Details

sample21.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	7
1	7
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
28.9b	(sqrt (+ (* x x) (* y y)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

9.0ms	(+ (* x x) (* y y))
7.0ms	(sqrt (+ (* x x) (* y y)))

series91.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ (* x x) (* y y))
57.0ms	(sqrt (+ (* x x) (* y y)))

simplify476.0ms

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
2	770
1	142
0	48

prune143.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.5b

localize19.0ms

Local error

Found 4 expressions with local error:

28.9b	(sqrt (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))))
29.9b	(cbrt (+ (* x x) (* y y)))
29.9b	(cbrt (+ (* x x) (* y y)))
29.9b	(cbrt (+ (* x x) (* y y)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

110.0ms	(sqrt (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))))
8.0ms	(cbrt (+ (* x x) (* y y)))
7.0ms	(cbrt (+ (* x x) (* y y)))
8.0ms	(cbrt (+ (* x x) (* y y)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(sqrt (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))))
156.0ms	(cbrt (+ (* x x) (* y y)))
128.0ms	(cbrt (+ (* x x) (* y y)))
151.0ms	(cbrt (+ (* x x) (* y y)))

simplify1.9s

Counts

101 → 101

Iterations

Iter	Nodes
done	5004
3	2997
2	701
1	305
0	164

prune609.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.5b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
5.8b	(exp (log (sqrt (+ (* x x) (* y y)))))
28.9b	(sqrt (+ (* x x) (* y y)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `log-prod` `exp-prod` `exp-sum` `sqrt-prod`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`flip3-+` `add-cbrt-cube` `add-exp-log` `log-pow` `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:

12.0ms	(+ (* x x) (* y y))
16.0ms	(exp (log (sqrt (+ (* x x) (* y y)))))
13.0ms	(sqrt (+ (* x x) (* y y)))

series167.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(+ (* x x) (* y y))
51.0ms	(exp (log (sqrt (+ (* x x) (* y y)))))
59.0ms	(sqrt (+ (* x x) (* y y)))

simplify603.0ms

Counts

57 → 57

Iterations

Iter	Nodes
done	5001
2	919
1	191
0	87

prune288.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.5b

localize47.0ms

Local error

Found 4 expressions with local error:

5.8b	(pow (exp (* (cbrt (log (sqrt (+ (* y y) (* x x))))) (cbrt (log (sqrt (+ (* y y) (* x x))))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))
28.9b	(sqrt (+ (* x x) (* y y)))
28.9b	(sqrt (+ (* y y) (* x x)))
28.9b	(sqrt (+ (* y y) (* x x)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

13.0ms	(pow (exp (* (cbrt (log (sqrt (+ (* y y) (* x x))))) (cbrt (log (sqrt (+ (* y y) (* x x))))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))
11.0ms	(sqrt (+ (* x x) (* y y)))
11.0ms	(sqrt (+ (* y y) (* x x)))
12.0ms	(sqrt (+ (* y y) (* x x)))

series543.0ms

Counts

4 → 12

Calls

4 calls:

362.0ms	(pow (exp (* (cbrt (log (sqrt (+ (* y y) (* x x))))) (cbrt (log (sqrt (+ (* y y) (* x x))))))) (cbrt (log (sqrt (+ (* x x) (* y y))))))
56.0ms	(sqrt (+ (* x x) (* y y)))
51.0ms	(sqrt (+ (* y y) (* x x)))
74.0ms	(sqrt (+ (* y y) (* x x)))

simplify564.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	930
1	282
0	115

prune691.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes604.0ms

Accuracy

43.9% (17.3b remaining)

Error of 17.7b against oracle of 0.4b and baseline of 31.2b

bsearch48.0ms

Steps

Iters	Range		Point
5	1.9240342807455842e+87	5.124373845119881e+87	5.0402268372340346e+87
9	-4.835830320260309e+116	-5.2561174750454686e+110	-3.678618962503878e+116

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	13

end0.0ms

sample759.0ms

Algorithm

intervals

Results

431.0ms

8000×

body

valid