Details

sample26.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
27.4b	(sqrt (+ (* x x) (* y y)))

rewrite26.0ms

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:

12.0ms	(+ (* x x) (* y y))
13.0ms	(sqrt (+ (* x x) (* y y)))

series96.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(+ (* x x) (* y y))
58.0ms	(sqrt (+ (* x x) (* y y)))

simplify2.3s

Counts

32 → 32

Iterations

Useful iterations: 2 (76.0ms)

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

prune114.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* x x) (* y y))))
27.4b	(sqrt (+ (* x x) (* y y)))
27.4b	(sqrt (+ (* x x) (* y y)))
27.4b	(sqrt (+ (* x x) (* y y)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

9.0ms	(cbrt (sqrt (+ (* x x) (* y y))))
12.0ms	(sqrt (+ (* x x) (* y y)))
9.0ms	(sqrt (+ (* x x) (* y y)))
12.0ms	(sqrt (+ (* x x) (* y y)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt (sqrt (+ (* x x) (* y y))))
56.0ms	(sqrt (+ (* x x) (* y y)))
47.0ms	(sqrt (+ (* x x) (* y y)))
59.0ms	(sqrt (+ (* x x) (* y y)))

simplify1.3s

Counts

73 → 73

Iterations

Useful iterations: 3 (175.0ms)

Iter	Nodes	Cost
0	70	952
1	149	853
2	323	761
3	693	750
4	1885	750
done	5001	750

prune299.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.3b

localize21.0ms

Local error

Found 4 expressions with local error:

4.3b	(exp (log (cbrt (sqrt (+ (* x x) (* y y))))))
27.4b	(sqrt (+ (* x x) (* y y)))
27.4b	(sqrt (+ (* x x) (* y y)))
27.4b	(sqrt (+ (* x x) (* y y)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

15.0ms	(exp (log (cbrt (sqrt (+ (* x x) (* y y))))))
13.0ms	(sqrt (+ (* x x) (* y y)))
18.0ms	(sqrt (+ (* x x) (* y y)))
11.0ms	(sqrt (+ (* x x) (* y y)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(exp (log (cbrt (sqrt (+ (* x x) (* y y))))))
47.0ms	(sqrt (+ (* x x) (* y y)))
44.0ms	(sqrt (+ (* x x) (* y y)))
38.0ms	(sqrt (+ (* x x) (* y y)))

simplify1.6s

Counts

81 → 81

Iterations

Useful iterations: 4 (617.0ms)

Iter	Nodes	Cost
0	111	1119
1	196	954
2	379	824
3	756	813
4	1966	801
done	5000	801

prune350.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.3b

localize44.0ms

Local error

Found 4 expressions with local error:

27.4b	(sqrt (+ (* x x) (* y y)))
27.4b	(sqrt (+ (* x x) (* y y)))
27.4b	(sqrt (+ (* x x) (* y y)))
27.4b	(sqrt (+ (* x x) (* y y)))

rewrite54.0ms

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:

13.0ms	(sqrt (+ (* x x) (* y y)))
12.0ms	(sqrt (+ (* x x) (* y y)))
13.0ms	(sqrt (+ (* x x) (* y y)))
13.0ms	(sqrt (+ (* x x) (* y y)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sqrt (+ (* x x) (* y y)))
59.0ms	(sqrt (+ (* x x) (* y y)))
53.0ms	(sqrt (+ (* x x) (* y y)))
58.0ms	(sqrt (+ (* x x) (* y y)))

simplify2.8s

Counts

72 → 72

Iterations

Useful iterations: 3 (146.0ms)

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

prune422.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 10.3b

regimes368.0ms

Accuracy

57.5% (10.1b remaining)

Error of 17.9b against oracle of 7.8b and baseline of 31.5b

bsearch128.0ms

Steps

Iters	Range		Point
8	9.007393288790337e+101	4.198803265377596e+104	1.921239608950814e+104
5	1.804245684862004e-220	4.755976263225887e-220	1.914133431995725e-220
9	-2.18846814877946e-261	-3.2700529469739983e-270	-3.6872979313797757e-267
7	-3.9404683775550396e+127	-1.0954634436734111e+126	-5.292452664608309e+126

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	36
1	20	36
done	20	36

end0.0ms

sample666.0ms

Algorithm

intervals

Results

399.0ms

8000×

body

valid