Details

sample47.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify4.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	22	15
2	48	15
3	101	15
4	188	15
5	346	15
6	579	15
7	875	15
8	2271	15
done	5000	15

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
16.6b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

14.0ms	(+ (* x x) (* y y))
31.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series121.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(+ (* x x) (* y y))
82.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify992.0ms

Counts

48 → 48

Iterations

Useful iterations: done (989.0ms)

Iter	Nodes	Cost
0	91	826
1	303	802
2	1443	662
done	5000	655

prune153.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
16.6b	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
41×	`associate-/r/`
29×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
20×	`frac-times`
17×	`flip3-+` `add-cbrt-cube` `flip-+`
16×	`associate-/r*`
15×	`flip3--` `flip--`
14×	`div-exp`
10×	`associate-r/` `associate-l/`
7×	`cbrt-undiv`
6×	`div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `prod-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `pow-flip` `sum-log` `inv-pow`

Counts

3 → 130

Calls

3 calls:

15.0ms	(+ (* x x) (* y y))
72.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
54.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

series272.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (* x x) (* y y))
105.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
119.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

simplify1.9s

Counts

139 → 139

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	220	3376
1	583	3136
2	2312	2794
done	5002	2759

prune336.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x x) (* y y))
0.0b	(/ (- (* x x) (* y y)) (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
16.6b	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))
16.6b	(/ (/ (- (* x x) (* y y)) (/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))) (* (+ x y) (- x y)))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

287×	`times-frac`
123×	`associate-/r/`
80×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
72×	`associate-/l*`
60×	`frac-times`
50×	`add-exp-log` `add-cbrt-cube`
47×	`flip3--` `flip--` `difference-of-squares`
46×	`flip3-+` `flip-+`
30×	`associate-r/` `associate-l/`
25×	`cbrt-undiv` `div-exp`
18×	`div-inv`
17×	`associate-/r*`
8×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`associate-/l/`
4×	`pow1`
3×	`frac-2neg` `div-sub` `clear-num`
1×	`sub-neg` `diff-log`

Counts

4 → 310

Calls

4 calls:

9.0ms	(- (* x x) (* y y))
49.0ms	(/ (- (* x x) (* y y)) (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
67.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))
104.0ms	(/ (/ (- (* x x) (* y y)) (/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))) (* (+ x y) (- x y)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* x x) (* y y))
214.0ms	(/ (- (* x x) (* y y)) (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
99.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))
67.0ms	(/ (/ (- (* x x) (* y y)) (/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))) (* (+ x y) (- x y)))

simplify1.6s

Counts

322 → 322

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	514	11820
1	1445	11546
done	5000	9572

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.3b

regimes103.0ms

Accuracy

78.4% (4.2b remaining)

Error of 4.6b against oracle of 0.4b and baseline of 19.9b

bsearch148.0ms

Steps

Iters	Range	Point
7	1.270532878618462e-164	1.8595605403829251e-162	1.8282600166370302e-162
7	-9.040093718271735e-161	-4.482309770999907e-162	-1.937646393364571e-161
10	-3.6321213431321147e+161	-2.5300323932420435e+146	-9.82178231331464e+153

Iters

Range

Point

1.270532878618462e-164

1.8595605403829251e-162

1.8282600166370302e-162

-9.040093718271735e-161

-4.482309770999907e-162

-1.937646393364571e-161

-3.6321213431321147e+161

-2.5300323932420435e+146

-9.82178231331464e+153

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	26	62
1	30	60
done	30	60

end0.0ms

sample1.2s

Algorithm

intervals

Results

765.0ms	8000×	body	80	valid
206.0ms	8000×	pre	80	true