Details

sample67.0ms

Algorithm

intervals

Results

22.0ms	61×	body	640	valid
13.0ms	132×	body	80	valid
8.0ms	29×	body	320	valid
5.0ms	13×	body	1280	valid
4.0ms	21×	body	160	valid

simplify153.0ms

Counts

1 → 1

Iterations

Iter	Nodes
11	195
10	195
9	187
8	132
7	94
6	83
5	75
4	63
3	43
2	33
1	19
0	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize23.0ms

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)))

rewrite211.0ms

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:

9.0ms	(/ 1 (+ x 1))
34.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
167.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series173.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(/ 1 (+ x 1))
25.0ms	(- (/ 1 (+ x 1)) (/ 2 x))
133.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify5.6s

Counts

100 → 100

Iterations

Iter	Nodes
3	4070
2	1127
1	394
0	166

prune781.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

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)))

rewrite210.0ms

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:

6.0ms	(sqrt (/ 1 (+ x 1)))
11.0ms	(sqrt (/ 1 (+ x 1)))
47.0ms	(* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))))
141.0ms	(+ (- (* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))

series217.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (/ 1 (+ x 1)))
38.0ms	(sqrt (/ 1 (+ x 1)))
25.0ms	(* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1))))
115.0ms	(+ (- (* (sqrt (/ 1 (+ x 1))) (sqrt (/ 1 (+ x 1)))) (/ 2 x)) (/ 1 (- x 1)))

simplify6.3s

Counts

229 → 229

Iterations

Iter	Nodes
3	5581
2	1515
1	584
0	271

prune2.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite194.0ms

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:

14.0ms	(- (* 1 x) (* (+ x 1) 2))
117.0ms	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
30.0ms	(* (* (+ x 1) x) (- x 1))
28.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

series254.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* 1 x) (* (+ x 1) 2))
91.0ms	(/ (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (* (* (+ x 1) x) (- x 1)))
116.0ms	(* (* (+ x 1) x) (- x 1))
3.0ms	(+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))

simplify2.5s

Counts

142 → 142

Iterations

Iter	Nodes
2	4827
1	1013
0	283

prune1.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 89

Calls

3 calls:

14.0ms	(* (+ x 1) x)
48.0ms	(* (* (+ x 1) x) (- x 1))
25.0ms	(/ 2 (* (* (+ x 1) x) (- x 1)))

series301.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(* (+ x 1) x)
161.0ms	(* (* (+ x 1) x) (- x 1))
76.0ms	(/ 2 (* (* (+ x 1) x) (- x 1)))

simplify7.1s

Counts

98 → 98

Iterations

Iter	Nodes
3	7569
2	1525
1	448
0	156

prune787.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes26.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	9
1	9
0	8

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.0s	1890×	body	640	valid
970.0ms	4144×	body	80	valid
418.0ms	572×	body	1280	valid
334.0ms	906×	body	320	valid
146.0ms	490×	body	160	valid