Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

452×

body

valid

simplify32.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

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: 0.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.2b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-log-exp`
7×	`sum-log`
2×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `flip-+`
1×	`associate-+l+`

Counts

2 → 25

Calls

2 calls:

8.0ms	(+ (* x x) (* y y))
108.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series67.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(+ (* x x) (* y y))
40.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify1.2s

Counts

31 → 31

Iterations

Useful iterations: 3 (444.0ms)

Iter	Nodes	Cost
0	56	526
1	177	469
2	602	399
3	2323	335
done	5002	335

prune67.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3 (pow y 2))
0.2b	(* 3 (pow y 2))
5.9b	(sqrt (+ (pow x 2) (* 3 (pow y 2))))
5.9b	(sqrt (+ (pow x 2) (* 3 (pow y 2))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
16×	`associate-r`
14×	`add-exp-log`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
6×	`pow1` `associate-l` `prod-exp` `sqrt-prod`
4×	`sqrt-div` `unpow2` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 84

Calls

4 calls:

12.0ms	(* 3 (pow y 2))
14.0ms	(* 3 (pow y 2))
12.0ms	(sqrt (+ (pow x 2) (* 3 (pow y 2))))
13.0ms	(sqrt (+ (pow x 2) (* 3 (pow y 2))))

series160.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 3 (pow y 2))
25.0ms	(* 3 (pow y 2))
54.0ms	(sqrt (+ (pow x 2) (* 3 (pow y 2))))
52.0ms	(sqrt (+ (pow x 2) (* 3 (pow y 2))))

simplify1.4s

Counts

96 → 96

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	83	988
1	176	832
2	405	766
3	1230	750
done	5001	744

prune254.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 3) y)
0.4b	(* (sqrt 3) y)
5.9b	(sqrt (+ (pow x 2) (* (* (sqrt 3) y) (* (sqrt 3) y))))
5.9b	(sqrt (+ (pow x 2) (* 3 (pow y 2))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
14×	`sqrt-prod`
12×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
10×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r`
4×	`sqrt-div` `add-log-exp` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 74

Calls

4 calls:

9.0ms	(* (sqrt 3) y)
9.0ms	(* (sqrt 3) y)
15.0ms	(sqrt (+ (pow x 2) (* (* (sqrt 3) y) (* (sqrt 3) y))))
13.0ms	(sqrt (+ (pow x 2) (* 3 (pow y 2))))

series240.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sqrt 3) y)
40.0ms	(* (sqrt 3) y)
104.0ms	(sqrt (+ (pow x 2) (* (* (sqrt 3) y) (* (sqrt 3) y))))
52.0ms	(sqrt (+ (pow x 2) (* 3 (pow y 2))))

simplify2.8s

Counts

86 → 86

Iterations

Useful iterations: 3 (601.0ms)

Iter	Nodes	Cost
0	95	926
1	187	726
2	549	684
3	2085	678
done	5001	678

prune248.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3 (pow y 2))
5.9b	(sqrt (+ (pow x 2) (* (* 3 (fabs y)) (sqrt (pow y 2)))))
5.9b	(sqrt (+ (pow x 2) (* 3 (pow y 2))))
20.0b	(sqrt (pow y 2))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
14×	`sqrt-prod`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log`
8×	`unpow-prod-down` `associate-r`
6×	`pow1` `rem-sqrt-square` `add-cbrt-cube`
4×	`sqrt-div` `unpow2` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`sqrt-pow1` `pow1/2` `associate-l` `prod-exp`
2×	`flip3-+` `flip-+`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 78

Calls

4 calls:

11.0ms	(* 3 (pow y 2))
12.0ms	(sqrt (+ (pow x 2) (* (* 3 (fabs y)) (sqrt (pow y 2)))))
13.0ms	(sqrt (+ (pow x 2) (* 3 (pow y 2))))
3.0ms	(sqrt (pow y 2))

series145.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 3 (pow y 2))
58.0ms	(sqrt (+ (pow x 2) (* (* 3 (fabs y)) (sqrt (pow y 2)))))
51.0ms	(sqrt (+ (pow x 2) (* 3 (pow y 2))))
12.0ms	(sqrt (pow y 2))

simplify1.9s

Counts

90 → 90

Iterations

Useful iterations: 3 (655.0ms)

Iter	Nodes	Cost
0	148	1034
1	323	872
2	792	702
3	2868	687
done	5001	687

prune313.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes169.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample616.0ms

Algorithm

intervals

Results

318.0ms

14125×

body

valid