Details

sample42.0ms

Algorithm

intervals

Results

18.0ms

256×

body

valid

simplify21.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	20	12
3	22	12
done	22	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
35.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 39

Calls

3 calls:

15.0ms	(+ (* x x) (* y y))
54.0ms	(+ (+ (* x x) (* y y)) (* z z))
67.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series278.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ (* x x) (* y y))
63.0ms	(+ (+ (* x x) (* y y)) (* z z))
169.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify976.0ms

Counts

48 → 48

Iterations

Useful iterations: 2 (222.0ms)

Iter	Nodes	Cost
0	74	742
1	245	696
2	1298	621
done	5002	621

prune347.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
0.6b	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
35.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite483.0ms

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:

61.0ms	(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
294.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
63.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
55.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series706.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
174.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
182.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
182.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.8s

Counts

146 → 146

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	130	4100
1	290	2689
2	1472	2489
done	5000	2442

prune868.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 16.2b

localize93.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (cbrt (sqrt (sqrt (+ (+ (* y y) (* z z)) (* x x))))) (+ 3 1))
35.7b	(sqrt (+ (+ (* y y) (* z z)) (* x x)))
35.7b	(sqrt (+ (+ (* y y) (* z z)) (* x x)))
35.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

18×	`sqrt-prod`
15×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt` `unpow-prod-down`
9×	`cbrt-prod`
8×	`pow1`
6×	`sqrt-div`
5×	`add-exp-log`
4×	`pow-unpow` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`pow-pow`
1×	`unpow-prod-up` `pow-to-exp` `pow1/3` `pow-exp` `distribute-lft-out` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

68.0ms	(pow (cbrt (sqrt (sqrt (+ (+ (* y y) (* z z)) (* x x))))) (+ 3 1))
50.0ms	(sqrt (+ (+ (* y y) (* z z)) (* x x)))
52.0ms	(sqrt (+ (+ (* y y) (* z z)) (* x x)))
53.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series697.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(pow (cbrt (sqrt (sqrt (+ (+ (* y y) (* z z)) (* x x))))) (+ 3 1))
170.0ms	(sqrt (+ (+ (* y y) (* z z)) (* x x)))
161.0ms	(sqrt (+ (+ (* y y) (* z z)) (* x x)))
160.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.0s

Counts

86 → 86

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	141	1801
1	398	1535
2	1539	1431
done	5001	1429

prune902.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 16.2b

localize4.0ms

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 (3 fresh and 3 done)

Merged error: 16.2b

regimes1.2s

Accuracy

62.5% (7.3b remaining)

Error of 25.7b against oracle of 18.4b and baseline of 38.0b

bsearch209.0ms

Steps

Iters	Range		Point
9	6.578703183529628e+91	1.1448241580470724e+99	1.119152176003768e+99
10	-7.556856097197653e-296	2.9792793194115403e-307	-1.7754786637459033e-299
9	-1.1739783025602866e-268	-1.5231580497035754e-273	-1.5378615096700336e-273
8	-1.4374651696982963e+145	-2.0346029743301018e+142	-3.983694464815315e+143

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	44
1	24	44
done	24	44

end0.0ms

sample1.1s

Algorithm

intervals

Results

698.0ms

8000×

body

valid