Details

sample33.0ms

Algorithm

intervals

Results

12.0ms	131×	body	80	valid
7.0ms	51×	body	1280	valid
5.0ms	39×	body	640	valid
2.0ms	26×	body	320	valid
1.0ms	9×	body	160	valid

simplify206.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
15	168
14	165
13	136
12	114
11	99
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
2.5b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity`
60×	`times-frac`
57×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
20×	`distribute-lft-out`
18×	`distribute-lft-out--`
14×	`difference-of-squares`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`difference-of-sqr-1` `add-log-exp`
4×	`associate-/r/`
3×	`pow1` `insert-posit16`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `flip-+` `div-inv` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 117

Calls

3 calls:

22.0ms	(/ x (+ x 1))
48.0ms	(/ (+ x 1) (- x 1))
115.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series157.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(/ x (+ x 1))
34.0ms	(/ (+ x 1) (- x 1))
93.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.8s

Counts

126 → 126

Iterations

Iter	Nodes
done	5008
3	3663
2	1074
1	399
0	180

prune505.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1))
0.1b	(* (/ (+ x 1) (- (* x x) (* 1 1))) (+ x 1))
7.8b	(- (/ x (+ x 1)) (* (/ (+ x 1) (- (* x x) (* 1 1))) (+ x 1)))
14.3b	(/ (+ x 1) (- (* x x) (* 1 1)))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity`
45×	`times-frac`
38×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
22×	`associate-l`
14×	`distribute-lft-out`
13×	`add-cbrt-cube` `add-exp-log`
9×	`difference-of-squares`
8×	`associate-/r*`
7×	`associate-/l*`
6×	`pow1` `flip3-+` `associate-/r/` `flip-+` `add-log-exp`
5×	`frac-sub`
4×	`frac-times` `associate-r` `associate-*r/` `insert-posit16`
3×	`cbrt-undiv` `flip3--` `div-exp` `div-inv` `flip--`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `associate-*l/` `prod-exp` `cbrt-unprod` `associate--r+` `unswap-sqr` `associate-/l/`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 144

Calls

4 calls:

10.0ms	(/ x (+ x 1))
98.0ms	(* (/ (+ x 1) (- (* x x) (* 1 1))) (+ x 1))
94.0ms	(- (/ x (+ x 1)) (* (/ (+ x 1) (- (* x x) (* 1 1))) (+ x 1)))
26.0ms	(/ (+ x 1) (- (* x x) (* 1 1)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ x (+ x 1))
53.0ms	(* (/ (+ x 1) (- (* x x) (* 1 1))) (+ x 1))
133.0ms	(- (/ x (+ x 1)) (* (/ (+ x 1) (- (* x x) (* 1 1))) (+ x 1)))
37.0ms	(/ (+ x 1) (- (* x x) (* 1 1)))

simplify3.0s

Counts

156 → 156

Iterations

Iter	Nodes
done	5002
2	2838
1	759
0	232

prune525.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* x x) (* 1 1)) (- x 1))
0.1b	(* (- (* x x) (* 1 1)) (- x 1))
0.1b	(* (+ x 1) (- (* x x) (* 1 1)))
25.5b	(- (* x (* (- (* x x) (* 1 1)) (- x 1))) (* (+ x 1) (* (+ x 1) (- (* x x) (* 1 1)))))

rewrite391.0ms

Algorithm

rewrite-expression-head

Rules

384×	`associate-*r/`
340×	`frac-times`
246×	`flip3--` `flip--`
208×	`frac-sub`
147×	`flip3-+` `flip-+`
124×	`associate-*l/`
24×	`add-sqr-sqrt`
22×	`distribute-rgt-in` `distribute-lft-in`
18×	`-un-lft-identity` `associate-r*`
15×	`sub-neg`
12×	`associate-l`
10×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
8×	`associate--l+` `associate--r+`
7×	`difference-of-squares`
6×	`add-log-exp`
4×	`insert-posit16`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`difference-of-sqr-1` `distribute-lft-out--` `sub-div`
1×	`diff-log` `distribute-lft-out`

Counts

4 → 344

Calls

4 calls:

