Details

sample43.0ms

Algorithm

intervals

Results

21.0ms

461×

body

valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (27.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	23	13
3	35	9
4	43	9
5	46	9
done	46	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.0b	(+ (* x x) (* y y))
0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
10×	`sum-log`
3×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`associate-+l+`

Counts

3 → 38

Calls

3 calls:

33.0ms	(+ (+ (* x x) (* y y)) (* y y))
8.0ms	(+ (* x x) (* y y))
124.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series118.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ (+ (* x x) (* y y)) (* y y))
30.0ms	(+ (* x x) (* y y))
43.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify2.0s

Counts

47 → 47

Iterations

Useful iterations: 3 (679.0ms)

Iter	Nodes	Cost
0	70	791
1	211	667
2	724	591
3	2860	513
done	5000	513

prune141.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2))))) (* y y))
0.2b	(* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2)))))
9.3b	(sqrt (+ (pow x 2) (* 2 (pow y 2))))
9.3b	(sqrt (+ (pow x 2) (* 2 (pow y 2))))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 98

Calls

4 calls:

48.0ms	(+ (* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2))))) (* y y))
105.0ms	(* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2)))))
24.0ms	(sqrt (+ (pow x 2) (* 2 (pow y 2))))
26.0ms	(sqrt (+ (pow x 2) (* 2 (pow y 2))))

series241.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2))))) (* y y))
54.0ms	(* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2)))))
77.0ms	(sqrt (+ (pow x 2) (* 2 (pow y 2))))
70.0ms	(sqrt (+ (pow x 2) (* 2 (pow y 2))))

simplify2.8s

Counts

110 → 110

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	108	2708
1	247	1699
2	822	1551
3	3241	1429
done	5001	1401

prune345.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

0.2b	(* y (* 3 y))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1×	`associate-r` `*-commutative` `add-log-exp`

Counts

1 → 18

Calls

1 calls:

30.0ms

(* y (* 3 y))

series28.0ms

Counts

1 → 3

Calls

1 calls:

28.0ms

(* y (* 3 y))

simplify3.8s

Counts

21 → 21

Iterations

Useful iterations: 5 (1.4s)

Iter	Nodes	Cost
0	34	154
1	84	143
2	241	123
3	456	115
4	654	115
5	1432	114
done	5000	114

prune43.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y (* 3 y))
0.3b	(* (sqrt (* y (* 3 y))) (sqrt (* y (* 3 y))))
20.7b	(sqrt (* y (* 3 y)))
20.7b	(sqrt (* y (* 3 y)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

148×	`pow1`
80×	`pow-prod-down`
66×	`sqrt-pow1`
17×	`pow-prod-up`
14×	`pow1/2`
11×	`add-exp-log` `add-sqr-sqrt` `pow-sqr` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-l`
6×	`sqrt-prod`
5×	`associate-r`
4×	`swap-sqr` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`*-commutative`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `unswap-sqr`

Counts

4 → 108

Calls

4 calls:

17.0ms	(* y (* 3 y))
122.0ms	(* (sqrt (* y (* 3 y))) (sqrt (* y (* 3 y))))
17.0ms	(sqrt (* y (* 3 y)))
21.0ms	(sqrt (* y (* 3 y)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* y (* 3 y))
102.0ms	(* (sqrt (* y (* 3 y))) (sqrt (* y (* 3 y))))
45.0ms	(sqrt (* y (* 3 y)))
58.0ms	(sqrt (* y (* 3 y)))

simplify3.1s

Counts

120 → 120

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	80	1100
1	164	724
2	501	643
3	1979	558
done	5001	531

prune255.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes127.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	10	15
done	10	15

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.3s

14329×

body

valid