Details

sample75.0ms

Algorithm

intervals

Results

20.0ms	66×	body	640	valid
16.0ms	249×	body	80	nan
10.0ms	32×	body	1280	valid
9.0ms	121×	body	80	valid
4.0ms	20×	body	320	valid
3.0ms	17×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	17
2	17
1	13
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
4.4b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
97×	`*-un-lft-identity` `times-frac`
64×	`sqrt-prod`
42×	`add-cube-cbrt`
25×	`difference-of-squares`
13×	`associate-/r*` `distribute-lft-out--`
12×	`add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube` `distribute-lft-out`
6×	`div-inv` `pow-flip` `associate-/l*` `add-log-exp`
4×	`sqrt-div` `div-exp` `insert-posit16`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `associate-/r/` `flip-+` `inv-pow`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 167

Calls

4 calls:

9.0ms	(sqrt (+ x 1))
17.0ms	(/ 1 (sqrt (+ x 1)))
10.0ms	(/ 1 (sqrt x))
46.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series199.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt (+ x 1))
57.0ms	(/ 1 (sqrt (+ x 1)))
28.0ms	(/ 1 (sqrt x))
87.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify1.7s

Counts

179 → 179

Iterations

Iter	Nodes
4	3357
3	1666
2	902
1	394
0	208

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.3b	(* (sqrt x) (sqrt (+ x 1)))
4.4b	(- (sqrt (+ x 1)) (sqrt x))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
39×	`sqrt-prod`
36×	`*-un-lft-identity`
12×	`difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
10×	`times-frac` `associate-/l*`
9×	`pow1` `distribute-lft-out--`
7×	`associate-r`
6×	`sqrt-div` `associate-l` `add-log-exp`
5×	`distribute-lft-out`
4×	`associate-*r/` `insert-posit16` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-unprod` `diff-log` `div-sub` `-commutative` `div-inv`

Counts

4 → 112

Calls

4 calls:

8.0ms	(sqrt (+ x 1))
72.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
29.0ms	(* (sqrt x) (sqrt (+ x 1)))
44.0ms	(- (sqrt (+ x 1)) (sqrt x))

series382.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ x 1))
192.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
75.0ms	(* (sqrt x) (sqrt (+ x 1)))
85.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify2.8s

Counts

124 → 124

Iterations

Iter	Nodes
3	5195
2	1271
1	399
0	164

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.3b	(* (sqrt x) (sqrt (+ x 1)))
0.3b	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
78×	`times-frac`
55×	`sqrt-prod`
47×	`add-sqr-sqrt`
45×	`distribute-lft-out`
39×	`add-cube-cbrt`
32×	`add-exp-log`
27×	`associate-/l*`
20×	`add-cbrt-cube`
14×	`div-exp`
9×	`pow1`
8×	`associate-/r/`
7×	`cbrt-undiv` `associate-/r` `associate-r*`
6×	`flip3-+` `associate-l` `flip-+` `add-log-exp`
5×	`prod-exp`
4×	`sqrt-div` `associate-*r/` `insert-posit16` `div-inv` `unswap-sqr`
3×	`rec-exp` `1-exp` `pow-prod-down` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log` `sqrt-unprod` `*-commutative` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 170

Calls

4 calls:

18.0ms	(+ (sqrt (+ x 1)) (sqrt x))
26.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
18.0ms	(* (sqrt x) (sqrt (+ x 1)))
47.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))

series401.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (sqrt (+ x 1)) (sqrt x))
72.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
62.0ms	(* (sqrt x) (sqrt (+ x 1)))
209.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))

simplify1.7s

Counts

182 → 182

Iterations

Iter	Nodes
3	5297
2	1572
1	544
0	226

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (+ x 1)) (sqrt (+ x 1)))
0.5b	(* (sqrt x) (sqrt x))
3.9b	(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
11.0b	(* (/ 1 (+ (* x (sqrt x)) (* (sqrt (+ 1 x)) (+ 1 x)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
60×	`sqrt-div`
44×	`*-un-lft-identity` `sqrt-prod`
38×	`frac-times`
36×	`pow1`
33×	`flip3-+` `flip-+`
32×	`frac-add`
31×	`associate-l`
29×	`add-cube-cbrt`
28×	`associate-*r/`
19×	`swap-sqr`
17×	`flip3--` `add-exp-log` `flip--`
16×	`sqrt-pow1` `pow1/2` `associate-r`
14×	`times-frac`
13×	`add-cbrt-cube`
11×	`associate-*l/` `unswap-sqr`
10×	`pow-prod-up`
7×	`pow-prod-down`
6×	`prod-exp` `pow-sqr` `distribute-lft-out` `add-log-exp`
4×	`cbrt-unprod` `insert-posit16`
3×	`cube-unmult` `pow3` `sum-cubes` `*-commutative`
2×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `div-exp` `associate-/r/`
1×	`distribute-rgt-in` `cbrt-undiv` `rec-exp` `sub-neg` `distribute-lft-in` `distribute-rgt-out--` `diff-log` `1-exp` `div-inv`

Counts

4 → 206

Calls

4 calls:

24.0ms	(* (sqrt (+ x 1)) (sqrt (+ x 1)))
8.0ms	(* (sqrt x) (sqrt x))
10.0ms	(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
159.0ms	(* (/ 1 (+ (* x (sqrt x)) (* (sqrt (+ 1 x)) (+ 1 x)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (sqrt (+ x 1)) (sqrt (+ x 1)))
17.0ms	(* (sqrt x) (sqrt x))
87.0ms	(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
172.0ms	(* (/ 1 (+ (* x (sqrt x)) (* (sqrt (+ 1 x)) (+ 1 x)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))

simplify1.6s

Counts

218 → 218

Iterations

Iter	Nodes
2	5811
1	1418
0	364

prune2.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes52.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	29
1	29
0	19

end0.0ms

sample2.4s

Algorithm

intervals

Results

838.0ms	1847×	body	640	valid
446.0ms	7978×	body	80	nan
420.0ms	1132×	body	1280	valid
276.0ms	4106×	body	80	valid
146.0ms	605×	body	320	valid
56.0ms	310×	body	160	valid