Details

sample66.0ms

Algorithm

intervals

Results

36.0ms	256×	body	80	valid
14.0ms	256×	pre	80	true

simplify2.2s

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.8b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite460.0ms

Algorithm

rewrite-expression-head

Rules

586×	`*-un-lft-identity`
546×	`add-sqr-sqrt`
264×	`times-frac`
250×	`difference-of-squares`
190×	`swap-sqr`
180×	`associate-l`
175×	`distribute-lft-out`
100×	`*-commutative` `unswap-sqr`
50×	`distribute-lft-out--`
46×	`add-cube-cbrt`
33×	`associate-/l*`
8×	`associate-/r*`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `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 → 383

Calls

3 calls:

71.0ms	(+ (* x x) (* y y))
77.0ms	(- (* y y) (* x x))
255.0ms	(/ (- (* y y) (* x x)) (+ (* x x) (* y y)))

series163.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ (* x x) (* y y))
48.0ms	(- (* y y) (* x x))
71.0ms	(/ (- (* y y) (* x x)) (+ (* x x) (* y y)))

simplify1.7s

Counts

392 → 392

Iterations

Iter	Nodes
done	5001
2	1528
1	509
0	197

prune559.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(- (/ (* y y) (+ (* x x) (* y y))) (/ (* x x) (+ (* x x) (* y y))))
14.7b	(/ (* x x) (+ (* x x) (* y y)))
23.8b	(/ (* y y) (+ (* x x) (* y y)))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

2468×	`*-un-lft-identity`
918×	`associate-l`
810×	`associate-/l*`
722×	`add-sqr-sqrt`
705×	`distribute-lft-out`
676×	`frac-sub`
580×	`times-frac`
520×	`associate-/r*`
496×	`swap-sqr`
450×	`add-cube-cbrt`
210×	`associate-r`
141×	`distribute-lft-out--`
82×	`*-commutative` `unswap-sqr`
56×	`frac-2neg`
54×	`clear-num`
52×	`sub-div`
36×	`difference-of-squares`
14×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r/` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `div-exp` `insert-posit16` `div-inv`
3×	`distribute-rgt-out--`
2×	`prod-exp` `cbrt-unprod`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 1258

Calls

4 calls:

66.0ms	(+ (* x x) (* y y))
1.6s	(- (/ (* y y) (+ (* x x) (* y y))) (/ (* x x) (+ (* x x) (* y y))))
96.0ms	(/ (* x x) (+ (* x x) (* y y)))
122.0ms	(/ (* y y) (+ (* x x) (* y y)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (* x x) (* y y))
115.0ms	(- (/ (* y y) (+ (* x x) (* y y))) (/ (* x x) (+ (* x x) (* y y))))
84.0ms	(/ (* x x) (+ (* x x) (* y y)))
78.0ms	(/ (* y y) (+ (* x x) (* y y)))

simplify3.4s

Counts

1270 → 1270

Iterations

Iter	Nodes
done	5000
1	4949
0	1357

prune2.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* y y) (+ (* x x) (* y y))) (/ 1 (/ (+ (* x x) (* y y)) (* x x))))
0.6b	(/ 1 (/ (+ (* x x) (* y y)) (* x x)))
14.4b	(/ (+ (* x x) (* y y)) (* x x))
23.8b	(/ (* y y) (+ (* x x) (* y y)))

rewrite5.1s

Algorithm

rewrite-expression-head

Rules

10475×	`*-un-lft-identity`
4495×	`times-frac`
4426×	`associate-/r*`
3842×	`add-sqr-sqrt`
3757×	`associate-l`
3380×	`frac-sub`
3169×	`distribute-lft-out`
2747×	`add-cube-cbrt`
2426×	`swap-sqr`
2123×	`associate-/l*`
1167×	`associate-r`
414×	`*-commutative` `unswap-sqr`
171×	`clear-num`
160×	`frac-2neg`
96×	`associate-/r/`
78×	`distribute-lft-out--` `difference-of-squares`
35×	`add-exp-log`
34×	`div-inv`
23×	`add-cbrt-cube`
16×	`div-exp`
9×	`cbrt-undiv`
6×	`remove-double-div` `add-log-exp`
5×	`pow1` `prod-exp`
4×	`insert-posit16` `associate-/l/`
3×	`rec-exp` `flip3-+` `1-exp` `cbrt-unprod` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `pow-flip` `flip--` `inv-pow`

Counts

4 → 4427

Calls

4 calls:

3.9s	(- (/ (* y y) (+ (* x x) (* y y))) (/ 1 (/ (+ (* x x) (* y y)) (* x x))))
257.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* x x)))
236.0ms	(/ (+ (* x x) (* y y)) (* x x))
105.0ms	(/ (* y y) (+ (* x x) (* y y)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (/ (* y y) (+ (* x x) (* y y))) (/ 1 (/ (+ (* x x) (* y y)) (* x x))))
62.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* x x)))
70.0ms	(/ (+ (* x x) (* y y)) (* x x))
71.0ms	(/ (* y y) (+ (* x x) (* y y)))

simplify5.3s

Counts

4439 → 4439

Iterations

Iter	Nodes
done	5000
0	3636

prune5.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize2.0ms

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

prune0.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

regimes103.0ms

Accuracy

75.2% (4.7b remaining)

Error of 5.2b against oracle of 0.5b and baseline of 19.5b

bsearch156.0ms

Steps

Iters	Range	Point
9	8.224021888767988e-168	6.368480921027092e-162	1.8050510261731553e-162
10	-1.3799571515971478e-154	-1.8563905140027056e-164	-3.564256890674104e-158
7	-6.914140684613533e+154	-5.409346264960912e+152	-1.367949010508958e+154

Iters

Range

Point

8.224021888767988e-168

6.368480921027092e-162

1.8050510261731553e-162

-1.3799571515971478e-154

-1.8563905140027056e-164

-3.564256890674104e-158

-6.914140684613533e+154

-5.409346264960912e+152

-1.367949010508958e+154

simplify12.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.0s	8000×	body	80	valid
812.0ms	8000×	pre	80	true