Details

sample110.0ms

Algorithm

intervals

Results

27.0ms	64×	body	640	valid
27.0ms	270×	body	80	nan
20.0ms	40×	body	1280	valid
14.0ms	128×	body	80	valid
5.0ms	16×	body	320	valid
1.0ms	8×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	15
2	15
1	11
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize30.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
2.1b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
97×	`times-frac`
93×	`*-un-lft-identity`
60×	`sqrt-prod`
40×	`add-cube-cbrt`
25×	`difference-of-squares`
13×	`associate-/r*` `distribute-lft-out--`
11×	`add-exp-log`
7×	`pow1` `add-cbrt-cube` `distribute-lft-out`
6×	`div-inv` `pow-flip` `associate-/l*`
5×	`add-log-exp`
4×	`div-exp`
3×	`insert-posit16`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `1-exp` `associate-/r/` `inv-pow`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `frac-sub` `flip-+` `flip--`

Counts

3 → 150

Calls

3 calls:

9.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))
62.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series180.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ 1 (sqrt (+ x 1)))
50.0ms	(/ 1 (sqrt x))
81.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify10.4s

Counts

159 → 159

Iterations

Iter	Nodes
4	3886
3	1930
2	885
1	369
0	196

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.7b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.2b	(* (sqrt x) (sqrt (+ x 1)))
2.1b	(- (sqrt (+ x 1)) (sqrt x))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 95

Calls

3 calls:

106.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
16.0ms	(* (sqrt x) (sqrt (+ x 1)))
40.0ms	(- (sqrt (+ x 1)) (sqrt x))

series370.0ms

Counts

3 → 9

Calls

3 calls:

228.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
71.0ms	(* (sqrt x) (sqrt (+ x 1)))
70.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify2.3s

Counts

104 → 104

Iterations

Iter	Nodes
3	4526
2	1197
1	372
0	151

prune917.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite132.0ms

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:

20.0ms	(+ (sqrt (+ x 1)) (sqrt x))
28.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
64.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
16.0ms	(* (sqrt x) (sqrt (+ x 1)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+ (sqrt (+ x 1)) (sqrt x))
91.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
216.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
59.0ms	(* (sqrt x) (sqrt (+ x 1)))

simplify1.0m

Counts

182 → 182

Iterations

Iter	Nodes
3	7329
2	1659
1	541
0	226

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

768×	`sqrt-prod`
730×	`*-un-lft-identity`
657×	`times-frac`
303×	`add-sqr-sqrt` `add-cube-cbrt`
240×	`distribute-lft-out`
60×	`associate-/l*`
36×	`associate-/r/`
25×	`associate-/r*`
19×	`div-inv`
18×	`flip3-+` `flip-+`
16×	`add-exp-log`
12×	`add-cbrt-cube`
6×	`pow1` `div-exp`
4×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-div` `insert-posit16` `add-log-exp`
2×	`rec-exp` `sqrt-undiv` `1-exp` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 542

Calls

4 calls:

25.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
26.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
43.0ms	(/ (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ x 1)))
39.0ms	(/ (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt x))

series398.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
65.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
117.0ms	(/ (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ x 1)))
150.0ms	(/ (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt x))

simplify1.8s

Counts

554 → 554

Iterations

Iter	Nodes
3	3780
2	1512
1	811
0	497

prune3.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes48.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	15
1	15
0	12

end0.0ms

sample2.2s

Algorithm

intervals

Results

469.0ms	7889×	body	80	nan
464.0ms	1160×	body	1280	valid
434.0ms	1849×	body	640	valid
340.0ms	582×	body	320	valid
260.0ms	4113×	body	80	valid
33.0ms	296×	body	160	valid