Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

sample17.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

valid

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	90	6
1	90	6

prune5.0ms (0.1%)

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: 0.0b

Counts

2 → 1

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt (- 1.0 (* x x)))
0.0b	(- 1.0 (* x x))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`sqrt-prod` `add-log-exp`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
2×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

2 → 28

Calls

2 calls:

3.0ms	(- 1.0 (* x x))
3.0ms	(sqrt (- 1.0 (* x x)))

series8.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

4.0ms	(sqrt (- 1.0 (* x x)))
4.0ms	(- 1.0 (* x x))

simplify39.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4986	310
1	4986	310

prune59.0ms (1.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	1	35

Merged error: 0.0b

Counts

35 → 1

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(- (pow 1.0 3) (pow x 6))
0.0b	(/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* 1.0 (+ 1.0 (* x x)))))
0.0b	(sqrt (/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* 1.0 (+ 1.0 (* x x))))))

rewrite53.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

183×	`add-sqr-sqrt`
97×	`times-frac`
96×	`difference-of-squares`
60×	`*-un-lft-identity`
56×	`unpow-prod-down` `sqr-pow`
54×	`sqrt-prod`
44×	`add-cube-cbrt`
24×	`cube-prod`
16×	`associate-/l*`
8×	`distribute-lft-out--`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r/`
3×	`associate-/r*`
2×	`rem-sqrt-square` `flip3--` `flip3-+` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `div-sub` `div-exp` `clear-num`

Counts

3 → 174

Calls

3 calls:

18.0ms	(/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* 1.0 (+ 1.0 (* x x)))))
16.0ms	(sqrt (/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* 1.0 (+ 1.0 (* x x))))))
9.0ms	(- (pow 1.0 3) (pow x 6))

series34.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

14.0ms	(/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* 1.0 (+ 1.0 (* x x)))))
10.0ms	(- (pow 1.0 3) (pow x 6))
9.0ms	(sqrt (/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* 1.0 (+ 1.0 (* x x))))))

simplify87.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4944	5609
1	4944	5609

prune700.0ms (19.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	182	2	184

Merged error: 0b

Counts

184 → 2

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(- (pow 1.0 3) (pow x 6))
0.0b	(/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* 1.0 (+ 1.0 (* x x)))))
0.0b	(sqrt (/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* 1.0 (+ 1.0 (* x x))))))
0.0b	(pow (sqrt (/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* 1.0 (+ 1.0 (* x x)))))) 3)

rewrite84.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

329×	`add-sqr-sqrt`
193×	`times-frac`
168×	`difference-of-squares`
162×	`sqrt-prod`
155×	`unpow-prod-down`
116×	`*-un-lft-identity`
99×	`cube-prod` `sqr-pow`
88×	`add-cube-cbrt`
16×	`associate-/l*`
14×	`distribute-lft-out--`
8×	`associate-/r/`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`flip3-+` `flip-+` `div-inv`
3×	`pow-unpow` `pow-pow` `associate-/r*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `sqrt-div` `flip--` `associate-/l/`
1×	`cbrt-undiv` `cube-div` `cube-mult` `pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sqrt-pow2` `rem-cube-cbrt`

Counts

4 → 309

Calls

4 calls:

22.0ms	(pow (sqrt (/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* 1.0 (+ 1.0 (* x x)))))) 3)
16.0ms	(sqrt (/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* 1.0 (+ 1.0 (* x x))))))
15.0ms	(/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* 1.0 (+ 1.0 (* x x)))))
9.0ms	(- (pow 1.0 3) (pow x 6))

series45.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* 1.0 (+ 1.0 (* x x)))))
12.0ms	(pow (sqrt (/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* 1.0 (+ 1.0 (* x x)))))) 3)
10.0ms	(- (pow 1.0 3) (pow x 6))
9.0ms	(sqrt (/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* 1.0 (+ 1.0 (* x x))))))

simplify131.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5036	11161

prune1.9s (54.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	321	0	321
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	321	2	323

Merged error: 0b

Counts

323 → 2

regimes26.0ms (0.7%)

Accuracy

Total 0.0b remaining (25%)

Threshold costs 0.0b (25%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	20
1	28	20

end0.0ms (0%)

sample296.0ms (8.3%)

Algorithm

1×

intervals

Results

199.0ms

8000×

body

valid

Details

analyze4.0ms (0.1%)

sample17.0ms (0.5%)

simplify7.0ms (0.2%)

prune5.0ms (0.1%)

localize4.0ms (0.1%)

rewrite6.0ms (0.2%)

series8.0ms (0.2%)

simplify39.0ms (1.1%)

prune59.0ms (1.6%)

localize12.0ms (0.3%)

rewrite53.0ms (1.5%)

series34.0ms (0.9%)

simplify87.0ms (2.4%)

prune700.0ms (19.6%)

localize18.0ms (0.5%)

rewrite84.0ms (2.4%)

series45.0ms (1.3%)

simplify131.0ms (3.7%)

prune1.9s (54.2%)

regimes26.0ms (0.7%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample296.0ms (8.3%)

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