Details

sample50.0ms

Algorithm

intervals

Results

25.0ms

443×

body

valid

simplify80.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (33.0ms)

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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite246.0ms

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:

19.0ms	(+ (* x x) (* y y))
42.0ms	(+ (+ (* x x) (* y y)) (* y y))
182.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series157.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(+ (* x x) (* y y))
62.0ms	(+ (+ (* x x) (* y y)) (* y y))
51.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify2.4s

Counts

47 → 47

Iterations

Useful iterations: 3 (957.0ms)

Iter	Nodes	Cost
0	70	791
1	211	667
2	725	591
3	2852	513
done	5000	513

prune145.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
0.1b	(+ (+ (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (* y y)) (* y y))
6.1b	(sqrt (+ (* x x) (* y y)))
6.1b	(sqrt (+ (* x x) (* y y)))

rewrite231.0ms

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-+` `add-log-exp`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `sum-log` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `associate-+l+` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 100

Calls

4 calls:

55.0ms	(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
141.0ms	(+ (+ (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (* y y)) (* y y))
14.0ms	(sqrt (+ (* x x) (* y y)))
14.0ms	(sqrt (+ (* x x) (* y y)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
50.0ms	(+ (+ (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (* y y)) (* y y))
58.0ms	(sqrt (+ (* x x) (* y y)))
71.0ms	(sqrt (+ (* x x) (* y y)))

simplify2.3s

Counts

112 → 112

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	111	2347
1	249	1542
2	778	1300
3	2800	1201
done	5000	1179

prune302.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

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)))))
6.1b	(sqrt (+ (pow x 2) (* 2 (pow y 2))))
6.1b	(sqrt (+ (pow x 2) (* 2 (pow y 2))))

rewrite182.0ms

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:

39.0ms	(+ (* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2))))) (* y y))
84.0ms	(* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2)))))
29.0ms	(sqrt (+ (pow x 2) (* 2 (pow y 2))))
26.0ms	(sqrt (+ (pow x 2) (* 2 (pow y 2))))

series291.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(+ (* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2))))) (* y y))
68.0ms	(* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2)))))
82.0ms	(sqrt (+ (pow x 2) (* 2 (pow y 2))))
84.0ms	(sqrt (+ (pow x 2) (* 2 (pow y 2))))

simplify2.9s

Counts

110 → 110

Iterations

Useful iterations: done (2.9s)

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

prune362.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (pow x 2) (* y (* 3 y)))
0.2b	(* y (* 3 y))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+`

Counts

2 → 29

Calls

2 calls:

23.0ms	(+ (pow x 2) (* y (* 3 y)))
35.0ms	(* y (* 3 y))

series82.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(+ (pow x 2) (* y (* 3 y)))
30.0ms	(* y (* 3 y))

simplify3.6s

Counts

35 → 35

Iterations

Useful iterations: 4 (2.0s)

Iter	Nodes	Cost
0	56	362
1	155	326
2	477	294
3	1323	282
4	3717	280
done	5002	280

prune87.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes122.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	12	25
done	12	25

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.1s

14232×

body

valid