Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify99.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	19
1	17	19
2	35	19
3	70	19
4	119	19
5	167	19
6	187	19
7	188	19
done	188	19

prune3.0ms

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: 31.9b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
4.8b	(- (* x x) (* (* y 4.0) y))
31.3b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite18.0ms

Algorithm

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 → 55

Calls

3 calls:

4.0ms	(+ (* x x) (* (* y 4.0) y))
4.0ms	(- (* x x) (* (* y 4.0) y))
9.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series31.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(+ (* x x) (* (* y 4.0) y))
8.0ms	(- (* x x) (* (* y 4.0) y))
13.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify844.0ms

Counts

64 → 64

Iterations

Useful iterations: 3 (271.0ms)

Iter	Nodes	Cost
0	87	1404
1	232	1375
2	893	1233
3	3253	1226
done	5000	1226

prune116.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	4	65

Merged error: 0.3b

Counts

65 → 4

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune10.0ms

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: 0.3b

Counts

4 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* x x) (* (* y 4.0) y))
31.3b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
31.3b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
31.3b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r` `associate-/l`
6×	`associate-/r/` `associate-/l/` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
3×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`sub-neg` `diff-log`

Counts

4 → 108

Calls

4 calls:

4.0ms	(- (* x x) (* (* y 4.0) y))
10.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
10.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
9.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* x x) (* (* y 4.0) y))
13.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
13.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
13.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify807.0ms

Counts

120 → 120

Iterations

Useful iterations: done (803.0ms)

Iter	Nodes	Cost
0	82	3148
1	219	3096
2	848	2810
3	3051	2802
done	5000	2799

prune359.0ms

Filtered

100 candidates to 120 candidates (-20.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	120	4	124

Merged error: 0.3b

Counts

124 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
0.0b	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
4.8b	(- (* x x) (* (* y 4.0) y))
31.3b	(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`div-exp` `add-log-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`rec-exp` `frac-2neg` `flip3-+` `1-exp` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `pow-flip` `diff-log` `sum-log` `inv-pow`

Counts

4 → 138

Calls

4 calls:

4.0ms	(+ (* x x) (* (* y 4.0) y))
10.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
4.0ms	(- (* x x) (* (* y 4.0) y))
10.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* x x) (* (* y 4.0) y))
16.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
8.0ms	(- (* x x) (* (* y 4.0) y))
13.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

simplify423.0ms

Counts

150 → 150

Iterations

Useful iterations: done (417.0ms)

Iter	Nodes	Cost
0	192	4490
1	470	4272
2	1691	3827
done	5000	3805

prune216.0ms

Filtered

89 candidates to 150 candidates (-68.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	150	4	154

Merged error: 0.3b

Counts

154 → 4

regimes243.0ms

Accuracy

61.7% (11.9b remaining)

Error of 12.3b against oracle of 0.4b and baseline of 31.4b

bsearch23.0ms

Steps

Iters	Range		Point
5	1.5424462366052938e+171	5.844591147925292e+171	5.497534214446919e+171
9	1.5174842357679145e-261	1.3532945271366174e-252	5.8839237203771254e-260

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	80
1	26	80
done	26	80

end0.0ms

sample634.0ms

Algorithm

intervals

Results

388.0ms

8000×

body

valid

Details

sample23.0ms

simplify99.0ms

prune3.0ms

localize8.0ms

rewrite18.0ms

series31.0ms

simplify844.0ms

prune116.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify1.0ms

prune10.0ms

localize12.0ms

rewrite36.0ms

series46.0ms

simplify807.0ms

prune359.0ms

localize10.0ms

rewrite34.0ms

series44.0ms

simplify423.0ms

prune216.0ms

regimes243.0ms

bsearch23.0ms

simplify2.0ms

end0.0ms

sample634.0ms

Profiling