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: 29.3b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

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:

8.0ms	(+ (* x x) (* y y))
9.0ms	(sqrt (+ (* x x) (* y y)))

series79.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(+ (* x x) (* y y))
41.0ms	(sqrt (+ (* x x) (* y y)))

simplify2.5s

Counts

32 → 32

Iterations

Useful iterations: 2 (81.0ms)

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

prune86.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
5.5b	(exp (log (sqrt (+ (* x x) (* y y)))))
27.4b	(sqrt (+ (* x x) (* y y)))

rewrite29.0ms

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:

8.0ms	(+ (* x x) (* y y))
11.0ms	(exp (log (sqrt (+ (* x x) (* y y)))))
8.0ms	(sqrt (+ (* x x) (* y y)))

series118.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* x x) (* y y))
40.0ms	(exp (log (sqrt (+ (* x x) (* y y)))))
45.0ms	(sqrt (+ (* x x) (* y y)))

simplify2.4s

Counts

57 → 57

Iterations

Useful iterations: 4 (1.2s)

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

prune154.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
6.3b	(pow (exp 1/2) (log (+ (* x x) (* y y))))
28.4b	(log (+ (* x x) (* y y)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `log-prod`
5×	`add-log-exp`
4×	`add-exp-log` `log-div` `pow-unpow` `pow-pow`
3×	`unpow-prod-up` `unpow-prod-down` `exp-prod` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`log-pow` `pow-sub`
1×	`+-commutative` `pow-to-exp` `rem-log-exp` `pow-exp` `sum-log` `sqr-pow`

Counts

3 → 51

Calls

3 calls:

11.0ms	(+ (* x x) (* y y))
20.0ms	(pow (exp 1/2) (log (+ (* x x) (* y y))))
9.0ms	(log (+ (* x x) (* y y)))

series232.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (* x x) (* y y))
129.0ms	(pow (exp 1/2) (log (+ (* x x) (* y y))))
63.0ms	(log (+ (* x x) (* y y)))

simplify2.6s

Counts

60 → 60

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	96	872
1	239	822
2	572	714
3	1369	714
4	3795	714
done	5001	708

prune217.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.3b

localize47.0ms

Local error

Found 4 expressions with local error:

5.8b	(pow (pow (exp 1/2) (* (cbrt (log (+ (* x x) (* y y)))) (cbrt (log (+ (* x x) (* y y)))))) (cbrt (log (+ (* x x) (* y y)))))
28.4b	(log (+ (* x x) (* y y)))
28.4b	(log (+ (* x x) (* y y)))
28.4b	(log (+ (* x x) (* y y)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

9.0ms	(pow (pow (exp 1/2) (* (cbrt (log (+ (* x x) (* y y)))) (cbrt (log (+ (* x x) (* y y)))))) (cbrt (log (+ (* x x) (* y y)))))
7.0ms	(log (+ (* x x) (* y y)))
7.0ms	(log (+ (* x x) (* y y)))
7.0ms	(log (+ (* x x) (* y y)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

431.0ms	(pow (pow (exp 1/2) (* (cbrt (log (+ (* x x) (* y y)))) (cbrt (log (+ (* x x) (* y y)))))) (cbrt (log (+ (* x x) (* y y)))))
57.0ms	(log (+ (* x x) (* y y)))
54.0ms	(log (+ (* x x) (* y y)))
53.0ms	(log (+ (* x x) (* y y)))

simplify2.7s

Counts

81 → 81

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	111	1966
1	252	1846
2	543	1603
3	1372	1562
4	4016	1561
done	5000	1561

prune332.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.3b

regimes430.0ms

Accuracy

58.6% (9.6b remaining)

Error of 17.5b against oracle of 7.9b and baseline of 31.2b

bsearch65.0ms

Steps

Iters	Range		Point
9	3.828787491213863e+135	1.1582935083099526e+141	2.931608767883357e+138
9	-2.0350997751618612e+124	-4.455739765009825e+115	-8.953163933293596e+119

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample732.0ms

Algorithm

intervals

Results

445.0ms

8000×

body

valid