Details

sample65.0ms

Algorithm

intervals

Results

19.0ms	53×	body	640	valid
13.0ms	137×	body	80	valid
9.0ms	34×	body	320	valid
9.0ms	19×	body	1280	valid
3.0ms	13×	body	160	valid

simplify299.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	475
9	475
8	357
7	164
6	102
5	81
4	65
3	45
2	35
1	21
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
0.0b	(/ 1 (+ x 1))
2.7b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite342.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
58×	`add-sqr-sqrt`
56×	`times-frac`
25×	`add-cube-cbrt`
18×	`distribute-lft-out--`
17×	`distribute-lft-out`
14×	`difference-of-squares`
12×	`add-exp-log`
11×	`associate-/r*` `add-log-exp`
8×	`add-cbrt-cube` `div-inv`
6×	`pow1` `associate-/l*`
4×	`difference-of-sqr-1` `div-exp` `associate-/r/` `insert-posit16`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `rec-exp` `associate-+l+` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `1-exp` `frac-sub` `flip-+` `pow-flip` `inv-pow`
1×	`+-commutative` `associate-+l-`

Counts

4 → 141

Calls

4 calls:

18.0ms	(/ 1 (- x 1))
66.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
17.0ms	(/ 1 (+ x 1))
237.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series185.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1 (- x 1))
38.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
20.0ms	(/ 1 (+ x 1))
112.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify3.7s

Counts

153 → 153

Iterations

Iter	Nodes
done	5014
3	4675
2	1509
1	510
0	219

prune590.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))
15.9b	(+ (- (/ (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ 2 x)) (/ 1 (- x 1)))

rewrite601.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
12×	`cbrt-prod` `times-frac`
11×	`distribute-lft-out`
9×	`add-log-exp`
8×	`distribute-lft-out--`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `div-inv`
3×	`pow1/3` `frac-add`
2×	`associate-+l+` `sum-log`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `frac-sub` `associate-+l-` `flip--`

Counts

4 → 72

Calls

4 calls:

6.0ms	(cbrt (+ x 1))
6.0ms	(cbrt (+ x 1))
6.0ms	(cbrt (+ x 1))
582.0ms	(+ (- (/ (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ 2 x)) (/ 1 (- x 1)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(cbrt (+ x 1))
63.0ms	(cbrt (+ x 1))
45.0ms	(cbrt (+ x 1))
136.0ms	(+ (- (/ (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ 2 x)) (/ 1 (- x 1)))

simplify1.7s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	1301
1	370
0	140

prune421.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))
7.4b	(/ (+ (* (cbrt (+ x 1)) x) (* (+ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* -2 (cbrt (+ x 1)))) (+ x -1))) (* (* (cbrt (+ x 1)) x) (+ x -1)))
21.7b	(+ (* (cbrt (+ x 1)) x) (* (+ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* -2 (cbrt (+ x 1)))) (+ x -1)))

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

90×	`cbrt-div`
82×	`flip3-+` `flip-+`
80×	`associate-*l/` `frac-add`
36×	`frac-times`
34×	`associate-*r/`
30×	`associate-/l/`
13×	`add-exp-log`
12×	`*-un-lft-identity` `add-cbrt-cube`
8×	`cbrt-prod` `add-sqr-sqrt` `associate-/r/` `add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `insert-posit16`
3×	`cbrt-undiv` `times-frac` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`associate-+r+` `pow1/3` `distribute-lft-out`
1×	`distribute-rgt-in` `+-commutative` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `distribute-lft-in` `div-inv`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (+ x 1))
3.0ms	(cbrt (+ x 1))
242.0ms	(/ (+ (* (cbrt (+ x 1)) x) (* (+ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* -2 (cbrt (+ x 1)))) (+ x -1))) (* (* (cbrt (+ x 1)) x) (+ x -1)))
72.0ms	(+ (* (cbrt (+ x 1)) x) (* (+ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* -2 (cbrt (+ x 1)))) (+ x -1)))

series822.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(cbrt (+ x 1))
70.0ms	(cbrt (+ x 1))
495.0ms	(/ (+ (* (cbrt (+ x 1)) x) (* (+ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* -2 (cbrt (+ x 1)))) (+ x -1))) (* (* (cbrt (+ x 1)) x) (+ x -1)))
213.0ms	(+ (* (cbrt (+ x 1)) x) (* (+ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* -2 (cbrt (+ x 1)))) (+ x -1)))

simplify2.8s

Counts

146 → 146

Iterations

Iter	Nodes
done	5002
1	1414
0	397

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
0.0b	(- (* 1 x) (* (+ x 1) 2))
0.1b	(* (* (+ x 1) x) (- x 1))
14.3b	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

88×	`associate-*l/`
32×	`frac-add`
31×	`flip3--` `flip--`
24×	`frac-times` `flip3-+` `flip-+`
18×	`add-cbrt-cube` `add-exp-log` `associate-/l/`
12×	`associate-*r/`
11×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`pow1`
8×	`associate-/r/` `add-log-exp`
7×	`associate-r` `add-cube-cbrt`
6×	`prod-exp` `cbrt-unprod`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `insert-posit16`
3×	`cbrt-undiv` `times-frac` `div-exp` `pow-prod-down` `associate-/l*`
2×	`difference-of-squares`
1×	`+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `diff-log` `difference-of-sqr-1` `associate-l` `-commutative` `div-inv` `distribute-lft-out--`

Counts

4 → 130

Calls

4 calls:

115.0ms	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
9.0ms	(- (* 1 x) (* (+ x 1) 2))
44.0ms	(* (* (+ x 1) x) (- x 1))
34.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

series243.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
37.0ms	(- (* 1 x) (* (+ x 1) 2))
106.0ms	(* (* (+ x 1) x) (- x 1))
2.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

simplify1.7s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
1	1051
0	283

prune809.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes46.0ms

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	13
1	13
0	8

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	4153×	body	80	valid
947.0ms	1890×	body	640	valid
378.0ms	936×	body	320	valid
362.0ms	557×	body	1280	valid
141.0ms	467×	body	160	valid