Details

sample30.0ms

Algorithm

intervals

Results

6.0ms	251×	body	80	nan
5.0ms	54×	body	1280	valid
3.0ms	135×	body	80	valid
3.0ms	37×	body	640	valid
1.0ms	21×	body	320	valid
0.0ms	9×	body	160	valid

simplify1.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.3b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite61.0ms

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:

7.0ms	(sqrt (+ x 1.0))
53.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series133.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(sqrt (+ x 1.0))
90.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify100.0ms

Counts: 41 → 41

prune101.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

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)))

rewrite149.0ms

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:

15.0ms	(sqrt (+ x 1.0))
70.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
58.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series382.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(sqrt (+ x 1.0))
107.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
231.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify100.0ms

Counts: 80 → 80

prune275.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

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))))

rewrite342.0ms

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:

39.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
42.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
45.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
177.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series978.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
196.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
392.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
172.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify121.0ms

Counts: 457 → 457

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite873.0ms

Algorithm

rewrite-expression-head

Rules

848×	`sqrt-prod`
658×	`*-un-lft-identity`
496×	`times-frac`
412×	`add-sqr-sqrt`
236×	`distribute-lft-out`
229×	`add-cube-cbrt`
126×	`swap-sqr`
60×	`associate-r` `associate-l`
25×	`unswap-sqr`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
14×	`sqrt-div`
12×	`pow1` `associate-/r/` `associate-/l*`
7×	`flip3-+` `flip-+`
6×	`cbrt-undiv` `sqrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-unprod` `associate-r/` `pow-prod-down` `associate-l/` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 483

Calls

4 calls:

45.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
391.0ms	(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
69.0ms	(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
315.0ms	(* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

242.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
481.0ms	(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
463.0ms	(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
212.0ms	(* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify209.0ms

Counts: 495 → 495

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes55.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

434.0ms	1737×	body	1280	valid
307.0ms	8028×	body	80	nan
229.0ms	4108×	body	80	valid
175.0ms	1307×	body	640	valid
131.0ms	574×	body	320	valid
64.0ms	274×	body	160	valid