Details

sample27.0ms

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify200.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	177
7	177
6	168
5	143
4	100
3	59
2	34
1	17
0	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
3.4b	(- (* x x) (* (* y 4.0) y))
32.2b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

3 → 58

Calls

3 calls:

10.0ms	(+ (* x x) (* (* y 4.0) y))
9.0ms	(- (* x x) (* (* y 4.0) y))
35.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series200.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(+ (* x x) (* (* y 4.0) y))
66.0ms	(- (* x x) (* (* y 4.0) y))
72.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify2.4s

Counts

67 → 67

Iterations

Iter	Nodes
done	5059
3	3850
2	861
1	249
0	90

prune266.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune9.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize21.0ms

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))))
3.4b	(- (* x x) (* (* y 4.0) y))
32.2b	(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`div-exp` `add-log-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16`
2×	`rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 142

Calls

4 calls:

11.0ms	(+ (* x x) (* (* y 4.0) y))
29.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
11.0ms	(- (* x x) (* (* y 4.0) y))
48.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* x x) (* (* y 4.0) y))
89.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
64.0ms	(- (* x x) (* (* y 4.0) y))
89.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

simplify1.2s

Counts

154 → 154

Iterations

Iter	Nodes
done	5000
2	1539
1	524
0	196

prune430.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* x x) (* (* y 4.0) y))
30.6b	(sqrt (+ (* x x) (* (* y 4.0) y)))
30.6b	(sqrt (+ (* x x) (* (* y 4.0) y)))
30.6b	(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
4×	`insert-posit16`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 90

Calls

4 calls:

12.0ms	(- (* x x) (* (* y 4.0) y))
9.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
14.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
33.0ms	(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* x x) (* (* y 4.0) y))
73.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
59.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
135.0ms	(/ (- (* x x) (* (* y 4.0) y)) (sqrt (+ (* x x) (* (* y 4.0) y))))

simplify1.8s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
3	3158
2	820
1	285
0	118

prune391.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes180.0ms

Accuracy

61.6% (12.3b remaining)

Error of 12.6b against oracle of 0.4b and baseline of 32.3b

bsearch171.0ms

Steps

Iters	Range		Point
10	6.851870411809504e+252	2.8918088282269027e+264	3.1031769081973586e+257
10	6.21501595672588e+44	7.598010549864809e+58	6.296502919195928e+44
9	861150181369349.2	2.6348779428485677e+23	9.758857908001147e+18
0	1.4667909825551e-317	1.4216135248906e-313	7.1088010196971e-314

simplify7.0ms

Iterations

Iter	Nodes
done	29
1	29
0	24

end0.0ms

sample1.0s

Algorithm

intervals

Results

861.0ms

8000×

body

valid