Details

sample19.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
35.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite73.0ms

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))
60.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series165.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(+ (* x x) (* y y))
132.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.7s

Counts

32 → 32

Iterations

Useful iterations: 3 (265.0ms)

Iter	Nodes	Cost
0	63	471
1	172	417
2	496	387
3	1364	377
4	4252	377
done	5001	377

prune103.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.1b

localize25.0ms

Local error

Found 4 expressions with local error:

31.0b	(cbrt (+ (* x x) (* y y)))
31.0b	(cbrt (+ (* x x) (* y y)))
31.0b	(cbrt (+ (* x x) (* y y)))
35.1b	(sqrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

8.0ms	(cbrt (+ (* x x) (* y y)))
8.0ms	(cbrt (+ (* x x) (* y y)))
8.0ms	(cbrt (+ (* x x) (* y y)))
156.0ms	(sqrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(cbrt (+ (* x x) (* y y)))
106.0ms	(cbrt (+ (* x x) (* y y)))
109.0ms	(cbrt (+ (* x x) (* y y)))
134.0ms	(sqrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

simplify3.2s

Counts

66 → 66

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	83	1438
1	204	1347
2	480	829
3	1257	814
4	4436	814
done	5001	793

prune339.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 17.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
35.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite169.0ms

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:

31.0ms	(cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
53.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
50.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series549.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
153.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
130.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
121.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.8s

Counts

73 → 73

Iterations

Useful iterations: 3 (312.0ms)

Iter	Nodes	Cost
0	77	1358
1	163	1230
2	426	1156
3	1273	1106
4	4525	1106
done	5002	1106

prune270.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 17.1b

localize18.0ms

Local error

Found 4 expressions with local error:

4.4b	(exp (log (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
35.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite138.0ms

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:

32.0ms	(exp (log (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
34.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
32.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
38.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series551.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(exp (log (cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
142.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
139.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
132.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.7s

Counts

81 → 81

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	118	1561
1	210	1367
2	483	1231
3	1348	1181
4	4604	1169
done	5000	1169

prune392.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 17.1b

regimes446.0ms

Accuracy

61.8% (7.5b remaining)

Error of 25.4b against oracle of 17.9b and baseline of 37.5b

bsearch36.0ms

Steps

Iters	Range		Point
10	4.022397810881141e+88	1.565796980266273e+101	1.537188568549187e+101
1	-4.90105109200061e+89	-4.6551667645331244e+89	-4.839580010133739e+89

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	23
1	18	23
done	18	23

end0.0ms

sample776.0ms

Algorithm

intervals

Results

537.0ms

8000×

body

valid