Details

sample26.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
7	1519
6	575
5	339
4	177
3	95
2	46
1	22
0	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* y y) (* x x))
0.0b	(+ (* x x) (* y y))
17.6b	(/ (- (* y y) (* x x)) (+ (* x x) (* y y)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
4×	`associate-/l*`
3×	`pow1` `associate-/r*` `insert-posit16`
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 → 63

Calls

3 calls:

9.0ms	(- (* y y) (* x x))
9.0ms	(+ (* x x) (* y y))
30.0ms	(/ (- (* y y) (* x x)) (+ (* x x) (* y y)))

series149.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(- (* y y) (* x x))
32.0ms	(+ (* x x) (* y y))
60.0ms	(/ (- (* y y) (* x x)) (+ (* x x) (* y y)))

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	964
1	289
0	101

prune287.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y y) (* x x))
0.0b	(- (* y y) (* x x))
17.6b	(/ (- (* y y) (* x x)) (+ (* y y) (* x x)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
4×	`associate-/l*`
3×	`pow1` `associate-/r*` `insert-posit16`
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 → 63

Calls

3 calls:

11.0ms	(+ (* y y) (* x x))
15.0ms	(- (* y y) (* x x))
28.0ms	(/ (- (* y y) (* x x)) (+ (* y y) (* x x)))

series175.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(+ (* y y) (* x x))
59.0ms	(- (* y y) (* x x))
70.0ms	(/ (- (* y y) (* x x)) (+ (* y y) (* x x)))

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	955
1	266
0	96

prune270.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize5.0ms

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 (2 fresh and 2 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 4 expressions with local error:

17.5b	(sqrt (- (* y y) (* x x)))
18.6b	(cbrt (+ (* y y) (* x x)))
18.6b	(cbrt (+ (* y y) (* x x)))
18.6b	(cbrt (+ (* y y) (* x x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `sqrt-prod` `insert-posit16` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--` `difference-of-squares`

Counts

4 → 59

Calls

4 calls:

9.0ms	(sqrt (- (* y y) (* x x)))
5.0ms	(cbrt (+ (* y y) (* x x)))
6.0ms	(cbrt (+ (* y y) (* x x)))
5.0ms	(cbrt (+ (* y y) (* x x)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (- (* y y) (* x x)))
140.0ms	(cbrt (+ (* y y) (* x x)))
162.0ms	(cbrt (+ (* y y) (* x x)))
107.0ms	(cbrt (+ (* y y) (* x x)))

simplify1.6s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
3	1234
2	396
1	165
0	79

prune428.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

regimes92.0ms

Accuracy

77.3% (4.4b remaining)

Error of 4.9b against oracle of 0.5b and baseline of 20.1b

bsearch122.0ms

Steps

Iters	Range	Point
8	4.11345058662494e-165	1.7020681544470525e-162	1.5708400865028228e-162
6	-1.9200771764723128e-160	-2.13457590843716e-161	-1.1638085591132404e-160
10	-2.8560409620991146e+162	-9.907787135739815e+151	-1.3341061642710286e+154

Iters

Range

Point

4.11345058662494e-165

1.7020681544470525e-162

1.5708400865028228e-162

-1.9200771764723128e-160

-2.13457590843716e-161

-1.1638085591132404e-160

-2.8560409620991146e+162

-9.907787135739815e+151

-1.3341061642710286e+154

simplify22.0ms

Iterations

Iter	Nodes
done	29
1	29
0	21

end0.0ms

sample963.0ms

Algorithm

intervals

Results

554.0ms	8000×	body	80	valid
251.0ms	8000×	pre	80	true