1/2)))))))
9.9b	(sqrt (+ x (+ 2 (* x (* x 1/2)))))
9.9b	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`sqrt-prod`
54×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
38×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
20×	`add-cube-cbrt` `pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `pow-prod-up` `flip-+` `distribute-lft-out` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 142

Calls

4 calls:

17.0ms	(* (sqrt (sqrt (+ x (+ 2 (* x (* x 1/2)))))) (sqrt (sqrt (+ x (+ 2 (* x (* x 1/2)))))))
8.0ms	(sqrt (sqrt (+ x (+ 2 (* x (* x 1/2))))))
5.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))
4.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

series21.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (sqrt (+ x (+ 2 (* x (* x 1/2))))))
5.0ms	(* (sqrt (sqrt (+ x (+ 2 (* x (* x 1/2)))))) (sqrt (sqrt (+ x (+ 2 (* x (* x 1/2)))))))
5.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))
4.0ms	(sqrt (+ x (+ 2 (* x (* x 1/2)))))

simplify114.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5225	2308

prune374.0ms (8.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	154	3	157

Merged error: 0b

Counts

157 → 3

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2.0)
0.0b	(pow (exp x) 2)
5.3b	(- (pow (exp x) 2.0) 1.0)
5.3b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `pow-pow` `add-log-exp`
7×	`difference-of-squares`
6×	`pow1` `pow-unpow` `exp-prod`
4×	`add-exp-log` `add-cbrt-cube` `sqr-pow`
2×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `flip--` `unpow2`
1×	`distribute-lft-out--`

Counts

4 → 71

Calls

4 calls:

5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
5.0ms	(- (pow (exp x) 2.0) 1.0)
3.0ms	(pow (exp x) 2)
3.0ms	(pow (exp x) 2.0)

series25.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(pow (exp x) 2.0)
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
4.0ms	(- (pow (exp x) 2.0) 1.0)
3.0ms	(pow (exp x) 2)

simplify28.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4908	612
1	4908	612

prune179.0ms (4.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	83	3	86

Merged error: 0b

Counts

86 → 3

regimes39.0ms (0.9%)

Accuracy

Total 0.2b remaining (87.9%)

Threshold costs 0.2b (87.9%)

bsearch21.0ms (0.5%)

Steps

Iters	Range		Point
10	-0.0130322730991205	-2.77060252745321e-13	-1.4142710662085361e-05

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	35
1	48	35

end0.0ms (0%)

sample1.7s (38%)

Algorithm

1×

intervals

Results

844.0ms	2329×	body	1280	valid
387.0ms	1642×	body	640	valid
125.0ms	839×	body	320	valid
124.0ms	2770×	body	80	valid
42.0ms	420×	body	160	valid
0.0ms	3×	body	80	invalid

Details

analyze673.0ms (15.3%)

sample58.0ms (1.3%)

simplify495.0ms (11.3%)

prune10.0ms (0.2%)

localize10.0ms (0.2%)

rewrite32.0ms (0.7%)

series54.0ms (1.2%)

simplify91.0ms (2.1%)

prune278.0ms (6.3%)

localize7.0ms (0.2%)

rewrite10.0ms (0.2%)

series8.0ms (0.2%)

simplify39.0ms (0.9%)

prune69.0ms (1.6%)

localize9.0ms (0.2%)

rewrite40.0ms (0.9%)

series21.0ms (0.5%)

simplify114.0ms (2.6%)

prune374.0ms (8.5%)

localize15.0ms (0.3%)

rewrite19.0ms (0.4%)

series25.0ms (0.6%)

simplify28.0ms (0.6%)

prune179.0ms (4.1%)

regimes39.0ms (0.9%)

bsearch21.0ms (0.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.7s (38%)

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