Details

sample33.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 7 (1.0s)

Iter	Nodes	Cost
0	9	282
1	22	282
2	48	282
3	103	282
4	208	282
5	403	282
6	840	282
7	3699	202
done	5000	242

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize27.0ms

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)))

rewrite76.0ms

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:

43.0ms	(* (- x y) (+ x y))
6.0ms	(+ (* x x) (* y y))
22.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series164.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* (- x y) (+ x y))
46.0ms	(+ (* x x) (* y y))
71.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify2.2s

Counts

82 → 82

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	127	25151
1	454	20364
2	3386	18924
done	5001	18804

prune406.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

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

prune12.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize35.0ms

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))

rewrite111.0ms

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:

11.0ms	(+ (* x x) (* y y))
44.0ms	(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
38.0ms	(/ (+ (* x x) (* y y)) (+ x y))

series225.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (* x x) (* y y))
78.0ms	(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
105.0ms	(/ (+ (* x x) (* y y)) (+ x y))

simplify1.1s

Counts

186 → 186

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	245	94455
1	816	86794
done	5000	85821

prune825.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize40.0ms

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))))

rewrite54.0ms

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:

12.0ms	(sqrt (+ (* x x) (* y y)))
12.0ms	(sqrt (+ (* x x) (* y y)))
12.0ms	(sqrt (+ (* x x) (* y y)))
15.0ms	(/ (* y y) (sqrt (+ (* x x) (* y y))))

series262.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt (+ (* x x) (* y y)))
66.0ms	(sqrt (+ (* x x) (* y y)))
65.0ms	(sqrt (+ (* x x) (* y y)))
87.0ms	(/ (* y y) (sqrt (+ (* x x) (* y y))))

simplify1.7s

Counts

86 → 86

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	77	21676
1	211	19442
2	1111	19482
done	5000	19362

prune527.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

regimes112.0ms

Accuracy

76.8% (4.5b remaining)

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

bsearch134.0ms

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

simplify16.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	22	757
1	29	757
done	29	757

end0.0ms

sample996.0ms

Algorithm

intervals

Results

584.0ms	8000×	body	80	valid
194.0ms	8000×	pre	80	true