Details

sample78.0ms

Algorithm

intervals

Results

19.0ms	45×	body	640	valid
16.0ms	49×	body	1280	valid
15.0ms	249×	body	80	nan
9.0ms	137×	body	80	valid
2.0ms	12×	body	320	valid
2.0ms	13×	body	160	valid

simplify12.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize10.0ms

Local error

Found 2 expressions with local error:

2.7b	(- (sqrt (+ x 1)) (sqrt x))
0.0b	(sqrt (+ x 1))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `distribute-lft-out`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 37

Calls

2 calls:

Slowest

52.0ms	(- (sqrt (+ x 1)) (sqrt x))
9.0ms	(sqrt (+ x 1))

series125.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

97.0ms	(- (sqrt (+ x 1)) (sqrt x))
28.0ms	(sqrt (+ x 1))

simplify1.6s

Counts: 43 → 43

prune373.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
7×	`add-exp-log`
6×	`associate-/r*`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `insert-posit16` `associate-/l*`
2×	`sqrt-div` `div-exp` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

3 → 78

Calls

3 calls:

Slowest

38.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
35.0ms	(+ (sqrt (+ x 1)) (sqrt x))
9.0ms	(sqrt (+ x 1))

series224.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

117.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
68.0ms	(+ (sqrt (+ x 1)) (sqrt x))
39.0ms	(sqrt (+ x 1))

simplify1.6s

Counts: 87 → 87

prune675.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
0.1b	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
700×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
254×	`add-sqr-sqrt`
252×	`add-cube-cbrt`
36×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
17×	`add-exp-log`
15×	`pow1`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-cbrt-cube`
8×	`div-exp` `pow-flip`
7×	`sqrt-pow1` `pow1/2`
6×	`pow-div`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `1-exp` `inv-pow`
1×	`associate-/l/`

Counts

4 → 463

Calls

4 calls:

Slowest

102.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
51.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
42.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
40.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

series537.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

157.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
146.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
129.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
104.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify1.3s

Counts: 475 → 475

prune5.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sqrt (+ (sqrt (+ x 1)) (sqrt x))) -2)
0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.0b	(sqrt (+ x 1))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
28×	`sqrt-prod`
13×	`distribute-lft-out`
11×	`add-sqr-sqrt`
9×	`unpow-prod-down` `add-cube-cbrt`
8×	`pow1`
6×	`add-log-exp`
5×	`add-exp-log`
4×	`add-cbrt-cube` `sqrt-div` `insert-posit16`
3×	`pow-unpow` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`rem-sqrt-square`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

Slowest

30.0ms	(pow (sqrt (+ (sqrt (+ x 1)) (sqrt x))) -2)
27.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
17.0ms	(+ (sqrt (+ x 1)) (sqrt x))
4.0ms	(sqrt (+ x 1))

series616.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

359.0ms	(pow (sqrt (+ (sqrt (+ x 1)) (sqrt x))) -2)
161.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
66.0ms	(+ (sqrt (+ x 1)) (sqrt x))
28.0ms	(sqrt (+ x 1))

simplify1.2s

Counts: 90 → 90

prune825.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes77.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample2.4s

Algorithm

intervals

Results

756.0ms	1299×	body	640	valid
600.0ms	1693×	body	1280	valid
445.0ms	7752×	body	80	nan
253.0ms	4078×	body	80	valid
97.0ms	620×	body	320	valid
32.0ms	310×	body	160	valid