Details

sample17.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
done	7	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
28.2b	(sqrt (+ (* x x) (* y y)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-log-exp`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

2 → 26

Calls

2 calls:

17.0ms	(+ (* x x) (* y y))
16.0ms	(sqrt (+ (* x x) (* y y)))

series123.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(+ (* x x) (* y y))
71.0ms	(sqrt (+ (* x x) (* y y)))

simplify539.0ms

Counts

32 → 32

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	48	379
1	143	347
2	758	295
done	5000	295

prune142.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ (* x x) (* y y))))
0.5b	(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
28.2b	(sqrt (+ (* x x) (* y y)))
28.2b	(sqrt (+ (* x x) (* y y)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
20×	`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` `rem-sqrt-square` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

19.0ms	(sqrt (sqrt (+ (* x x) (* y y))))
115.0ms	(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
9.0ms	(sqrt (+ (* x x) (* y y)))
9.0ms	(sqrt (+ (* x x) (* y y)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(sqrt (sqrt (+ (* x x) (* y y))))
49.0ms	(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
49.0ms	(sqrt (+ (* x x) (* y y)))
65.0ms	(sqrt (+ (* x x) (* y y)))

simplify940.0ms

Counts

146 → 146

Iterations

Useful iterations: done (933.0ms)

Iter	Nodes	Cost
0	127	2962
1	292	1887
2	1142	1671
done	5000	1642

prune305.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.1b

localize21.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* x x) (* y y))
9.6b	(- (pow x 4) (pow y 4))
28.2b	(sqrt (/ (- (pow x 4) (pow y 4)) (- (* x x) (* y y))))
38.7b	(/ (- (pow x 4) (pow y 4)) (- (* x x) (* y y)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

166×	`add-sqr-sqrt`
120×	`difference-of-squares`
113×	`times-frac`
83×	`*-un-lft-identity`
80×	`unpow-prod-down`
62×	`sqrt-prod`
60×	`sqr-pow`
43×	`add-cube-cbrt`
20×	`distribute-lft-out--`
14×	`associate-/l*`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `flip--`
4×	`associate-/r*` `associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 201

Calls

4 calls:

16.0ms	(- (* x x) (* y y))
22.0ms	(- (pow x 4) (pow y 4))
55.0ms	(sqrt (/ (- (pow x 4) (pow y 4)) (- (* x x) (* y y))))
74.0ms	(/ (- (pow x 4) (pow y 4)) (- (* x x) (* y y)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* x x) (* y y))
65.0ms	(- (pow x 4) (pow y 4))
114.0ms	(sqrt (/ (- (pow x 4) (pow y 4)) (- (* x x) (* y y))))
126.0ms	(/ (- (pow x 4) (pow y 4)) (- (* x x) (* y y)))

simplify2.6s

Counts

213 → 213

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	337	5423
1	689	5012
2	3391	4873
done	5000	4757

prune848.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 7.1b

localize1.0ms

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

prune0.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 7.1b

regimes379.0ms

Accuracy

58.7% (9.9b remaining)

Error of 18.0b against oracle of 8.2b and baseline of 32.1b

bsearch58.0ms

Steps

Iters	Range		Point
9	5.544110015415869e+89	8.73093819312065e+95	3.1246465155572506e+95
10	-7.015537041391403e+155	-1.2785578264641574e+145	-1.517398075841732e+145

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	14	19
done	14	19

end0.0ms

sample698.0ms

Algorithm

intervals

Results

405.0ms

8000×

body

valid