Details

analyze12.0ms (0.8%)

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
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

sample27.0ms (1.8%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

valid

simplify63.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5027	19

prune9.0ms (0.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 34.6b

Counts

2 → 1

localize8.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
5.3b	(- (* x x) (* (* y 4.0) y))
34.0b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite17.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 54

Calls

3 calls:

8.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
4.0ms	(+ (* x x) (* (* y 4.0) y))
4.0ms	(- (* x x) (* (* y 4.0) y))

series25.0ms (1.7%)

Counts

3 → 9

Calls

3 calls:

11.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
7.0ms	(- (* x x) (* (* y 4.0) y))
6.0ms	(+ (* x x) (* (* y 4.0) y))

simplify66.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4943	1204
1	4943	1204

prune111.0ms (7.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	59	4	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	4	64

Merged error: 0.2b

Counts

64 → 4

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune8.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Merged error: 0.2b

Counts

4 → 4

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune6.0ms (0.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Merged error: 0.2b

Counts

4 → 4

localize10.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (- (* x x) (* y (* y 4.0))) (+ (* x x) (* y (* y 4.0)))) 3)
0.0b	(cbrt (pow (/ (- (* x x) (* y (* y 4.0))) (+ (* x x) (* y (* y 4.0)))) 3))
5.3b	(- (* x x) (* y (* y 4.0)))
34.0b	(/ (- (* x x) (* y (* y 4.0))) (+ (* x x) (* y (* y 4.0))))

rewrite36.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`cbrt-prod`
30×	`unpow-prod-down` `cube-prod`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `flip3-+` `flip-+` `div-inv`
3×	`pow-unpow` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `cube-div` `cube-mult` `flip3--` `unpow3` `div-exp` `pow-exp` `flip--` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-sub` `clear-num` `rem-cbrt-cube`

Counts

4 → 139

Calls

4 calls:

10.0ms	(pow (/ (- (* x x) (* y (* y 4.0))) (+ (* x x) (* y (* y 4.0)))) 3)
9.0ms	(cbrt (pow (/ (- (* x x) (* y (* y 4.0))) (+ (* x x) (* y (* y 4.0)))) 3))
8.0ms	(/ (- (* x x) (* y (* y 4.0))) (+ (* x x) (* y (* y 4.0))))
4.0ms	(- (* x x) (* y (* y 4.0)))

series46.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(pow (/ (- (* x x) (* y (* y 4.0))) (+ (* x x) (* y (* y 4.0)))) 3)
14.0ms	(/ (- (* x x) (* y (* y 4.0))) (+ (* x x) (* y (* y 4.0))))
11.0ms	(cbrt (pow (/ (- (* x x) (* y (* y 4.0))) (+ (* x x) (* y (* y 4.0)))) 3))
7.0ms	(- (* x x) (* y (* y 4.0)))

simplify58.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5109	3881

prune294.0ms (19.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	151	4	155

Merged error: 0.2b

Counts

155 → 4

regimes174.0ms (11.6%)

Accuracy

Total 14.5b remaining (98.2%)

Threshold costs 0b (0%)

bsearch60.0ms (4%)

Steps

Iters	Range		Point
8	8.829667198714222e+79	2.7454474867920204e+82	2.248804362437393e+81
9	4.124411015621216e-18	3.0462877333983428e-09	2.992724529533424e-09
6	7.025561636108856e-62	1.0209734135524725e-60	7.37508648907558e-62
3	-2.787121811229255e-33	-2.1502970253019634e-33	-2.1900985744224192e-33
10	-7.006984133473917e+156	-2.85307605768799e+144	-1.1567941219743209e+146

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	68
1	68	68

end0.0ms (0%)

sample464.0ms (30.9%)

Algorithm

1×

intervals

Results

338.0ms

8000×

body

valid

Details

analyze12.0ms (0.8%)

sample27.0ms (1.8%)

simplify63.0ms (4.2%)

prune9.0ms (0.6%)

localize8.0ms (0.5%)

rewrite17.0ms (1.1%)

series25.0ms (1.7%)

simplify66.0ms (4.4%)

prune111.0ms (7.4%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify2.0ms (0.2%)

prune8.0ms (0.5%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify2.0ms (0.1%)

prune6.0ms (0.4%)

localize10.0ms (0.7%)

rewrite36.0ms (2.4%)

series46.0ms (3.1%)

simplify58.0ms (3.9%)

prune294.0ms (19.6%)

regimes174.0ms (11.6%)

bsearch60.0ms (4%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample464.0ms (30.9%)

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