49.0ms	(* (- (* x x) (* 1 1)) (- x 1))
45.0ms	(* (- (* x x) (* 1 1)) (- x 1))
80.0ms	(* (+ x 1) (- (* x x) (* 1 1)))
182.0ms	(- (* x (* (- (* x x) (* 1 1)) (- x 1))) (* (+ x 1) (* (+ x 1) (- (* x x) (* 1 1)))))

series160.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (- (* x x) (* 1 1)) (- x 1))
39.0ms	(* (- (* x x) (* 1 1)) (- x 1))
36.0ms	(* (+ x 1) (- (* x x) (* 1 1)))
54.0ms	(- (* x (* (- (* x x) (* 1 1)) (- x 1))) (* (+ x 1) (* (+ x 1) (- (* x x) (* 1 1)))))

simplify3.3s

Counts

356 → 356

Iterations

Iter	Nodes
done	5000
1	3881
0	954

prune2.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x x) (* x x))
6.0b	(/ (- (* x (* (- (* x x) (* 1 1)) (- x 1))) (* (+ x 1) (/ (* (+ x 1) (+ (* (* x x) (* x x)) -1)) (+ (* x x) (* 1 1))))) (* (+ x 1) (* (- (* x x) (* 1 1)) (- x 1))))
18.7b	(/ (* (+ x 1) (+ (* (* x x) (* x x)) -1)) (+ (* x x) (* 1 1)))
28.2b	(- (* x (* (- (* x x) (* 1 1)) (- x 1))) (* (+ x 1) (/ (* (+ x 1) (+ (* (* x x) (* x x)) -1)) (+ (* x x) (* 1 1)))))

rewrite484.0ms

Algorithm

rewrite-expression-head

Rules

136×	`associate-*r/`
115×	`pow1`
104×	`frac-times`
82×	`flip--`
80×	`flip3--` `frac-sub`
64×	`associate-*l/`
51×	`associate-/l/`
48×	`flip3-+` `flip-+`
36×	`pow-prod-up`
30×	`add-cbrt-cube` `add-exp-log`
28×	`associate-/r/`
23×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
13×	`pow2`
12×	`prod-exp` `cbrt-unprod`
8×	`distribute-rgt-in` `add-sqr-sqrt` `*-un-lft-identity` `distribute-lft-in` `associate--l+` `add-cube-cbrt`
6×	`times-frac` `add-log-exp`
5×	`cbrt-undiv` `sub-neg` `div-exp`
4×	`associate-/r` `insert-posit16` `associate-/l`
2×	`clear-num` `frac-2neg` `div-inv` `sub-div`
1×	`diff-log` `div-sub` `swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

4 → 252

Calls

4 calls:

29.0ms	(* (* x x) (* x x))
225.0ms	(/ (- (* x (* (- (* x x) (* 1 1)) (- x 1))) (* (+ x 1) (/ (* (+ x 1) (+ (* (* x x) (* x x)) -1)) (+ (* x x) (* 1 1))))) (* (+ x 1) (* (- (* x x) (* 1 1)) (- x 1))))
108.0ms	(/ (* (+ x 1) (+ (* (* x x) (* x x)) -1)) (+ (* x x) (* 1 1)))
107.0ms	(- (* x (* (- (* x x) (* 1 1)) (- x 1))) (* (+ x 1) (/ (* (+ x 1) (+ (* (* x x) (* x x)) -1)) (+ (* x x) (* 1 1)))))

series650.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* x x) (* x x))
321.0ms	(/ (- (* x (* (- (* x x) (* 1 1)) (- x 1))) (* (+ x 1) (/ (* (+ x 1) (+ (* (* x x) (* x x)) -1)) (+ (* x x) (* 1 1))))) (* (+ x 1) (* (- (* x x) (* 1 1)) (- x 1))))
61.0ms	(/ (* (+ x 1) (+ (* (* x x) (* x x)) -1)) (+ (* x x) (* 1 1)))
231.0ms	(- (* x (* (- (* x x) (* 1 1)) (- x 1))) (* (+ x 1) (/ (* (+ x 1) (+ (* (* x x) (* x x)) -1)) (+ (* x x) (* 1 1)))))

simplify2.3s

Counts

264 → 264

Iterations

Iter	Nodes
done	5000
1	2153
0	519

prune1.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.5b

bsearch138.0ms

Steps

Iters	Range		Point
8	29.100869698027953	73049.03827748532	10392.525291699138
9	-343836526097.91516	-3489.5785602046144	-10953.989244522425

simplify13.0ms

Iterations

Iter	Nodes
done	47
3	47
2	43
1	35
0	23

end0.0ms

sample1.8s

Algorithm

intervals

Results

662.0ms	678×	body	320	valid
491.0ms	1660×	body	1280	valid
242.0ms	1207×	body	640	valid
210.0ms	4154×	body	80	valid
29.0ms	301×	body	160	valid