Details

sample103.0ms

Algorithm

intervals

Results

46.0ms	61×	body	640	valid
17.0ms	132×	body	80	valid
11.0ms	29×	body	320	valid
8.0ms	13×	body	1280	valid
5.0ms	21×	body	160	valid

simplify610.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ x 1))
0.0b	(- (/ 1 (+ x 1)) (/ 2 x))
2.8b	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
35×	`times-frac`
29×	`add-sqr-sqrt`
17×	`distribute-lft-out`
14×	`distribute-lft-out--`
12×	`add-cube-cbrt`
10×	`add-log-exp`
7×	`add-exp-log` `div-inv`
6×	`difference-of-squares`
5×	`add-cbrt-cube`
4×	`pow1` `associate-/r*`
3×	`frac-add` `insert-posit16` `associate-/l*`
2×	`associate-+l+` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `div-exp` `associate-/r/` `frac-sub` `flip-+` `flip--`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-+l-` `pow-flip` `inv-pow`

Counts

3 → 91

Calls

3 calls:

15.0ms	(/ 1 (+ x 1))
62.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
182.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(/ 1 (+ x 1))
41.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
143.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify1.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	2002
3	2002
2	1399
1	408
0	166

prune772.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ 1 (+ x 1)))
0.0b	(sqrt (/ 1 (+ x 1)))
0.2b	(* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))))
7.0b	(+ (- (* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

150×	`sqrt-prod`
129×	`*-un-lft-identity`
112×	`add-sqr-sqrt`
104×	`times-frac`
60×	`add-cube-cbrt`
31×	`pow1` `swap-sqr`
30×	`sqrt-pow1`
26×	`distribute-lft-out`
21×	`associate-r` `associate-l`
16×	`unswap-sqr`
12×	`associate-/r/`
10×	`pow1/2` `sqrt-div` `pow-flip` `inv-pow`
9×	`pow-prod-up` `div-inv` `add-log-exp`
7×	`flip3-+` `flip-+`
6×	`rem-sqrt-square` `add-cbrt-cube` `add-exp-log`
5×	`pow-prod-down` `frac-add` `pow-sqr`
4×	`insert-posit16`
3×	`frac-sub`
2×	`frac-times` `associate-+l+` `sum-log` `associate-l/` `associate-r/`
1×	`pow2` `+-commutative` `sub-neg` `rem-square-sqrt` `pow-plus` `flip3--` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `associate-+l-` `cbrt-unprod` `flip--`

Counts

4 → 217

Calls

4 calls:

11.0ms	(sqrt (/ 1 (+ x 1)))
13.0ms	(sqrt (/ 1 (+ x 1)))
36.0ms	(* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))))
175.0ms	(+ (- (* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (/ 1 (+ x 1)))
55.0ms	(sqrt (/ 1 (+ x 1)))
24.0ms	(* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))))
136.0ms	(+ (- (* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))

simplify1.4s

Counts

229 → 229

Iterations

Iter	Nodes
done	2000
3	2000
2	1746
1	608
0	271

prune2.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize74.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ 1 (+ x 1)))
0.1b	(* (* (sqrt (/ 1 (+ x 1))) (sqrt 1)) x)
2.0b	(/ (+ (* (- (* (* (sqrt (/ 1 (+ x 1))) (sqrt 1)) x) (* (sqrt (+ x 1)) 2)) (- x 1)) (* (* (sqrt (+ x 1)) x) 1)) (* (* (sqrt (+ x 1)) x) (- x 1)))
9.0b	(+ (* (- (* (* (sqrt (/ 1 (+ x 1))) (sqrt 1)) x) (* (sqrt (+ x 1)) 2)) (- x 1)) (* (* (sqrt (+ x 1)) x) 1))

rewrite599.0ms

Algorithm

rewrite-expression-head

Rules

210×	`associate-*l/`
112×	`sqrt-div`
56×	`frac-add`
46×	`flip3-+` `flip-+`
36×	`frac-times`
35×	`flip3--` `flip--`
30×	`associate-/l/`
24×	`frac-sub`
22×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
17×	`times-frac`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`associate-*r/` `associate-/r/`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`associate-+l+` `insert-posit16`
3×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `div-exp` `associate-r` `pow-prod-down` `distribute-lft-out` `associate-/l*`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-inv`
1×	`+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `pow1/2` `associate-l` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 160

