Details

sample26.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	3699
6	840
5	403
4	208
3	103
2	48
1	22
0	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- x y) (+ x y))
0.0b	(+ (* x x) (* y y))
17.7b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cbrt-cube` `add-exp-log`
8×	`frac-times` `flip3-+` `flip-+` `associate-/l/`
7×	`add-cube-cbrt`
6×	`flip3--` `flip--`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-r` `associate-l/` `associate-r/`
3×	`associate-/r*` `times-frac`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`distribute-rgt-in` `+-commutative` `clear-num` `sum-log` `frac-2neg` `distribute-lft-in` `pow-prod-down` `-commutative` `div-inv` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 73

Calls

3 calls:

45.0ms	(* (- x y) (+ x y))
9.0ms	(+ (* x x) (* y y))
27.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series184.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* (- x y) (+ x y))
48.0ms	(+ (* x x) (* y y))
79.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify2.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	3386
1	454
0	127

prune444.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

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

prune21.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
16.8b	(/ (+ (* x x) (* y y)) (+ x y))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
161×	`*-un-lft-identity`
117×	`add-sqr-sqrt`
79×	`add-cube-cbrt`
22×	`associate-/r*` `distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
10×	`add-cbrt-cube` `add-exp-log`
9×	`flip3-+` `flip-+`
8×	`div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log` `flip3--` `div-sub` `flip--`

Counts

3 → 177

Calls

3 calls:

10.0ms	(+ (* x x) (* y y))
33.0ms	(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
51.0ms	(/ (+ (* x x) (* y y)) (+ x y))

series204.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* x x) (* y y))
85.0ms	(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
80.0ms	(/ (+ (* x x) (* y y)) (+ x y))

simplify905.0ms

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
1	816
0	245

prune733.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize54.0ms

Local error

Found 4 expressions with local error:

16.8b	(sqrt (+ (* x x) (* y y)))
16.8b	(sqrt (+ (* x x) (* y y)))
16.8b	(sqrt (+ (* x x) (* y y)))
16.8b	(/ (* y y) (sqrt (+ (* x x) (* y y))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

15×	`sqrt-prod`
14×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`add-cbrt-cube` `add-exp-log`
8×	`sqrt-div`
7×	`pow1`
6×	`associate-/r*` `times-frac`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

6.0ms	(sqrt (+ (* x x) (* y y)))
9.0ms	(sqrt (+ (* x x) (* y y)))
12.0ms	(sqrt (+ (* x x) (* y y)))
26.0ms	(/ (* y y) (sqrt (+ (* x x) (* y y))))

series236.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt (+ (* x x) (* y y)))
41.0ms	(sqrt (+ (* x x) (* y y)))
55.0ms	(sqrt (+ (* x x) (* y y)))
76.0ms	(/ (* y y) (sqrt (+ (* x x) (* y y))))

simplify1.2s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1111
1	211
0	77

prune482.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

regimes110.0ms

Accuracy

76.8% (4.5b remaining)

Error of 5.0b against oracle of 0.4b and baseline of 20.0b

bsearch107.0ms

Steps

Iters	Range	Point
8	1.4224717713323527e-167	8.131351164067834e-164	7.961862811311691e-164
4	-1.857850302800927e-158	-9.802288210601573e-159	-1.3292537611752237e-158
9	-2.741116183037804e+158	-4.389998254864137e+150	-5.797856225877881e+150

Iters

Range

Point

1.4224717713323527e-167

8.131351164067834e-164

7.961862811311691e-164

-1.857850302800927e-158

-9.802288210601573e-159

-1.3292537611752237e-158

-2.741116183037804e+158

-4.389998254864137e+150

-5.797856225877881e+150

simplify10.0ms

Iterations

Iter	Nodes
done	29
1	29
0	22

end0.0ms

sample1.2s

Algorithm

intervals

Results

641.0ms	8000×	body	80	valid
216.0ms	8000×	pre	80	true