Details

sample33.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	7
1	7
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
28.4b	(sqrt (+ (* x x) (* y y)))

rewrite25.0ms

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:

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

series92.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify1.1s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
2	770
1	142
0	48

prune249.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.5b	(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
28.4b	(sqrt (+ (* x x) (* y y)))
28.4b	(sqrt (+ (* x x) (* y y)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

6.0ms	(+ (* x x) (* y y))
52.0ms	(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
6.0ms	(sqrt (+ (* x x) (* y y)))
13.0ms	(sqrt (+ (* x x) (* y y)))

series184.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x x) (* y y))
54.0ms	(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
50.0ms	(sqrt (+ (* x x) (* y y)))
50.0ms	(sqrt (+ (* x x) (* y y)))

simplify2.0s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
2	1649
1	292
0	121

prune604.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 9.0b

localize20.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (* x x) (* y y))
3.3b	(- (* x x) (* y y))
28.4b	(sqrt (/ (* (+ (* x x) (* y y)) (- (* x x) (* y y))) (- (* x x) (* y y))))
39.2b	(/ (* (+ (* x x) (* y y)) (- (* x x) (* y y))) (- (* x x) (* y y)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

10×	`sqrt-prod`
9×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `times-frac` `add-cube-cbrt` `add-log-exp` `associate-/l/`
7×	`flip3--` `flip--`
5×	`pow1` `difference-of-squares`
4×	`frac-times` `associate-/r*` `associate-/r/`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-l/` `associate-r/` `div-inv`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `prod-exp` `cbrt-unprod` `associate-/l*`

Counts

4 → 80

Calls

4 calls:

6.0ms	(- (* x x) (* y y))
8.0ms	(- (* x x) (* y y))
35.0ms	(sqrt (/ (* (+ (* x x) (* y y)) (- (* x x) (* y y))) (- (* x x) (* y y))))
44.0ms	(/ (* (+ (* x x) (* y y)) (- (* x x) (* y y))) (- (* x x) (* y y)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* x x) (* y y))
45.0ms	(- (* x x) (* y y))
47.0ms	(sqrt (/ (* (+ (* x x) (* y y)) (- (* x x) (* y y))) (- (* x x) (* y y))))
46.0ms	(/ (* (+ (* x x) (* y y)) (- (* x x) (* y y))) (- (* x x) (* y y)))

simplify2.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	2684
1	356
0	112

prune372.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 9.0b

localize3.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune1.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 9.0b

regimes530.0ms

Accuracy

56.3% (10.4b remaining)

Error of 18.0b against oracle of 7.6b and baseline of 31.5b

bsearch71.0ms

Steps

Iters	Range		Point
10	1.770057870633885e+84	1.1610867076317608e+95	1.1493803764036757e+95
9	-7.317563595848081e+70	-3.473568020675254e+63	-1.9401195934627838e+70

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	13

end0.0ms

sample569.0ms

Algorithm

intervals

Results

290.0ms

8000×

body

valid