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: 31.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
29.1b	(sqrt (+ (* x x) (* y y)))

rewrite18.0ms

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:

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

series90.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(+ (* x x) (* y y))
59.0ms	(sqrt (+ (* x x) (* y y)))

simplify2.8s

Counts

32 → 32

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	48	379
1	124	347
2	343	295
3	968	295
4	2668	295
done	5000	295

prune94.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.5b	(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
29.1b	(sqrt (+ (* x x) (* y y)))
29.1b	(sqrt (+ (* x x) (* y y)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`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` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
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 → 124

Calls

4 calls:

16.0ms	(+ (* x x) (* y y))
84.0ms	(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
11.0ms	(sqrt (+ (* x x) (* y y)))
8.0ms	(sqrt (+ (* x x) (* y y)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (* x x) (* y y))
48.0ms	(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
49.0ms	(sqrt (+ (* x x) (* y y)))
62.0ms	(sqrt (+ (* x x) (* y y)))

simplify2.1s

Counts

136 → 136

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	121	2803
1	233	1759
2	638	1533
3	2187	1496
done	5000	1457

prune337.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.9b

localize32.0ms

Local error

Found 4 expressions with local error:

29.1b	(sqrt (+ (* x x) (* y y)))
29.1b	(sqrt (+ (* x x) (* y y)))
29.1b	(sqrt (+ (* x x) (* y y)))
29.1b	(sqrt (+ (* x x) (* y y)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

14.0ms	(sqrt (+ (* x x) (* y y)))
15.0ms	(sqrt (+ (* x x) (* y y)))
17.0ms	(sqrt (+ (* x x) (* y y)))
17.0ms	(sqrt (+ (* x x) (* y y)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (+ (* x x) (* y y)))
71.0ms	(sqrt (+ (* x x) (* y y)))
58.0ms	(sqrt (+ (* x x) (* y y)))
53.0ms	(sqrt (+ (* x x) (* y y)))

simplify3.3s

Counts

72 → 72

Iterations

Useful iterations: 3 (164.0ms)

Iter	Nodes	Cost
0	38	852
1	91	744
2	205	680
3	444	656
4	1114	656
5	3182	656
done	5001	656

prune402.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
5.9b	(exp (log (sqrt (+ (* x x) (* y y)))))
29.1b	(sqrt (+ (* x x) (* y y)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 48

Calls

3 calls:

13.0ms	(+ (* x x) (* y y))
17.0ms	(exp (log (sqrt (+ (* x x) (* y y)))))
18.0ms	(sqrt (+ (* x x) (* y y)))

series156.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* x x) (* y y))
62.0ms	(exp (log (sqrt (+ (* x x) (* y y)))))
57.0ms	(sqrt (+ (* x x) (* y y)))

simplify2.3s

Counts

57 → 57

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	87	739
1	169	626
2	398	534
3	1056	534
4	2807	528
done	5001	528

prune121.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 9.9b

regimes432.0ms

Accuracy

58.2% (9.9b remaining)

Error of 17.8b against oracle of 7.9b and baseline of 31.6b

bsearch53.0ms

Steps

Iters	Range		Point
8	9.20494146023971e+137	8.337939306029303e+141	1.3595155319523303e+138
7	-5.792006846201835e+113	-3.7885935661345695e+111	-1.1564076018637175e+112

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample665.0ms

Algorithm

intervals

Results

388.0ms

8000×

body

valid