Details

sample39.0ms

Algorithm

intervals

Results

13.0ms	200×	body	80	nan
6.0ms	53×	body	1280	valid
3.0ms	38×	body	640	valid
3.0ms	130×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	11×	body	160	valid

simplify3.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite58.0ms

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-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

13.0ms	(sqrt (+ x 1.0))
44.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series110.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(sqrt (+ x 1.0))
74.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify52.0ms

Counts: 41 → 41

prune83.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite95.0ms

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`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 71

Calls

3 calls:

7.0ms	(sqrt (+ x 1.0))
36.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
48.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series252.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(sqrt (+ x 1.0))
71.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
149.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify39.0ms

Counts: 80 → 80

prune173.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite314.0ms

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*`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 445

Calls

4 calls:

41.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
43.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
49.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
135.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series854.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
175.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
352.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
151.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify131.0ms

Counts: 457 → 457

prune613.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.2b	(/ (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.3b	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

849×	`*-un-lft-identity`
840×	`sqrt-prod`
756×	`times-frac`
324×	`add-sqr-sqrt` `add-cube-cbrt`
300×	`distribute-lft-out`
216×	`cbrt-prod`
36×	`associate-/l*`
28×	`sqrt-div` `associate-/r/`
16×	`flip3-+` `flip-+`
15×	`add-exp-log` `associate-/r*` `div-inv`
11×	`add-cbrt-cube`
7×	`div-exp`
6×	`cbrt-div`
5×	`pow1`
4×	`cbrt-undiv` `pow1/3` `add-log-exp`
3×	`sqrt-pow1`
2×	`pow-flip` `frac-2neg` `clear-num` `pow-div`
1×	`rec-exp` `pow1/2` `1-exp` `associate-/l/`

Counts

4 → 521

Calls

4 calls:

6.0ms	(/ 1.0 (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
134.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
21.0ms	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
22.0ms	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ 1.0 (fabs (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
466.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
322.0ms	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
319.0ms	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify116.0ms

Counts: 533 → 533

prune975.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

603.0ms	1751×	body	1280	valid
232.0ms	7813×	body	80	nan
161.0ms	1258×	body	640	valid
140.0ms	4064×	body	80	valid
87.0ms	628×	body	320	valid
14.0ms	299×	body	160	valid