Details

sample31.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify4.1s

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: 21.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
21.7b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite59.0ms

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:

8.0ms	(+ (* x x) (* y y))
49.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series122.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+ (* x x) (* y y))
85.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify878.0ms

Counts

48 → 48

Iterations

Useful iterations: done (876.0ms)

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

prune144.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

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))))
21.7b	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

rewrite117.0ms

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:

13.0ms	(+ (* x x) (* y y))
52.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
42.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

series200.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (* x x) (* y y))
84.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
81.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

simplify1.6s

Counts

139 → 139

Iterations

Useful iterations: done (1.6s)

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

prune263.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y))))
21.4b	(sqrt (+ (* x x) (* y y)))
21.4b	(sqrt (+ (* x x) (* y y)))
21.5b	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
72×	`sqrt-prod`
59×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
22×	`sqrt-div`
18×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
14×	`flip3-+` `flip-+`
13×	`associate-/l*`
12×	`associate-/r*`
9×	`div-inv` `associate-/l/`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`frac-times` `add-log-exp`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`

Counts

4 → 176

Calls

4 calls:

72.0ms	(/ (/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y))))
18.0ms	(sqrt (+ (* x x) (* y y)))
11.0ms	(sqrt (+ (* x x) (* y y)))
42.0ms	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y))))
56.0ms	(sqrt (+ (* x x) (* y y)))
61.0ms	(sqrt (+ (* x x) (* y y)))
107.0ms	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

simplify1.3s

Counts

188 → 188

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	222	6005
1	607	5306
2	2261	4817
done	5001	4687

prune639.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (* (/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y))) (+ x y)))
0.2b	(* (/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y))) (+ x y))
21.5b	(/ (+ (* x x) (* y y)) (- x y))
21.6b	(/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y)))

rewrite564.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
99×	`add-exp-log`
78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
61×	`add-cbrt-cube`
45×	`add-cube-cbrt`
43×	`div-exp`
33×	`associate-l`
30×	`prod-exp`
29×	`associate-/r/`
27×	`associate-/l*`
25×	`cbrt-undiv`
17×	`flip3-+` `flip-+`
16×	`cbrt-unprod`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`frac-times`
9×	`pow1`
8×	`associate-*r/`
7×	`associate-/r*` `div-inv`
6×	`rec-exp` `1-exp` `associate-*l/`
4×	`flip3--` `associate-r` `flip--` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/` `unswap-sqr`
2×	`pow-flip` `pow-prod-down`
1×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `distribute-lft-out` `inv-pow`

Counts

4 → 224

Calls

4 calls:

184.0ms	(/ 1 (* (/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y))) (+ x y)))
190.0ms	(* (/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y))) (+ x y))
63.0ms	(/ (+ (* x x) (* y y)) (- x y))
114.0ms	(/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ 1 (* (/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y))) (+ x y)))
97.0ms	(* (/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y))) (+ x y))
102.0ms	(/ (+ (* x x) (* y y)) (- x y))
87.0ms	(/ (/ (+ (* x x) (* y y)) (- x y)) (* (+ x y) (+ x y)))

simplify2.5s

Counts

236 → 236

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	301	6091
1	981	5886
2	3750	4434
done	5001	4424

prune825.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

regimes88.0ms

Accuracy

77.4% (4.5b remaining)

Error of 5.0b against oracle of 0.5b and baseline of 20.5b

bsearch127.0ms

Steps

Iters	Range		Point
6	1.520145198895703e-167	2.1557865162740726e-166	2.1155504904828537e-166
7	-5.771560909560032e-159	-2.816861526094086e-161	-7.718474411270338e-160
9	-108.06719872485291	-0.00012163823945093722	-106.83622190829594

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	23	66
1	31	40
done	31	40

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.0s	8000×	body	80	valid
224.0ms	8000×	pre	80	true