Details

sample26.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify263.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
3.8b	(- (* x x) (* (* y 4.0) y))
28.6b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite66.0ms

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:

15.0ms	(+ (* x x) (* (* y 4.0) y))
11.0ms	(- (* x x) (* (* y 4.0) y))
38.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (* x x) (* (* y 4.0) y))
43.0ms	(- (* x x) (* (* y 4.0) y))
68.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify3.2s

Counts

64 → 64

Iterations

Useful iterations: done (3.2s)

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

prune210.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
0.0b	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
20.9b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
21.8b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

8.0ms	(+ (* x x) (* (* y 4.0) y))
100.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
44.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
33.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+ (* x x) (* (* y 4.0) y))
116.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
76.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
69.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

simplify1.6s

Counts

91 → 91

Iterations

Useful iterations: 2 (313.0ms)

Iter	Nodes	Cost
0	142	2132
1	384	2013
2	1397	1747
done	5000	1747

prune301.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

9.6b	(sqrt (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
20.9b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
20.9b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
21.8b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

27.0ms	(sqrt (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
45.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
56.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
17.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(sqrt (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
66.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
79.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
71.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

simplify1.5s

Counts

105 → 105

Iterations

Useful iterations: 2 (232.0ms)

Iter	Nodes	Cost
0	128	2114
1	320	2009
2	1232	1683
done	5000	1683

prune411.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

9.6b	(sqrt (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
20.9b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
20.9b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
21.8b	(/ (+ (* x x) (* (* y 4.0) y)) (* x x))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

20.0ms	(sqrt (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
33.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
63.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
47.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (* x x))

series387.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(sqrt (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
94.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
88.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
72.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (* x x))

simplify1.6s

Counts

105 → 105

Iterations

Useful iterations: 2 (359.0ms)

Iter	Nodes	Cost
0	133	2141
1	334	2032
2	1248	1702
done	5000	1702

prune489.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

regimes243.0ms

Accuracy

56.4% (13.4b remaining)

Error of 13.9b against oracle of 0.4b and baseline of 31.2b

bsearch290.0ms

Steps

Iters	Range		Point
9	9556.682540875734	15966983906.555069	98355.24381927797
9	4.924640387312937e-45	2.5480243600333034e-37	8.134021215145638e-38
9	1.5895540584967369e-59	9.417139633880594e-52	1.5753976874379915e-55
7	-4.0684965810982345e-160	-4.482309770999907e-162	-1.636890293131895e-160
10	-2.7913152028957945e+157	-7.954806027061161e+143	-4.75816735826197e+148

simplify12.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	31	124
1	36	124
done	36	124

end0.0ms

sample813.0ms

Algorithm

intervals

Results

549.0ms

8000×

body

valid