Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify306.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	17	19
2	35	19
3	67	19
4	111	19
5	158	19
6	173	19
7	174	19
done	174	19

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
4.7b	(- (* x x) (* (* y 4.0) y))
30.6b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

17.0ms	(+ (* x x) (* (* y 4.0) y))
16.0ms	(- (* x x) (* (* y 4.0) y))
53.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series241.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(+ (* x x) (* (* y 4.0) y))
71.0ms	(- (* x x) (* (* y 4.0) y))
111.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify2.5s

Counts

64 → 64

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	87	1404
1	233	1375
2	769	1233
3	2891	1226
done	5001	1210

prune189.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize1.0ms

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

prune11.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
0.0b	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
4.7b	(- (* x x) (* (* y 4.0) y))
30.6b	(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`div-exp` `add-log-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`rec-exp` `frac-2neg` `flip3-+` `1-exp` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `pow-flip` `diff-log` `sum-log` `inv-pow`

Counts

4 → 138

Calls

4 calls:

14.0ms	(+ (* x x) (* (* y 4.0) y))
45.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
13.0ms	(- (* x x) (* (* y 4.0) y))
55.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ (* x x) (* (* y 4.0) y))
67.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
48.0ms	(- (* x x) (* (* y 4.0) y))
67.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

simplify3.0s

Counts

150 → 150

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	192	4490
1	447	4224
2	1158	3827
3	4188	3710
done	5001	3710

prune365.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

localize14.0ms

Local error

Found 4 expressions with local error:

4.7b	(- (* x x) (* (* y 4.0) y))
29.1b	(sqrt (+ (* x x) (* (* y 4.0) y)))
29.1b	(sqrt (+ (* x x) (* (* y 4.0) y)))
30.6b	(/ (- (* x x) (* (* y 4.0) y)) (* (sqrt (+ (* x x) (* (* y 4.0) y))) (sqrt (+ (* x x) (* (* y 4.0) y)))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

11.0ms	(- (* x x) (* (* y 4.0) y))
8.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
13.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
49.0ms	(/ (- (* x x) (* (* y 4.0) y)) (* (sqrt (+ (* x x) (* (* y 4.0) y))) (sqrt (+ (* x x) (* (* y 4.0) y)))))

series331.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (* x x) (* (* y 4.0) y))
101.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
68.0ms	(sqrt (+ (* x x) (* (* y 4.0) y)))
88.0ms	(/ (- (* x x) (* (* y 4.0) y)) (* (sqrt (+ (* x x) (* (* y 4.0) y))) (sqrt (+ (* x x) (* (* y 4.0) y)))))

simplify2.4s

Counts

86 → 86

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	108	2118
1	289	1662
2	923	1450
3	3586	1426
done	5000	1426

prune291.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.6b

regimes204.0ms

Accuracy

61.6% (12.1b remaining)

Error of 12.4b against oracle of 0.4b and baseline of 31.8b

bsearch135.0ms

Steps

Iters	Range		Point
9	8.159449298811563e+284	2.5807847408175677e+291	7.251271519567313e+285
6	5.513526497765108e+28	7.5214253074415e+29	5.630971785438847e+28
10	1730015830381252.2	5.608395996213628e+25	2.5951328951665388e+25
8	1.6369066125026377e-180	2.6572673748491515e-176	1.8839870956276886e-179

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	25	81
1	30	77
done	30	77

end0.0ms

sample901.0ms

Algorithm

intervals

Results

594.0ms

8000×

body

valid