Calls

4 calls:

12.0ms	(sqrt (/ 1 (+ x 1)))
81.0ms	(* (* (sqrt (/ 1 (+ x 1))) (sqrt 1)) x)
348.0ms	(/ (+ (* (- (* (* (sqrt (/ 1 (+ x 1))) (sqrt 1)) x) (* (sqrt (+ x 1)) 2)) (- x 1)) (* (* (sqrt (+ x 1)) x) 1)) (* (* (sqrt (+ x 1)) x) (- x 1)))
149.0ms	(+ (* (- (* (* (sqrt (/ 1 (+ x 1))) (sqrt 1)) x) (* (sqrt (+ x 1)) 2)) (- x 1)) (* (* (sqrt (+ x 1)) x) 1))

series966.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (/ 1 (+ x 1)))
67.0ms	(* (* (sqrt (/ 1 (+ x 1))) (sqrt 1)) x)
653.0ms	(/ (+ (* (- (* (* (sqrt (/ 1 (+ x 1))) (sqrt 1)) x) (* (sqrt (+ x 1)) 2)) (- x 1)) (* (* (sqrt (+ x 1)) x) 1)) (* (* (sqrt (+ x 1)) x) (- x 1)))
211.0ms	(+ (* (- (* (* (sqrt (/ 1 (+ x 1))) (sqrt 1)) x) (* (sqrt (+ x 1)) 2)) (- x 1)) (* (* (sqrt (+ x 1)) x) 1))

simplify1.3s

Counts

172 → 172

Iterations

Iter	Nodes
done	2001
2	2001
1	1411
0	444

prune2.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (* (+ x 1) 2))
0.0b	(/ (+ (* (+ x -1) (- x (* (+ x 1) 2))) (* (+ x 1) x)) (* (* (+ x 1) x) (+ x -1)))
0.1b	(* (* (+ x 1) x) (+ x -1))
16.8b	(+ (* (+ x -1) (- x (* (+ x 1) 2))) (* (+ x 1) x))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

5.0ms	(- x (* (+ x 1) 2))
63.0ms	(/ (+ (* (+ x -1) (- x (* (+ x 1) 2))) (* (+ x 1) x)) (* (* (+ x 1) x) (+ x -1)))
34.0ms	(* (* (+ x 1) x) (+ x -1))
16.0ms	(+ (* (+ x -1) (- x (* (+ x 1) 2))) (* (+ x 1) x))

series197.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- x (* (+ x 1) 2))
72.0ms	(/ (+ (* (+ x -1) (- x (* (+ x 1) 2))) (* (+ x 1) x)) (* (* (+ x 1) x) (+ x -1)))
92.0ms	(* (* (+ x 1) x) (+ x -1))
2.0ms	(+ (* (+ x -1) (- x (* (+ x 1) 2))) (* (+ x 1) x))

simplify1.0s

Counts

138 → 138

Iterations

Iter	Nodes
done	2003
2	2003
1	1073
0	280

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes66.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 25.9b

bsearch207.0ms

Steps

Iters	Range		Point
10	186.95626557948964	3373396396890550.5	4091.211296656346
9	-24078.920296370652	-0.35383103211093586	-960.5059570047206

simplify33.0ms

Iterations

Iter	Nodes
done	58
1	58
0	37

end0.0ms

sample2.8s

Algorithm

intervals

Results

889.0ms	1890×	body	640	valid
795.0ms	572×	body	1280	valid
604.0ms	4144×	body	80	valid
300.0ms	906×	body	320	valid
102.0ms	490×	body	160	valid