Details

sample31.0ms

Algorithm

intervals

Results

9.0ms	54×	body	1280	valid
5.0ms	44×	body	640	valid
4.0ms	132×	body	80	valid
2.0ms	19×	body	320	valid
0.0ms	7×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
12	4085
11	1745
10	535
9	183
8	79
7	58
6	39
5	27
4	21
3	19
2	16
1	12
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ 1.0 x))
0.0b	(/ (+ 1.0 x) (- x 1.0))
2.7b	(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (- x 1.0)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
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 → 104

Calls

3 calls:

20.0ms	(/ x (+ 1.0 x))
33.0ms	(/ (+ 1.0 x) (- x 1.0))
112.0ms	(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (- x 1.0)))

series290.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ x (+ 1.0 x))
57.0ms	(/ (+ 1.0 x) (- x 1.0))
191.0ms	(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (- x 1.0)))

simplify907.0ms

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	1826
1	417
0	178

prune441.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ x (+ 1.0 x)) (/ (+ 1.0 x) (- x 1.0)))
0.0b	(* (/ (+ 1.0 x) (- x 1.0)) (/ (+ 1.0 x) (- x 1.0)))
0.0b	(* (/ x (+ 1.0 x)) (/ x (+ 1.0 x)))
2.6b	(- (* (/ x (+ 1.0 x)) (/ x (+ 1.0 x))) (* (/ (+ 1.0 x) (- x 1.0)) (/ (+ 1.0 x) (- x 1.0))))

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

342×	`*-un-lft-identity`
208×	`times-frac`
152×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
73×	`distribute-lft-out`
72×	`swap-sqr`
44×	`associate-r` `associate-l`
36×	`distribute-lft-out--`
28×	`add-cbrt-cube` `add-exp-log`
21×	`difference-of-squares`
18×	`pow1`
16×	`associate-/r/`
9×	`frac-sub`
8×	`frac-times` `cbrt-undiv` `div-exp` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `div-inv` `add-log-exp` `unswap-sqr`
5×	`flip3-+` `flip3--` `flip-+` `flip--`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log` `frac-add`

Counts

4 → 259

Calls

4 calls:

91.0ms	(+ (/ x (+ 1.0 x)) (/ (+ 1.0 x) (- x 1.0)))
91.0ms	(* (/ (+ 1.0 x) (- x 1.0)) (/ (+ 1.0 x) (- x 1.0)))
88.0ms	(* (/ x (+ 1.0 x)) (/ x (+ 1.0 x)))
17.0ms	(- (* (/ x (+ 1.0 x)) (/ x (+ 1.0 x))) (* (/ (+ 1.0 x) (- x 1.0)) (/ (+ 1.0 x) (- x 1.0))))

series570.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(+ (/ x (+ 1.0 x)) (/ (+ 1.0 x) (- x 1.0)))
88.0ms	(* (/ (+ 1.0 x) (- x 1.0)) (/ (+ 1.0 x) (- x 1.0)))
58.0ms	(* (/ x (+ 1.0 x)) (/ x (+ 1.0 x)))
303.0ms	(- (* (/ x (+ 1.0 x)) (/ x (+ 1.0 x))) (* (/ (+ 1.0 x) (- x 1.0)) (/ (+ 1.0 x) (- x 1.0))))

simplify646.0ms

Counts

271 → 271

Iterations

Iter	Nodes
done	5000
1	1269
0	367

prune854.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (- x 1.0) x) (* (+ 1.0 x) (+ 1.0 x))) (* (+ 1.0 x) (- x 1.0)))
0.0b	(* (+ 1.0 x) (+ 1.0 x))
0.0b	(* (+ 1.0 x) (- x 1.0))
18.5b	(- (* (- x 1.0) x) (* (+ 1.0 x) (+ 1.0 x)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

46×	`associate-*l/`
36×	`flip3-+` `flip-+`
32×	`frac-sub`
30×	`*-un-lft-identity`
28×	`frac-times`
24×	`flip3--` `flip--`
18×	`add-sqr-sqrt` `associate-/l/`
14×	`associate-*r/`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`add-cube-cbrt`
9×	`associate-r`
8×	`associate-l` `associate-/r/`
7×	`distribute-lft-out`
6×	`swap-sqr` `add-log-exp`
4×	`distribute-rgt-in` `distribute-lft-in`
3×	`sub-neg` `times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `associate--r+` `unswap-sqr`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `diff-log` `div-sub` `pow-sqr` `pow-prod-up` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 151

Calls

4 calls:

67.0ms	(/ (- (* (- x 1.0) x) (* (+ 1.0 x) (+ 1.0 x))) (* (+ 1.0 x) (- x 1.0)))
51.0ms	(* (+ 1.0 x) (+ 1.0 x))
34.0ms	(* (+ 1.0 x) (- x 1.0))
26.0ms	(- (* (- x 1.0) x) (* (+ 1.0 x) (+ 1.0 x)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (- (* (- x 1.0) x) (* (+ 1.0 x) (+ 1.0 x))) (* (+ 1.0 x) (- x 1.0)))
31.0ms	(* (+ 1.0 x) (+ 1.0 x))
130.0ms	(* (+ 1.0 x) (- x 1.0))
51.0ms	(- (* (- x 1.0) x) (* (+ 1.0 x) (+ 1.0 x)))

simplify466.0ms

Counts

163 → 163

Iterations

Iter	Nodes
done	5001
1	879
0	256

prune846.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (* 3.0 x))
0.0b	(* (+ 1.0 x) (- x 1.0))
15.0b	(/ (- (+ 1.0 (* 3.0 x))) (* (+ 1.0 x) (- x 1.0)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
10×	`times-frac` `add-cbrt-cube` `add-exp-log` `associate-/l*`
8×	`frac-times` `flip3-+` `associate-/r/` `flip-+`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `flip3--` `flip--`
5×	`pow1` `associate-r` `add-log-exp`
4×	`associate-l` `associate-l/` `associate-r/`
2×	`distribute-rgt-in` `cbrt-undiv` `neg-mul-1` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `cbrt-unprod` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `div-sub` `pow-prod-down` `distribute-frac-neg` `-commutative` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 91

Calls

3 calls:

8.0ms	(+ 1.0 (* 3.0 x))
55.0ms	(* (+ 1.0 x) (- x 1.0))
44.0ms	(/ (- (+ 1.0 (* 3.0 x))) (* (+ 1.0 x) (- x 1.0)))

series337.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(+ 1.0 (* 3.0 x))
150.0ms	(* (+ 1.0 x) (- x 1.0))
118.0ms	(/ (- (+ 1.0 (* 3.0 x))) (* (+ 1.0 x) (- x 1.0)))

simplify1.3s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	3087
1	496
0	173

prune425.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	15
1	15
0	11

end0.0ms

sample1.7s

Algorithm

intervals

Results

904.0ms	1659×	body	1280	valid
279.0ms	1242×	body	640	valid
233.0ms	4183×	body	80	valid
87.0ms	629×	body	320	valid
26.0ms	287×	body	160	valid