Details

sample31.0ms

Algorithm

intervals

Results

17.0ms

461×

body

valid

simplify262.0ms

Counts: 1 → 1

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))

rewrite165.0ms

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:

30.0ms	(+ (+ (* x x) (* y y)) (* y y))
8.0ms	(+ (* x x) (* y y))
125.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series117.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(+ (+ (* x x) (* y y)) (* y y))
30.0ms	(+ (* x x) (* y y))
43.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify120.0ms

Counts: 47 → 47

prune109.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite268.0ms

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:

57.0ms	(+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y))
143.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))))
35.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
30.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series201.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y))
44.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))))
56.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
59.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify47.0ms

Counts: 110 → 110

prune242.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite846.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-log-exp`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `sum-log` `add-cbrt-cube`
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` `associate-+l+` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 101

Calls

4 calls:

113.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
491.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
117.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
121.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
41.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
62.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
58.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify43.0ms

Counts: 113 → 113

prune266.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* y y)))))
9.3b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
9.3b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
9.3b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

75×	`sqrt-prod`
52×	`add-sqr-sqrt`
35×	`sqrt-pow1`
30×	`pow1` `sqrt-div`
19×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `add-log-exp`
3×	`rem-sqrt-square`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 128

Calls

4 calls:

153.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* y y)))))
32.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
30.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
38.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* y y)))))
57.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
64.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
63.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify43.0ms

Counts: 140 → 140

prune321.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes186.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample963.0ms

Algorithm

intervals

Results

605.0ms

14329×

body

valid